Daily Papers

In an era where symbolic mathematical equations are indispensable for modeling complex natural phenomena, scientific inquiry often involves collecting observations and translating them into mathematical expressions. Recently, deep learning has emerged as a powerful tool for extracting insights from data. However, existing models typically specialize in either numeric or symbolic domains, and are usually trained in a supervised manner tailored to specific tasks. This approach neglects the substantial benefits that could arise from a task-agnostic unified understanding between symbolic equations and their numeric counterparts. To bridge the gap, we introduce SNIP, a Symbolic-Numeric Integrated Pre-training, which employs joint contrastive learning between symbolic and numeric domains, enhancing their mutual similarities in the pre-trained embeddings. By performing latent space analysis, we observe that SNIP provides cross-domain insights into the representations, revealing that symbolic supervision enhances the embeddings of numeric data and vice versa. We evaluate SNIP across diverse tasks, including symbolic-to-numeric mathematical property prediction and numeric-to-symbolic equation discovery, commonly known as symbolic regression. Results show that SNIP effectively transfers to various tasks, consistently outperforming fully supervised baselines and competing strongly with established task-specific methods, especially in few-shot learning scenarios where available data is limited.

Time series forecasting plays a vital role in supporting decision-making across a wide range of critical applications, including energy, healthcare, and finance. Despite recent advances, forecasting accuracy remains limited due to the challenge of integrating historical numerical sequences with contextual features, which often comprise unstructured textual data. To address this challenge, we propose TokenCast, an LLM-driven framework that leverages language-based symbolic representations as a unified intermediary for context-aware time series forecasting. Specifically, TokenCast employs a discrete tokenizer to transform continuous numerical sequences into temporal tokens, enabling structural alignment with language-based inputs. To bridge the semantic gap between modalities, both temporal and contextual tokens are embedded into a shared representation space via a pre-trained large language model (LLM), further optimized with autoregressive generative objectives. Building upon this unified semantic space, the aligned LLM is subsequently fine-tuned in a supervised manner to predict future temporal tokens, which are then decoded back into the original numerical space. Extensive experiments on diverse real-world datasets enriched with contextual features demonstrate the effectiveness and generalizability of TokenCast.

Despite high benchmark scores, Large Language Models (LLMs) often fail simple problem, raising a critical question: Do LLMs learn mathematical principles or merely memorize patterns? Rather than designing increasingly complex benchmarks like recent works, we investigate this using elementary two-integer addition (0 to 2^{64}), probing two core properties: commutativity (A+B=B+A) and compositional generalization (via isomorphic symbolic mappings, e.g., 7 rightarrow y). While state-of-the-art LLMs achieve 73.8-99.8\% accuracy on numerical addition, performance collapses to leq7.5\% under symbolic mapping, indicating failure to generalize learned rules. Non-monotonic performance scaling with digit count and frequent commutativity violations (over 1,700 cases of A+B neq B+A) further support this. Explicitly providing addition rules degrades performance by 81.2\% on average, while self-explanation maintains baseline accuracy, suggesting LLM arithmetic processing is misaligned with human-defined principles. Our findings indicate current LLMs rely on memory pattern over genuine rule learning, highlighting architectural limitations and the need for new approaches to achieve true mathematical reasoning.

Automatic program repair seeks to generate correct code from buggy programs, with most approaches searching the correct program in a discrete, symbolic space of source code tokens. This symbolic search is fundamentally limited by its inability to directly reason about program behavior. We introduce Gradient-Based Program Repair (GBPR), a new paradigm that reframes program repair as continuous optimization in a differentiable numerical program space. Our core insight is to compile symbolic programs into differentiable numerical representations, enabling search in the numerical program space directly guided by program behavior. To evaluate GBPR, we present RaspBugs, a new benchmark of 1,466 buggy symbolic RASP programs and their respective numerical representations. Our experiments demonstrate that GBPR can effectively repair buggy symbolic programs by gradient-based optimization in the numerical program space, with convincing repair trajectories. To our knowledge, we are the first to state program repair as continuous optimization in a numerical program space. Our work establishes a new direction for program repair research, bridging two rich worlds: continuous optimization and program behavior.

As mathematical computing becomes more democratized in high-level languages, high-performance symbolic-numeric systems are necessary for domain scientists and engineers to get the best performance out of their machine without deep knowledge of code optimization. Naturally, users need different term types either to have different algebraic properties for them, or to use efficient data structures. To this end, we developed Symbolics.jl, an extendable symbolic system which uses dynamic multiple dispatch to change behavior depending on the domain needs. In this work we detail an underlying abstract term interface which allows for speed without sacrificing generality. We show that by formalizing a generic API on actions independent of implementation, we can retroactively add optimized data structures to our system without changing the pre-existing term rewriters. We showcase how this can be used to optimize term construction and give a 113x acceleration on general symbolic transformations. Further, we show that such a generic API allows for complementary term-rewriting implementations. We demonstrate the ability to swap between classical term-rewriting simplifiers and e-graph-based term-rewriting simplifiers. We showcase an e-graph ruleset which minimizes the number of CPU cycles during expression evaluation, and demonstrate how it simplifies a real-world reaction-network simulation to halve the runtime. Additionally, we show a reaction-diffusion partial differential equation solver which is able to be automatically converted into symbolic expressions via multiple dispatch tracing, which is subsequently accelerated and parallelized to give a 157x simulation speedup. Together, this presents Symbolics.jl as a next-generation symbolic-numeric computing environment geared towards modeling and simulation.

Developing generative models to create or conditionally create symbolic music presents unique challenges due to the combination of limited data availability and the need for high precision in note pitch. To address these challenges, we introduce an efficient Fine-Grained Guidance (FGG) approach within diffusion models. FGG guides the diffusion models to generate music that aligns more closely with the control and intent of expert composers, which is critical to improve the accuracy, listenability, and quality of generated music. This approach empowers diffusion models to excel in advanced applications such as improvisation, and interactive music creation. We derive theoretical characterizations for both the challenges in symbolic music generation and the effects of the FGG approach. We provide numerical experiments and subjective evaluation to demonstrate the effectiveness of our approach. We have published a demo page to showcase performances, as one of the first in the symbolic music literature's demo pages that enables real-time interactive generation.

Symbolic regression (SR) is a powerful technique for discovering the underlying mathematical expressions from observed data. Inspired by the success of deep learning, recent efforts have focused on two categories for SR methods. One is using a neural network or genetic programming to search the expression tree directly. Although this has shown promising results, the large search space poses difficulties in learning constant factors and processing high-dimensional problems. Another approach is leveraging a transformer-based model training on synthetic data and offers advantages in inference speed. However, this method is limited to fixed small numbers of dimensions and may encounter inference problems when given data is out-of-distribution compared to the synthetic data. In this work, we propose DySymNet, a novel neural-guided Dynamic Symbolic Network for SR. Instead of searching for expressions within a large search space, we explore DySymNet with various structures and optimize them to identify expressions that better-fitting the data. With a topology structure like neural networks, DySymNet not only tackles the challenge of high-dimensional problems but also proves effective in optimizing constants. Based on extensive numerical experiments using low-dimensional public standard benchmarks and the well-known SRBench with more variables, our method achieves state-of-the-art performance in terms of fitting accuracy and robustness to noise.

Large Language Models (LLMs) are thought to struggle with arithmetic learning due to the inherent differences between language modeling and numerical computation, but concrete evidence has been lacking. This work responds to this claim through a two-side experiment. We first investigate whether LLMs leverage partial products during arithmetic learning. We find that although LLMs can identify some partial products after learning, they fail to leverage them for arithmetic tasks, conversely. We then explore how LLMs approach arithmetic symbolically by breaking tasks into subgroups, hypothesizing that difficulties arise from subgroup complexity and selection. Our results show that when subgroup complexity is fixed, LLMs treat a collection of different arithmetic operations similarly. By analyzing position-level accuracy across different training sizes, we further observe that it follows a U-shaped pattern: LLMs quickly learn the easiest patterns at the first and last positions, while progressively learning the more difficult patterns in the middle positions. This suggests that LLMs select subgroup following an easy-to-hard paradigm during learning. Our work confirms that LLMs are pure symbolic learners in arithmetic tasks and underscores the importance of understanding them deeply through subgroup-level quantification.

Approximating nonlinear differential equations using a neural network provides a robust and efficient tool for various scientific computing tasks, including real-time predictions, inverse problems, optimal controls, and surrogate modeling. Previous works have focused on embedding dynamical systems into networks through two approaches: learning a single solution operator (i.e., the mapping from input parametrized functions to solutions) or learning the governing system of equations (i.e., the constitutive model relative to the state variables). Both of these approaches yield different representations for the same underlying data or function. Additionally, observing that families of differential equations often share key characteristics, we seek one network representation across a wide range of equations. Our method, called Predicting Operators and Symbolic Expressions (PROSE), learns maps from multimodal inputs to multimodal outputs, capable of generating both numerical predictions and mathematical equations. By using a transformer structure and a feature fusion approach, our network can simultaneously embed sets of solution operators for various parametric differential equations using a single trained network. Detailed experiments demonstrate that the network benefits from its multimodal nature, resulting in improved prediction accuracy and better generalization. The network is shown to be able to handle noise in the data and errors in the symbolic representation, including noisy numerical values, model misspecification, and erroneous addition or deletion of terms. PROSE provides a new neural network framework for differential equations which allows for more flexibility and generality in learning operators and governing equations from data.

How can we perform computations over natural language representations to solve tasks that require symbolic and numeric reasoning? We propose natural language embedded programs (NLEP) as a unifying framework for addressing math/symbolic reasoning, natural language understanding, and instruction following tasks. Our approach prompts a language model to generate full Python programs that define functions over data structures which contain natural language representations of structured knowledge. A Python interpreter then executes the generated code and prints the output. Despite using a task-general prompt, we find that this approach can improve upon strong baselines across a range of different tasks including math and symbolic reasoning, text classification, question answering, and instruction following. We further find the generated programs are often interpretable and enable post-hoc verification of the intermediate reasoning steps.

With the recent advance in large pre-trained language models, researchers have achieved record performances in NLP tasks that mostly focus on language pattern matching. The community is experiencing the shift of the challenge from how to model language to the imitation of complex reasoning abilities like human beings. In this work, we investigate the application domain of finance that involves real-world, complex numerical reasoning. We propose a new large-scale dataset, ConvFinQA, aiming to study the chain of numerical reasoning in conversational question answering. Our dataset poses great challenge in modeling long-range, complex numerical reasoning paths in real-world conversations. We conduct comprehensive experiments and analyses with both the neural symbolic methods and the prompting-based methods, to provide insights into the reasoning mechanisms of these two divisions. We believe our new dataset should serve as a valuable resource to push forward the exploration of real-world, complex reasoning tasks as the next research focus. Our dataset and code is publicly available at https://github.com/czyssrs/ConvFinQA.

Recent advances in long-context large language models (LLMs) have led to the emerging paradigm of many-shot in-context learning (ICL), where it is observed that scaling many more demonstrating examples beyond the conventional few-shot setup in the context can lead to performance benefits. However, despite its promise, it is unclear what aspects dominate the benefits and whether simply scaling to more examples is the most effective way of improving many-shot ICL. In this work, we first provide an analysis of the factors driving many-shot ICL, and we find that 1) many-shot performance can still be attributed to often a few disproportionately influential examples and 2) identifying such influential examples ("optimize") and using them as demonstrations to regenerate new examples ("generate") can lead to further improvements. Inspired by the findings, we propose BRIDGE, an algorithm that alternates between the optimize step with Bayesian optimization to discover the influential sets of examples and the generate step to reuse this set to expand the reasoning paths of the examples back to the many-shot regime automatically. On Gemini, Claude, and Mistral LLMs of different sizes, we show that BRIDGE to significant improvements across a diverse set of tasks, including symbolic reasoning, numerical reasoning, and code generation.

EasyMath is a compact benchmark for practical math reasoning in small language models. It covers thirteen categories, from basic arithmetic and order of operations to word problems, algebraic expressions, edge cases, and omits specialist topics. We tested 23 models (14M to 4B parameters) using exact, numerical, and symbolic checks on free-form answers in a zero-shot setting. Accuracy rises with size and training, chain-of-thought adds modest gains, and consistency improves at scale.

We present AlphaApollo, a self-evolving agentic reasoning system that aims to address two bottlenecks in foundation model (FM) reasoning-limited model-intrinsic capacity and unreliable test-time iteration. AlphaApollo orchestrates multiple models with professional tools to enable deliberate, verifiable reasoning. It couples (i) a computation tool (Python with numerical and symbolic libraries) and (ii) a retrieval tool (task-relevant external information) to execute exact calculations and ground decisions. The system further supports multi-round, multi-model solution evolution via a shared state map that records candidates, executable checks, and feedback for iterative refinement. In evaluations on AIME 2024/2025 across multiple models, AlphaApollo delivers consistent gains: +5.15% Average@32 and +23.34% Pass@32 for Qwen2.5-14B-Instruct, and +8.91% Average@32 with +26.67% Pass@32 for Llama-3.3-70B-Instruct. Tool-use analysis shows that more than 80% of tool calls are successfully executed, with consistent outperformance of non-tool baselines, thereby lifting the capability ceiling of FMs. More empirical results and implementation details will be updated at https://github.com/tmlr-group/AlphaApollo.

Reasoning is a fundamental capability of Large Language Models. While prior research predominantly focuses on enhancing narrow skills like math or code generation, improving performance on many other reasoning tasks remains challenging due to sparse and fragmented training data. To address this issue, we propose CodeI/O, a novel approach that systematically condenses diverse reasoning patterns inherently embedded in contextually-grounded codes, through transforming the original code into a code input-output prediction format. By training models to predict inputs/outputs given code and test cases entirely in natural language as Chain-of-Thought (CoT) rationales, we expose them to universal reasoning primitives -- like logic flow planning, state-space searching, decision tree traversal, and modular decomposition -- while decoupling structured reasoning from code-specific syntax and preserving procedural rigor. Experimental results demonstrate CodeI/O leads to consistent improvements across symbolic, scientific, logic, math & numerical, and commonsense reasoning tasks. By matching the existing ground-truth outputs or re-executing the code with predicted inputs, we can verify each prediction and further enhance the CoTs through multi-turn revision, resulting in CodeI/O++ and achieving higher performance. Our data and models are available at https://github.com/hkust-nlp/CodeIO.

Large language models can perform various reasoning tasks by using chain-of-thought prompting, which guides them to find answers through step-by-step demonstrations. However, the quality of the prompts depends on the demonstrations given to the models, and creating many of them by hand is costly. We introduce Synthetic prompting, a method that leverages a few handcrafted examples to prompt the model to generate more examples by itself, and selects effective demonstrations to elicit better reasoning. Our method alternates between a backward and forward process to generate new examples. The backward process generates a question that match a sampled reasoning chain, so that the question is solvable and clear. The forward process produces a more detailed reasoning chain for the question, improving the quality of the example. We evaluate our method on numerical, symbolic, and algorithmic reasoning tasks, and show that it outperforms existing prompting techniques.

Large Language Models (LLMs) have made remarkable progress in mathematical reasoning, but still continue to struggle with high-precision tasks like numerical computation and formal symbolic manipulation. Integrating external tools has emerged as a promising approach to bridge this gap. Despite recent advances, existing methods struggle with three key challenges: constructing tool-integrated reasoning data, performing fine-grained optimization, and enhancing inference. To overcome these limitations, we propose THOR (Tool-Integrated Hierarchical Optimization via RL). First, we introduce TIRGen, a multi-agent actor-critic-based pipeline for constructing high-quality datasets of tool-integrated reasoning paths, aligning with the policy and generalizing well across diverse models. Second, to perform fine-grained hierarchical optimization, we introduce an RL strategy that jointly optimizes for both trajectory-level problem solving and step-level code generation. This is motivated by our key insight that the success of an intermediate tool call is a strong predictor of the final answer's correctness. Finally, THOR incorporates a self-correction mechanism that leverages immediate tool feedback to dynamically revise erroneous reasoning paths during inference. Our approach demonstrates strong generalization across diverse models, performing effectively in both reasoning and non-reasoning models. It further achieves state-of-the-art performance for models of a similar scale on multiple mathematical benchmarks, while also delivering consistent improvements on code benchmarks. Our code will be publicly available at https://github.com/JingMog/THOR.

Large language models (LLMs) now perform strongly on many public math suites, yet frontier separation within mathematics increasingly suffers from ceiling effects. We present two complementary benchmarks: SKYLENAGE-ReasoningMATH, a 100-item, structure-aware diagnostic set with per-item metadata on length, numeric density, and symbolic complexity; and SKYLENAGE-MATH, a 150-item contest-style suite spanning four stages from high school to doctoral under a seven-subject taxonomy. We evaluate fifteen contemporary LLM variants under a single setup and analyze subject x model and grade x model performance. On the contest suite, the strongest model reaches 44% while the runner-up reaches 37%; accuracy declines from high school to doctoral, and top systems exhibit a doctoral-to-high-school retention near 79%. On the reasoning set, the best model attains 81% overall, and hardest-slice results reveal clear robustness gaps between leaders and the mid-tier. In summary, we release SKYLENAGE-ReasoningMATH and report aggregate results for SKYLENAGE-MATH; together, SKYLENAGE provides a hard, reasoning-centered and broadly covering math benchmark with calibrated difficulty and rich metadata, serving as a reference benchmark for future evaluations of mathematical reasoning.

Large language models (LLMs) excel at program synthesis, yet their ability to produce symbolic graphics programs (SGPs) that render into precise visual content remains underexplored. We study symbolic graphics programming, where the goal is to generate an SGP from a natural-language description. This task also serves as a lens into how LLMs understand the visual world by prompting them to generate images rendered from SGPs. Among various SGPs, our paper sticks to scalable vector graphics (SVGs). We begin by examining the extent to which LLMs can generate SGPs. To this end, we introduce SGP-GenBench, a comprehensive benchmark covering object fidelity, scene fidelity, and compositionality (attribute binding, spatial relations, numeracy). On SGP-GenBench, we discover that frontier proprietary models substantially outperform open-source models, and performance correlates well with general coding capabilities. Motivated by this gap, we aim to improve LLMs' ability to generate SGPs. We propose a reinforcement learning (RL) with verifiable rewards approach, where a format-validity gate ensures renderable SVG, and a cross-modal reward aligns text and the rendered image via strong vision encoders (e.g., SigLIP for text-image and DINO for image-image). Applied to Qwen-2.5-7B, our method substantially improves SVG generation quality and semantics, achieving performance on par with frontier systems. We further analyze training dynamics, showing that RL induces (i) finer decomposition of objects into controllable primitives and (ii) contextual details that improve scene coherence. Our results demonstrate that symbolic graphics programming offers a precise and interpretable lens on cross-modal grounding.

We study the interpretability issue of task-oriented dialogue systems in this paper. Previously, most neural-based task-oriented dialogue systems employ an implicit reasoning strategy that makes the model predictions uninterpretable to humans. To obtain a transparent reasoning process, we introduce neuro-symbolic to perform explicit reasoning that justifies model decisions by reasoning chains. Since deriving reasoning chains requires multi-hop reasoning for task-oriented dialogues, existing neuro-symbolic approaches would induce error propagation due to the one-phase design. To overcome this, we propose a two-phase approach that consists of a hypothesis generator and a reasoner. We first obtain multiple hypotheses, i.e., potential operations to perform the desired task, through the hypothesis generator. Each hypothesis is then verified by the reasoner, and the valid one is selected to conduct the final prediction. The whole system is trained by exploiting raw textual dialogues without using any reasoning chain annotations. Experimental studies on two public benchmark datasets demonstrate that the proposed approach not only achieves better results, but also introduces an interpretable decision process.

Geometric spatial reasoning forms the foundation of many applications in artificial intelligence, yet the ability of large language models (LLMs) to operate over geometric spatial information expressed in procedural code remains underexplored. In this paper, we address this gap by formalizing the Program-to-Geometry task, which challenges models to translate programmatic drawing code into accurate and abstract geometric reasoning. To evaluate this capability, we present GeoGramBench, a benchmark of 500 carefully refined problems organized by a tailored three-level taxonomy that considers geometric complexity rather than traditional mathematical reasoning complexity. Our comprehensive evaluation of 17 frontier LLMs reveals consistent and pronounced deficiencies: even the most advanced models achieve less than 50% accuracy at the highest abstraction level. These results highlight the unique challenges posed by program-driven spatial reasoning and establish GeoGramBench as a valuable resource for advancing research in symbolic-to-spatial geometric reasoning. Project page: https://github.com/LiAuto-DSR/GeoGramBench.

Current video analytics approaches face a fundamental trade-off between flexibility and efficiency. End-to-end Vision Language Models (VLMs) often struggle with long-context processing and incur high computational costs, while neural-symbolic methods depend heavily on manual labeling and rigid rule design. In this paper, we introduce LazyVLM, a neuro-symbolic video analytics system that provides a user-friendly query interface similar to VLMs, while addressing their scalability limitation. LazyVLM enables users to effortlessly drop in video data and specify complex multi-frame video queries using a semi-structured text interface for video analytics. To address the scalability limitations of VLMs, LazyVLM decomposes multi-frame video queries into fine-grained operations and offloads the bulk of the processing to efficient relational query execution and vector similarity search. We demonstrate that LazyVLM provides a robust, efficient, and user-friendly solution for querying open-domain video data at scale.

Instruction tuning -- tuning large language models on instruction-output pairs -- is a promising technique for making models better adapted to the real world. Yet, the key factors driving the model's capability to understand and follow instructions not seen during training remain under-explored. Our investigation begins with a series of synthetic experiments within the theoretical framework of a Turing-complete algorithm called Markov algorithm, which allows fine-grained control over the instruction-tuning data. Generalization and robustness with respect to the training distribution emerge once a diverse enough set of tasks is provided, even though very few examples are provided for each task. We extend these initial results to a real-world application scenario of code generation and find that a more diverse instruction set, extending beyond code-related tasks, improves the performance of code generation. Our observations suggest that a more diverse semantic space for instruction-tuning sets greatly improves the model's ability to follow instructions and perform tasks.

Geometric Problem Solving (GPS) poses a unique challenge for Multimodal Large Language Models (MLLMs), requiring not only the joint interpretation of text and diagrams but also iterative visuospatial reasoning. While existing approaches process diagrams as static images, they lack the capacity for dynamic manipulation - a core aspect of human geometric reasoning involving auxiliary line construction and affine transformations. We present GeoSketch, a neural-symbolic framework that recasts geometric reasoning as an interactive perception-reasoning-action loop. GeoSketch integrates: (1) a Perception module that abstracts diagrams into structured logic forms, (2) a Symbolic Reasoning module that applies geometric theorems to decide the next deductive step, and (3) a Sketch Action module that executes operations such as drawing auxiliary lines or applying transformations, thereby updating the diagram in a closed loop. To train this agent, we develop a two-stage pipeline: supervised fine-tuning on 2,000 symbolic-curated trajectories followed by reinforcement learning with dense, symbolic rewards to enhance robustness and strategic exploration. To evaluate this paradigm, we introduce the GeoSketch Benchmark, a high-quality set of 390 geometry problems requiring auxiliary construction or affine transformations. Experiments on strong MLLM baselines demonstrate that GeoSketch significantly improves stepwise reasoning accuracy and problem-solving success over static perception methods. By unifying hierarchical decision-making, executable visual actions, and symbolic verification, GeoSketch advances multimodal reasoning from static interpretation to dynamic, verifiable interaction, establishing a new foundation for solving complex visuospatial problems.

Given ample experimental data from a system governed by differential equations, it is possible to use deep learning techniques to construct the underlying differential operators. In this work we perform symbolic discovery of differential operators in a situation where there is sparse experimental data. This small data regime in machine learning can be made tractable by providing our algorithms with prior information about the underlying dynamics. Physics Informed Neural Networks (PINNs) have been very successful in this regime (reconstructing entire ODE solutions using only a single point or entire PDE solutions with very few measurements of the initial condition). We modify the PINN approach by adding a neural network that learns a representation of unknown hidden terms in the differential equation. The algorithm yields both a surrogate solution to the differential equation and a black-box representation of the hidden terms. These hidden term neural networks can then be converted into symbolic equations using symbolic regression techniques like AI Feynman. In order to achieve convergence of these neural networks, we provide our algorithms with (noisy) measurements of both the initial condition as well as (synthetic) experimental data obtained at later times. We demonstrate strong performance of this approach even when provided with very few measurements of noisy data in both the ODE and PDE regime.

Proving geometric theorems constitutes a hallmark of visual reasoning combining both intuitive and logical skills. Therefore, automated theorem proving of Olympiad-level geometry problems is considered a notable milestone in human-level automated reasoning. The introduction of AlphaGeometry, a neuro-symbolic model trained with 100 million synthetic samples, marked a major breakthrough. It solved 25 of 30 International Mathematical Olympiad (IMO) problems whereas the reported baseline based on Wu's method solved only ten. In this note, we revisit the IMO-AG-30 Challenge introduced with AlphaGeometry, and find that Wu's method is surprisingly strong. Wu's method alone can solve 15 problems, and some of them are not solved by any of the other methods. This leads to two key findings: (i) Combining Wu's method with the classic synthetic methods of deductive databases and angle, ratio, and distance chasing solves 21 out of 30 methods by just using a CPU-only laptop with a time limit of 5 minutes per problem. Essentially, this classic method solves just 4 problems less than AlphaGeometry and establishes the first fully symbolic baseline strong enough to rival the performance of an IMO silver medalist. (ii) Wu's method even solves 2 of the 5 problems that AlphaGeometry failed to solve. Thus, by combining AlphaGeometry with Wu's method we set a new state-of-the-art for automated theorem proving on IMO-AG-30, solving 27 out of 30 problems, the first AI method which outperforms an IMO gold medalist.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks, yet they often struggle with spatial reasoning. This paper presents a novel neural-symbolic framework that enhances LLMs' spatial reasoning abilities through iterative feedback between LLMs and Answer Set Programming (ASP). We evaluate our approach on two benchmark datasets: StepGame and SparQA, implementing three distinct strategies: (1) direct prompting baseline, (2) Facts+Rules prompting, and (3) DSPy-based LLM+ASP pipeline with iterative refinement. Our experimental results demonstrate that the LLM+ASP pipeline significantly outperforms baseline methods, achieving an average 82% accuracy on StepGame and 69% on SparQA, marking improvements of 40-50% and 8-15% respectively over direct prompting. The success stems from three key innovations: (1) effective separation of semantic parsing and logical reasoning through a modular pipeline, (2) iterative feedback mechanism between LLMs and ASP solvers that improves program rate, and (3) robust error handling that addresses parsing, grounding, and solving failures. Additionally, we propose Facts+Rules as a lightweight alternative that achieves comparable performance on complex SparQA dataset, while reducing computational overhead.Our analysis across different LLM architectures (Deepseek, Llama3-70B, GPT-4.0 mini) demonstrates the framework's generalizability and provides insights into the trade-offs between implementation complexity and reasoning capability, contributing to the development of more interpretable and reliable AI systems.

Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's uses of shortcuts and wrong reasoning while the later poses challenges in accommodating alternative solutions. In this work, we seek to use symbolic programs as a means for automated evaluation if a model can consistently produce correct final answers across various inputs to the program. We begin by extracting programs for popular math datasets (GSM8K and MATH) using GPT4-o. For those executable programs verified using the original input-output pairs, they are found to encapsulate the proper reasoning required to solve the original text questions. We then prompt GPT4-o to generate new questions using alternative input-output pairs based the extracted program. We apply the resulting datasets to evaluate a collection of LLMs. In our experiments, we observe significant accuracy drops using our proposed evaluation compared with original static examples, suggesting the fragility of math reasoning in state-of-the-art LLMs.

Neural networks adapt very well to distributed and continuous representations, but struggle to generalize from small amounts of data. Symbolic systems commonly achieve data efficient generalization by exploiting modularity to benefit from local and discrete features of a representation. These features allow symbolic programs to be improved one module at a time and to experience combinatorial growth in the values they can successfully process. However, it is difficult to design a component that can be used to form symbolic abstractions and which is adequately overparametrized to learn arbitrary high-dimensional transformations. I present Graph-based Symbolically Synthesized Neural Networks (G-SSNNs), a class of neural modules that operate on representations modified with synthesized symbolic programs to include a fixed set of local and discrete features. I demonstrate that the choice of injected features within a G-SSNN module modulates the data efficiency and generalization of baseline neural models, creating predictable patterns of both heightened and curtailed generalization. By training G-SSNNs, we also derive information about desirable semantics of symbolic programs without manual engineering. This information is compact and amenable to abstraction, but can also be flexibly recontextualized for other high-dimensional settings. In future work, I will investigate data efficient generalization and the transferability of learned symbolic representations in more complex G-SSNN designs based on more complex classes of symbolic programs. Experimental code and data are available at https://github.com/shlomenu/symbolically_synthesized_networks .

Chain-of-thought prompting has demonstrated remarkable performance on various natural language reasoning tasks. However, it tends to perform poorly on tasks which requires solving problems harder than the exemplars shown in the prompts. To overcome this challenge of easy-to-hard generalization, we propose a novel prompting strategy, least-to-most prompting. The key idea in this strategy is to break down a complex problem into a series of simpler subproblems and then solve them in sequence. Solving each subproblem is facilitated by the answers to previously solved subproblems. Our experimental results on tasks related to symbolic manipulation, compositional generalization, and math reasoning reveal that least-to-most prompting is capable of generalizing to more difficult problems than those seen in the prompts. A notable finding is that when the GPT-3 code-davinci-002 model is used with least-to-most prompting, it can solve the compositional generalization benchmark SCAN in any split (including length split) with an accuracy of at least 99% using just 14 exemplars, compared to only 16% accuracy with chain-of-thought prompting. This is particularly noteworthy because neural-symbolic models in the literature that specialize in solving SCAN are trained on the entire training set containing over 15,000 examples. We have included prompts for all the tasks in the Appendix.

Supervised approaches for learning spatio-temporal scene graphs (STSG) from video are greatly hindered due to their reliance on STSG-annotated videos, which are labor-intensive to construct at scale. Is it feasible to instead use readily available video captions as weak supervision? To address this question, we propose LASER, a neuro-symbolic framework to enable training STSG generators using only video captions. LASER employs large language models to first extract logical specifications with rich spatio-temporal semantic information from video captions. LASER then trains the underlying STSG generator to align the predicted STSG with the specification. The alignment algorithm overcomes the challenges of weak supervision by leveraging a differentiable symbolic reasoner and using a combination of contrastive, temporal, and semantics losses. The overall approach efficiently trains low-level perception models to extract a fine-grained STSG that conforms to the video caption. In doing so, it enables a novel methodology for learning STSGs without tedious annotations. We evaluate our method on three video datasets: OpenPVSG, 20BN, and MUGEN. Our approach demonstrates substantial improvements over fully-supervised baselines, achieving a unary predicate prediction accuracy of 27.78% (+12.65%) and a binary recall@5 of 0.42 (+0.22) on OpenPVSG. Additionally, LASER exceeds baselines by 7% on 20BN and 5.2% on MUGEN in terms of overall predicate prediction accuracy.

The coronavirus disease (COVID-19) has resulted in a pandemic crippling the a breadth of services critical to daily life. Segmentation of lung infections in computerized tomography (CT) slices could be be used to improve diagnosis and understanding of COVID-19 in patients. Deep learning systems lack interpretability because of their black box nature. Inspired by human communication of complex ideas through language, we propose a symbolic framework based on emergent languages for the segmentation of COVID-19 infections in CT scans of lungs. We model the cooperation between two artificial agents - a Sender and a Receiver. These agents synergistically cooperate using emergent symbolic language to solve the task of semantic segmentation. Our game theoretic approach is to model the cooperation between agents unlike Generative Adversarial Networks (GANs). The Sender retrieves information from one of the higher layers of the deep network and generates a symbolic sentence sampled from a categorical distribution of vocabularies. The Receiver ingests the stream of symbols and cogenerates the segmentation mask. A private emergent language is developed that forms the communication channel used to describe the task of segmentation of COVID infections. We augment existing state of the art semantic segmentation architectures with our symbolic generator to form symbolic segmentation models. Our symbolic segmentation framework achieves state of the art performance for segmentation of lung infections caused by COVID-19. Our results show direct interpretation of symbolic sentences to discriminate between normal and infected regions, infection morphology and image characteristics. We show state of the art results for segmentation of COVID-19 lung infections in CT.

Integrating Large Language Models with symbolic planners is a promising direction for obtaining verifiable and grounded plans compared to planning in natural language, with recent works extending this idea to visual domains using Vision-Language Models (VLMs). However, rigorous comparison between VLM-grounded symbolic approaches and methods that plan directly with a VLM has been hindered by a lack of common environments, evaluation protocols and model coverage. We introduce ViPlan, the first open-source benchmark for Visual Planning with symbolic predicates and VLMs. ViPlan features a series of increasingly challenging tasks in two domains: a visual variant of the classic Blocksworld planning problem and a simulated household robotics environment. We benchmark nine open-source VLM families across multiple sizes, along with selected closed models, evaluating both VLM-grounded symbolic planning and using the models directly to propose actions. We find symbolic planning to outperform direct VLM planning in Blocksworld, where accurate image grounding is crucial, whereas the opposite is true in the household robotics tasks, where commonsense knowledge and the ability to recover from errors are beneficial. Finally, we show that across most models and methods, there is no significant benefit to using Chain-of-Thought prompting, suggesting that current VLMs still struggle with visual reasoning.

Existing methods fail to effectively steer Large Language Models (LLMs) between textual reasoning and code generation, leaving symbolic computing capabilities underutilized. We introduce CodeSteer, an effective method for guiding LLM code/text generation. We construct a comprehensive benchmark SymBench comprising 37 symbolic tasks with adjustable complexity and also synthesize datasets of 12k multi-round guidance/generation trajectories and 5.5k guidance comparison pairs. We fine-tune the Llama-3-8B model with a newly designed multi-round supervised fine-tuning (SFT) and direct preference optimization (DPO). The resulting model, CodeSteerLLM, augmented with the proposed symbolic and self-answer checkers, effectively guides the code/text generation of larger models. Augmenting GPT-4o with CodeSteer raises its average performance score from 53.3 to 86.4, even outperforming the existing best LLM OpenAI o1 (82.7), o1-preview (74.8), and DeepSeek R1 (76.8) across all 37 tasks (28 seen, 9 unseen). Trained for GPT-4o, CodeSteer demonstrates superior generalizability, providing an average 41.8 performance boost on Claude, Mistral, and GPT-3.5. CodeSteer-guided LLMs fully harness symbolic computing to maintain strong performance on highly complex tasks. Models, Datasets, and Codes are available at https://github.com/yongchao98/CodeSteer-v1.0.

Emerging Denoising Diffusion Probabilistic Models (DDPM) have become increasingly utilised because of promising results they have achieved in diverse generative tasks with continuous data, such as image and sound synthesis. Nonetheless, the success of diffusion models has not been fully extended to discrete symbolic music. We propose to combine a vector quantized variational autoencoder (VQ-VAE) and discrete diffusion models for the generation of symbolic music with desired composer styles. The trained VQ-VAE can represent symbolic music as a sequence of indexes that correspond to specific entries in a learned codebook. Subsequently, a discrete diffusion model is used to model the VQ-VAE's discrete latent space. The diffusion model is trained to generate intermediate music sequences consisting of codebook indexes, which are then decoded to symbolic music using the VQ-VAE's decoder. The results demonstrate our model can generate symbolic music with target composer styles that meet the given conditions with a high accuracy of 72.36%.

Neurosymbolic (NeSy) frameworks combine neural representations and learning with symbolic representations and reasoning. Combining the reasoning capacities, explainability, and interpretability of symbolic processing with the flexibility and power of neural computing allows us to solve complex problems with more reliability while being data-efficient. However, this recently growing topic poses a challenge to developers with its learning curve, lack of user-friendly tools, libraries, and unifying frameworks. In this paper, we characterize the technical facets of existing NeSy frameworks, such as the symbolic representation language, integration with neural models, and the underlying algorithms. A majority of the NeSy research focuses on algorithms instead of providing generic frameworks for declarative problem specification to leverage problem solving. To highlight the key aspects of Neurosymbolic modeling, we showcase three generic NeSy frameworks - DeepProbLog, Scallop, and DomiKnowS. We identify the challenges within each facet that lay the foundation for identifying the expressivity of each framework in solving a variety of problems. Building on this foundation, we aim to spark transformative action and encourage the community to rethink this problem in novel ways.

Complex Query Answering (CQA) over incomplete Knowledge Graphs (KGs) is a challenging task. Recently, a line of message-passing-based research has been proposed to solve CQA. However, they perform unsatisfactorily on negative queries and fail to address the noisy messages between variable nodes in the query graph. Moreover, they offer little interpretability and require complex query data and resource-intensive training. In this paper, we propose a Neural-Symbolic Message Passing (NSMP) framework based on pre-trained neural link predictors. By introducing symbolic reasoning and fuzzy logic, NSMP can generalize to arbitrary existential first order logic queries without requiring training while providing interpretable answers. Furthermore, we introduce a dynamic pruning strategy to filter out noisy messages between variable nodes. Experimental results show that NSMP achieves a strong performance. Additionally, through complexity analysis and empirical verification, we demonstrate the superiority of NSMP in inference time over the current state-of-the-art neural-symbolic method. Compared to this approach, NSMP demonstrates faster inference times across all query types on benchmark datasets, with speedup ranging from 2times to over 150times.

We propose a novel symbolic music representation and Generative Adversarial Network (GAN) framework specially designed for symbolic multitrack music generation. The main theme of symbolic music generation primarily encompasses the preprocessing of music data and the implementation of a deep learning framework. Current techniques dedicated to symbolic music generation generally encounter two significant challenges: training data's lack of information about chords and scales and the requirement of specially designed model architecture adapted to the unique format of symbolic music representation. In this paper, we solve the above problems by introducing new symbolic music representation with MusicLang chord analysis model. We propose our MMT-BERT architecture adapting to the representation. To build a robust multitrack music generator, we fine-tune a pre-trained MusicBERT model to serve as the discriminator, and incorporate relativistic standard loss. This approach, supported by the in-depth understanding of symbolic music encoded within MusicBERT, fortifies the consonance and humanity of music generated by our method. Experimental results demonstrate the effectiveness of our approach which strictly follows the state-of-the-art methods.

People see text. Humans read by recognizing words as visual objects, including their shapes, layouts, and patterns, before connecting them to meaning, which enables us to handle typos, distorted fonts, and various scripts effectively. Modern large language models (LLMs), however, rely on subword tokenization, fragmenting text into pieces from a fixed vocabulary. While effective for high-resource languages, this approach over-segments low-resource languages, yielding long, linguistically meaningless sequences and inflating computation. In this work, we challenge this entrenched paradigm and move toward a vision-centric alternative. Our method, SeeTok, renders text as images (visual-text) and leverages pretrained multimodal LLMs to interpret them, reusing strong OCR and text-vision alignment abilities learned from large-scale multimodal training. Across three different language tasks, SeeTok matches or surpasses subword tokenizers while requiring 4.43 times fewer tokens and reducing FLOPs by 70.5%, with additional gains in cross-lingual generalization, robustness to typographic noise, and linguistic hierarchy. SeeTok signals a shift from symbolic tokenization to human-like visual reading, and takes a step toward more natural and cognitively inspired language models.

We introduce TAPAS (Task-based Adaptation and Planning using AgentS), a multi-agent framework that integrates Large Language Models (LLMs) with symbolic planning to solve complex tasks without the need for manually defined environment models. TAPAS employs specialized LLM-based agents that collaboratively generate and adapt domain models, initial states, and goal specifications as needed using structured tool-calling mechanisms. Through this tool-based interaction, downstream agents can request modifications from upstream agents, enabling adaptation to novel attributes and constraints without manual domain redefinition. A ReAct (Reason+Act)-style execution agent, coupled with natural language plan translation, bridges the gap between dynamically generated plans and real-world robot capabilities. TAPAS demonstrates strong performance in benchmark planning domains and in the VirtualHome simulated real-world environment.

Large language models (LLMs) have demonstrated an impressive ability to synthesize plausible and fluent text. However they remain vulnerable to hallucinations, and thus their outputs generally require manual human verification for high-stakes applications, which can be time-consuming and difficult. This paper proposes symbolically grounded generation (SymGen) as a simple approach for enabling easier validation of an LLM's output. SymGen prompts an LLM to interleave its regular output text with explicit symbolic references to fields present in some conditioning data (e.g., a table in JSON format). The references can be used to display the provenance of different spans of text in the generation, reducing the effort required for manual verification. Across data-to-text and question answering experiments, we find that LLMs are able to directly output text that makes use of symbolic references while maintaining fluency and accuracy.

How does language inform our downstream thinking? In particular, how do humans make meaning from language -- and how can we leverage a theory of linguistic meaning to build machines that think in more human-like ways? In this paper, we propose rational meaning construction, a computational framework for language-informed thinking that combines neural models of language with probabilistic models for rational inference. We frame linguistic meaning as a context-sensitive mapping from natural language into a probabilistic language of thought (PLoT) -- a general-purpose symbolic substrate for probabilistic, generative world modeling. Our architecture integrates two powerful computational tools that have not previously come together: we model thinking with probabilistic programs, an expressive representation for flexible commonsense reasoning; and we model meaning construction with large language models (LLMs), which support broad-coverage translation from natural language utterances to code expressions in a probabilistic programming language. We illustrate our framework in action through examples covering four core domains from cognitive science: probabilistic reasoning, logical and relational reasoning, visual and physical reasoning, and social reasoning about agents and their plans. In each, we show that LLMs can generate context-sensitive translations that capture pragmatically-appropriate linguistic meanings, while Bayesian inference with the generated programs supports coherent and robust commonsense reasoning. We extend our framework to integrate cognitively-motivated symbolic modules to provide a unified commonsense thinking interface from language. Finally, we explore how language can drive the construction of world models themselves.

Formal proofs are challenging to write even for experienced experts. Recent progress in Neural Theorem Proving (NTP) shows promise in expediting this process. However, the formal corpora available on the Internet are limited compared to the general text, posing a significant data scarcity challenge for NTP. To address this issue, this work proposes Alchemy, a general framework for data synthesis that constructs formal theorems through symbolic mutation. Specifically, for each candidate theorem in Mathlib, we identify all invocable theorems that can be used to rewrite or apply to it. Subsequently, we mutate the candidate theorem by replacing the corresponding term in the statement with its equivalent form or antecedent. As a result, our method increases the number of theorems in Mathlib by an order of magnitude, from 110k to 6M. Furthermore, we perform continual pretraining and supervised finetuning on this augmented corpus for large language models. Experimental results demonstrate the effectiveness of our approach, achieving a 5% absolute performance improvement on Leandojo benchmark. Additionally, our synthetic data achieve a 2.5% absolute performance gain on the out-of-distribution miniF2F benchmark. To provide further insights, we conduct a comprehensive analysis of synthetic data composition and the training paradigm, offering valuable guidance for developing a strong theorem prover.

Symbolic execution is a powerful technique for software testing, but suffers from limitations when encountering external functions, such as native methods or third-party libraries. Existing solutions often require additional context, expensive SMT solvers, or manual intervention to approximate these functions through symbolic stubs. In this work, we propose a novel approach to automatically generate symbolic stubs for external functions during symbolic execution that leverages Genetic Programming. When the symbolic executor encounters an external function, AutoStub generates training data by executing the function on randomly generated inputs and collecting the outputs. Genetic Programming then derives expressions that approximate the behavior of the function, serving as symbolic stubs. These automatically generated stubs allow the symbolic executor to continue the analysis without manual intervention, enabling the exploration of program paths that were previously intractable. We demonstrate that AutoStub can automatically approximate external functions with over 90% accuracy for 55% of the functions evaluated, and can infer language-specific behaviors that reveal edge cases crucial for software testing.

A recent approach to neurosymbolic reasoning is to explicitly combine the strengths of large language models (LLMs) and symbolic solvers to tackle complex reasoning tasks. However, current approaches face significant limitations, including poor generalizability due to task-specific prompts, inefficiencies caused by the lack of separation between knowledge and queries, and restricted inferential capabilities. These shortcomings hinder their scalability and applicability across diverse domains. In this paper, we introduce VERUS-LM, a novel framework designed to address these challenges. VERUS-LM employs a generic prompting mechanism, clearly separates domain knowledge from queries, and supports a wide range of different logical reasoning tasks. This framework enhances adaptability, reduces computational cost, and allows for richer forms of reasoning, such as optimization and constraint satisfaction. We show that our approach succeeds in diverse reasoning on a novel dataset, markedly outperforming LLMs. Additionally, our system achieves competitive results on common reasoning benchmarks when compared to other state-of-the-art approaches, and significantly surpasses them on the difficult AR-LSAT dataset. By pushing the boundaries of hybrid reasoning, VERUS-LM represents a significant step towards more versatile neurosymbolic AI systems

Several adaptations of Transformers models have been developed in various domains since its breakthrough in Natural Language Processing (NLP). This trend has spread into the field of Music Information Retrieval (MIR), including studies processing music data. However, the practice of leveraging NLP tools for symbolic music data is not novel in MIR. Music has been frequently compared to language, as they share several similarities, including sequential representations of text and music. These analogies are also reflected through similar tasks in MIR and NLP. This survey reviews NLP methods applied to symbolic music generation and information retrieval studies following two axes. We first propose an overview of representations of symbolic music adapted from natural language sequential representations. Such representations are designed by considering the specificities of symbolic music. These representations are then processed by models. Such models, possibly originally developed for text and adapted for symbolic music, are trained on various tasks. We describe these models, in particular deep learning models, through different prisms, highlighting music-specialized mechanisms. We finally present a discussion surrounding the effective use of NLP tools for symbolic music data. This includes technical issues regarding NLP methods and fundamental differences between text and music, which may open several doors for further research into more effectively adapting NLP tools to symbolic MIR.

In robotic task planning, symbolic planners using rule-based representations like PDDL are effective but struggle with long-sequential tasks in complicated planning environments due to exponentially increasing search space. Recently, Large Language Models (LLMs) based on artificial neural networks have emerged as promising alternatives for autonomous robot task planning, offering faster inference and leveraging commonsense knowledge. However, they typically suffer from lower success rates. In this paper, to address the limitations of the current symbolic (slow speed) or LLM-based approaches (low accuracy), we propose a novel neuro-symbolic task planner that decomposes complex tasks into subgoals using LLM and carries out task planning for each subgoal using either symbolic or MCTS-based LLM planners, depending on the subgoal complexity. Generating subgoals helps reduce planning time and improve success rates by narrowing the overall search space and enabling LLMs to focus on smaller, more manageable tasks. Our method significantly reduces planning time while maintaining a competitive success rate, as demonstrated through experiments in different public task planning domains, as well as real-world and simulated robotics environments.

While deep learning has enjoyed significant success in computer vision tasks over the past decade, many shortcomings still exist from a Cognitive Science (CogSci) perspective. In particular, the ability to subitize, i.e., quickly and accurately identify the small (less than 6) count of items, is not well learned by current Convolutional Neural Networks (CNNs) or Vision Transformers (ViTs) when using a standard cross-entropy (CE) loss. In this paper, we demonstrate that adapting tools used in CogSci research can improve the subitizing generalization of CNNs and ViTs by developing an alternative loss function using Holographic Reduced Representations (HRRs). We investigate how this neuro-symbolic approach to learning affects the subitizing capability of CNNs and ViTs, and so we focus on specially crafted problems that isolate generalization to specific aspects of subitizing. Via saliency maps and out-of-distribution performance, we are able to empirically observe that the proposed HRR loss improves subitizing generalization though it does not completely solve the problem. In addition, we find that ViTs perform considerably worse compared to CNNs in most respects on subitizing, except on one axis where an HRR-based loss provides improvement.

Recent advances in methods focused on the grounding problem have resulted in techniques that can be used to construct a symbolic language associated with a specific domain. Inspired by how humans communicate complex ideas through language, we developed a generalized Symbolic Semantic (S^2) framework for interpretable segmentation. Unlike adversarial models (e.g., GANs), we explicitly model cooperation between two agents, a Sender and a Receiver, that must cooperate to achieve a common goal. The Sender receives information from a high layer of a segmentation network and generates a symbolic sentence derived from a categorical distribution. The Receiver obtains the symbolic sentences and co-generates the segmentation mask. In order for the model to converge, the Sender and Receiver must learn to communicate using a private language. We apply our architecture to segment tumors in the TCGA dataset. A UNet-like architecture is used to generate input to the Sender network which produces a symbolic sentence, and a Receiver network co-generates the segmentation mask based on the sentence. Our Segmentation framework achieved similar or better performance compared with state-of-the-art segmentation methods. In addition, our results suggest direct interpretation of the symbolic sentences to discriminate between normal and tumor tissue, tumor morphology, and other image characteristics.

Large Language Models (LLMs) have been the subject of active research, significantly advancing the field of Natural Language Processing (NLP). From BERT to BLOOM, LLMs have surpassed state-of-the-art results in various natural language tasks such as question answering, summarization, and text generation. Many ongoing efforts focus on understanding LLMs' capabilities, including their knowledge of the world, syntax, and semantics. However, extending the textual prowess of LLMs to symbolic reasoning has been slow and predominantly focused on tackling problems related to the mathematical field. In this paper, we explore the use of LLMs for automated planning - a branch of AI concerned with the realization of action sequences (plans) to achieve a goal, typically executed by intelligent agents, autonomous robots, and unmanned vehicles. We introduce Plansformer; an LLM fine-tuned on planning problems and capable of generating plans with favorable behavior in terms of correctness and length with reduced knowledge-engineering efforts. We also demonstrate the adaptability of Plansformer in solving different planning domains with varying complexities, owing to the transfer learning abilities of LLMs. For one configuration of Plansformer, we achieve ~97% valid plans, out of which ~95% are optimal for Towers of Hanoi - a puzzle-solving domain.

Large vision language models exhibit notable limitations on Geometry Problem Solving (GPS) because of their unreliable diagram interpretation and pure natural-language reasoning. A recent line of work mitigates this by using symbolic solvers: the model directly generates a formal program that a geometry solver can execute. However, this direct program generation lacks intermediate reasoning, making the decision process opaque and prone to errors. In this work, we explore a new approach that integrates Chain-of-Thought (CoT) with formal language. The model interleaves natural language reasoning with incremental emission of solver-executable code, producing a hybrid reasoning trace in which critical derivations are expressed in formal language. To teach this behavior at scale, we combine (1) supervised fine-tuning on an 11K newly developed synthetic dataset with interleaved natural language reasoning and automatic formalization, and (2) solver-in-the-loop reinforcement learning that jointly optimizes both the CoT narrative and the resulting program through outcome-based rewards. Built on Qwen2.5-VL-7B, our new model, named GF-Reasoner, achieves up to 15% accuracy improvements on standard GPS benchmarks, surpassing both 7B-scale peers and the much larger model Qwen2.5-VL-72B. By exploiting high-order geometric knowledge and offloading symbolic computation to the solver, the generated reasoning traces are noticeably shorter and cleaner. Furthermore, we present a comprehensive analysis of method design choices (e.g., reasoning paradigms, data synthesis, training epochs, etc.), providing actionable insights for future research.

Large Language Models (LLMs) excel in complex reasoning tasks but struggle with consistent rule application, exception handling, and explainability, particularly in domains like legal analysis that require both natural language understanding and precise logical inference. This paper introduces a structured prompting framework that decomposes reasoning into three verifiable steps: entity identification, property extraction, and symbolic rule application. By integrating neural and symbolic approaches, our method leverages LLMs' interpretive flexibility while ensuring logical consistency through formal verification. The framework externalizes task definitions, enabling domain experts to refine logical structures without altering the architecture. Evaluated on the LegalBench hearsay determination task, our approach significantly outperformed baselines, with OpenAI o-family models showing substantial improvements - o1 achieving an F1 score of 0.929 and o3-mini reaching 0.867 using structured decomposition with complementary predicates, compared to their few-shot baselines of 0.714 and 0.74 respectively. This hybrid neural-symbolic system offers a promising pathway for transparent and consistent rule-based reasoning, suggesting potential for explainable AI applications in structured legal reasoning tasks.

Generating music with deep neural networks has been an area of active research in recent years. While the quality of generated samples has been steadily increasing, most methods are only able to exert minimal control over the generated sequence, if any. We propose the self-supervised description-to-sequence task, which allows for fine-grained controllable generation on a global level. We do so by extracting high-level features about the target sequence and learning the conditional distribution of sequences given the corresponding high-level description in a sequence-to-sequence modelling setup. We train FIGARO (FIne-grained music Generation via Attention-based, RObust control) by applying description-to-sequence modelling to symbolic music. By combining learned high level features with domain knowledge, which acts as a strong inductive bias, the model achieves state-of-the-art results in controllable symbolic music generation and generalizes well beyond the training distribution.

We develop a general approach to distill symbolic representations of a learned deep model by introducing strong inductive biases. We focus on Graph Neural Networks (GNNs). The technique works as follows: we first encourage sparse latent representations when we train a GNN in a supervised setting, then we apply symbolic regression to components of the learned model to extract explicit physical relations. We find the correct known equations, including force laws and Hamiltonians, can be extracted from the neural network. We then apply our method to a non-trivial cosmology example-a detailed dark matter simulation-and discover a new analytic formula which can predict the concentration of dark matter from the mass distribution of nearby cosmic structures. The symbolic expressions extracted from the GNN using our technique also generalized to out-of-distribution data better than the GNN itself. Our approach offers alternative directions for interpreting neural networks and discovering novel physical principles from the representations they learn.

Visual reasoning, particularly spatial reasoning, is a challenging cognitive task that requires understanding object relationships and their interactions within complex environments, especially in robotics domain. Existing vision_language models (VLMs) excel at perception tasks but struggle with fine-grained spatial reasoning due to their implicit, correlation-driven reasoning and reliance solely on images. We propose a novel neuro_symbolic framework that integrates both panoramic-image and 3D point cloud information, combining neural perception with symbolic reasoning to explicitly model spatial and logical relationships. Our framework consists of a perception module for detecting entities and extracting attributes, and a reasoning module that constructs a structured scene graph to support precise, interpretable queries. Evaluated on the JRDB-Reasoning dataset, our approach demonstrates superior performance and reliability in crowded, human_built environments while maintaining a lightweight design suitable for robotics and embodied AI applications.

Recent advances in Multimodal Large Language Models (MLLMs) have achieved remarkable progress in general domains and demonstrated promise in multimodal mathematical reasoning. However, applying MLLMs to geometry problem solving (GPS) remains challenging due to lack of accurate step-by-step solution data and severe hallucinations during reasoning. In this paper, we propose GeoGen, a pipeline that can automatically generates step-wise reasoning paths for geometry diagrams. By leveraging the precise symbolic reasoning, GeoGen produces large-scale, high-quality question-answer pairs. To further enhance the logical reasoning ability of MLLMs, we train GeoLogic, a Large Language Model (LLM) using synthetic data generated by GeoGen. Serving as a bridge between natural language and symbolic systems, GeoLogic enables symbolic tools to help verifying MLLM outputs, making the reasoning process more rigorous and alleviating hallucinations. Experimental results show that our approach consistently improves the performance of MLLMs, achieving remarkable results on benchmarks for geometric reasoning tasks. This improvement stems from our integration of the strengths of LLMs and symbolic systems, which enables a more reliable and interpretable approach for the GPS task. Codes are available at https://github.com/ycpNotFound/GeoGen.

First-order logic (FOL) reasoning, which involves sequential deduction, is pivotal for intelligent systems and serves as a valuable task for evaluating reasoning capabilities, particularly in chain-of-thought (CoT) contexts. Existing benchmarks often rely on extensive human annotation or handcrafted templates, making it difficult to achieve the necessary complexity, scalability, and diversity for robust evaluation. To address these limitations, we propose a novel framework called ProverGen that synergizes the generative strengths of Large Language Models (LLMs) with the rigor and precision of symbolic provers, enabling the creation of a scalable, diverse, and high-quality FOL reasoning dataset, ProverQA. ProverQA is also distinguished by its inclusion of accessible and logically coherent intermediate reasoning steps for each problem. Our evaluation shows that state-of-the-art LLMs struggle to solve ProverQA problems, even with CoT prompting, highlighting the dataset's challenging nature. We also finetune Llama3.1-8B-Instruct on a separate training set generated by our framework. The finetuned model demonstrates consistent improvements on both in-distribution and out-of-distribution test sets, suggesting the value of our proposed data generation framework. Code available at: https://github.com/opendatalab/ProverGen

Recent advancements in AI safety have led to increased efforts in training and red-teaming large language models (LLMs) to mitigate unsafe content generation. However, these safety mechanisms may not be comprehensive, leaving potential vulnerabilities unexplored. This paper introduces MathPrompt, a novel jailbreaking technique that exploits LLMs' advanced capabilities in symbolic mathematics to bypass their safety mechanisms. By encoding harmful natural language prompts into mathematical problems, we demonstrate a critical vulnerability in current AI safety measures. Our experiments across 13 state-of-the-art LLMs reveal an average attack success rate of 73.6\%, highlighting the inability of existing safety training mechanisms to generalize to mathematically encoded inputs. Analysis of embedding vectors shows a substantial semantic shift between original and encoded prompts, helping explain the attack's success. This work emphasizes the importance of a holistic approach to AI safety, calling for expanded red-teaming efforts to develop robust safeguards across all potential input types and their associated risks.

Diffusion models have shown promising results for a wide range of generative tasks with continuous data, such as image and audio synthesis. However, little progress has been made on using diffusion models to generate discrete symbolic music because this new class of generative models are not well suited for discrete data while its iterative sampling process is computationally expensive. In this work, we propose a diffusion model combined with a Generative Adversarial Network, aiming to (i) alleviate one of the remaining challenges in algorithmic music generation which is the control of generation towards a target emotion, and (ii) mitigate the slow sampling drawback of diffusion models applied to symbolic music generation. We first used a trained Variational Autoencoder to obtain embeddings of a symbolic music dataset with emotion labels and then used those to train a diffusion model. Our results demonstrate the successful control of our diffusion model to generate symbolic music with a desired emotion. Our model achieves several orders of magnitude improvement in computational cost, requiring merely four time steps to denoise while the steps required by current state-of-the-art diffusion models for symbolic music generation is in the order of thousands.

Large Language Models (LLMs) have shown human-like reasoning abilities but still struggle with complex logical problems. This paper introduces a novel framework, Logic-LM, which integrates LLMs with symbolic solvers to improve logical problem-solving. Our method first utilizes LLMs to translate a natural language problem into a symbolic formulation. Afterward, a deterministic symbolic solver performs inference on the formulated problem. We also introduce a self-refinement module, which utilizes the symbolic solver's error messages to revise symbolic formalizations. We demonstrate Logic-LM's effectiveness on five logical reasoning datasets: ProofWriter, PrOntoQA, FOLIO, LogicalDeduction, and AR-LSAT. On average, Logic-LM achieves a significant performance boost of 39.2% over using LLM alone with standard prompting and 18.4% over LLM with chain-of-thought prompting. Our findings suggest that Logic-LM, by combining LLMs with symbolic logic, offers a promising avenue for faithful logical reasoning. Code and data are publicly available at https://github.com/teacherpeterpan/Logic-LLM.

We study the capabilities of generative autoregressive transformer models trained on large amounts of symbolic solo-piano transcriptions. After first pretraining on approximately 60,000 hours of music, we use a comparatively smaller, high-quality subset, to finetune models to produce musical continuations, perform symbolic classification tasks, and produce general-purpose contrastive MIDI embeddings by adapting the SimCLR framework to symbolic music. When evaluating piano continuation coherence, our generative model outperforms leading symbolic generation techniques and remains competitive with proprietary audio generation models. On MIR classification benchmarks, frozen representations from our contrastive model achieve state-of-the-art results in linear probe experiments, while direct finetuning demonstrates the generalizability of pretrained representations, often requiring only a few hundred labeled examples to specialize to downstream tasks.

Multimodal Large Language Models (MLLMs) demonstrate robust zero-shot capabilities across diverse vision-language tasks after training on mega-scale datasets. However, dense prediction tasks, such as semantic segmentation and keypoint detection, pose significant challenges for MLLMs when represented solely as text outputs. Simultaneously, current MLLMs utilizing latent embeddings for visual task decoding generally demonstrate limited adaptability to both multi-task learning and multi-granularity scenarios. In this work, we present REF-VLM, an end-to-end framework for unified training of various visual decoding tasks. To address complex visual decoding scenarios, we introduce the Triplet-Based Referring Paradigm (TRP), which explicitly decouples three critical dimensions in visual decoding tasks through a triplet structure: concepts, decoding types, and targets. TRP employs symbolic delimiters to enforce structured representation learning, enhancing the parsability and interpretability of model outputs. Additionally, we construct Visual-Task Instruction Following Dataset (VTInstruct), a large-scale multi-task dataset containing over 100 million multimodal dialogue samples across 25 task types. Beyond text inputs and outputs, VT-Instruct incorporates various visual prompts such as point, box, scribble, and mask, and generates outputs composed of text and visual units like box, keypoint, depth and mask. The combination of different visual prompts and visual units generates a wide variety of task types, expanding the applicability of REF-VLM significantly. Both qualitative and quantitative experiments demonstrate that our REF-VLM outperforms other MLLMs across a variety of standard benchmarks. The code, dataset, and demo available at https://github.com/MacavityT/REF-VLM.

Discrete adversarial attacks are symbolic perturbations to a language input that preserve the output label but lead to a prediction error. While such attacks have been extensively explored for the purpose of evaluating model robustness, their utility for improving robustness has been limited to offline augmentation only. Concretely, given a trained model, attacks are used to generate perturbed (adversarial) examples, and the model is re-trained exactly once. In this work, we address this gap and leverage discrete attacks for online augmentation, where adversarial examples are generated at every training step, adapting to the changing nature of the model. We propose (i) a new discrete attack, based on best-first search, and (ii) random sampling attacks that unlike prior work are not based on expensive search-based procedures. Surprisingly, we find that random sampling leads to impressive gains in robustness, outperforming the commonly-used offline augmentation, while leading to a speedup at training time of ~10x. Furthermore, online augmentation with search-based attacks justifies the higher training cost, significantly improving robustness on three datasets. Last, we show that our new attack substantially improves robustness compared to prior methods.

With powerful large language models (LLMs) demonstrating superhuman reasoning capabilities, a critical question arises: Do LLMs genuinely reason, or do they merely recall answers from their extensive, web-scraped training datasets? Publicly released benchmarks inevitably become contaminated once incorporated into subsequent LLM training sets, undermining their reliability as faithful assessments. To address this, we introduce KUMO, a generative evaluation framework designed specifically for assessing reasoning in LLMs. KUMO synergistically combines LLMs with symbolic engines to dynamically produce diverse, multi-turn reasoning tasks that are partially observable and adjustable in difficulty. Through an automated pipeline, KUMO continuously generates novel tasks across open-ended domains, compelling models to demonstrate genuine generalization rather than memorization. We evaluated 23 state-of-the-art LLMs on 5,000 tasks across 100 domains created by KUMO, benchmarking their reasoning abilities against university students. Our findings reveal that many LLMs have outperformed university-level performance on easy reasoning tasks, and reasoning-scaled LLMs reach university-level performance on complex reasoning challenges. Moreover, LLM performance on KUMO tasks correlates strongly with results on newly released real-world reasoning benchmarks, underscoring KUMO's value as a robust, enduring assessment tool for genuine LLM reasoning capabilities.

The pursuit of automated scientific discovery has fueled progress from symbolic logic to modern AI, forging new frontiers in reasoning and pattern recognition. Transformers function as potential systems, where every possible relationship remains latent potentiality until tasks impose constraints, akin to measurement. Yet, refining their sampling requires more than probabilistic selection: solutions must conform to specific structures or rules, ensuring consistency and the invocation of general principles. We present Graph-PReFLexOR (Graph-based Preference-based Recursive Language Modeling for Exploratory Optimization of Reasoning), a framework that combines graph reasoning with symbolic abstraction to dynamically expand domain knowledge. Inspired by reinforcement learning, Graph-PReFLexOR defines reasoning as a structured mapping, where tasks yield knowledge graphs, abstract patterns, and ultimately, final answers. Inspired by category theory, it encodes concepts as nodes and their relationships as edges, supporting hierarchical inference and adaptive learning through isomorphic representations. Demonstrations include hypothesis generation, materials design, and creative reasoning, such as discovering relationships between mythological concepts like 'thin places' with materials science. We propose a 'knowledge garden growth' strategy that integrates insights across domains, promoting interdisciplinary connections. Results with a 3-billion-parameter Graph-PReFLexOR model show superior reasoning depth and adaptability, underscoring the potential for transparent, multidisciplinary AI-driven discovery. It lays the groundwork for general autonomous reasoning solutions.

Humans interact with the environment using a combination of perception - transforming sensory inputs from their environment into symbols, and cognition - mapping symbols to knowledge about the environment for supporting abstraction, reasoning by analogy, and long-term planning. Human perception-inspired machine perception, in the context of AI, refers to large-scale pattern recognition from raw data using neural networks trained using self-supervised learning objectives such as next-word prediction or object recognition. On the other hand, machine cognition encompasses more complex computations, such as using knowledge of the environment to guide reasoning, analogy, and long-term planning. Humans can also control and explain their cognitive functions. This seems to require the retention of symbolic mappings from perception outputs to knowledge about their environment. For example, humans can follow and explain the guidelines and safety constraints driving their decision-making in safety-critical applications such as healthcare, criminal justice, and autonomous driving. This article introduces the rapidly emerging paradigm of Neurosymbolic AI combines neural networks and knowledge-guided symbolic approaches to create more capable and flexible AI systems. These systems have immense potential to advance both algorithm-level (e.g., abstraction, analogy, reasoning) and application-level (e.g., explainable and safety-constrained decision-making) capabilities of AI systems.

Neurosymbolic (NeSy) predictors combine neural perception with symbolic reasoning to solve tasks like visual reasoning. However, standard NeSy predictors assume conditional independence between the symbols they extract, thus limiting their ability to model interactions and uncertainty - often leading to overconfident predictions and poor out-of-distribution generalisation. To overcome the limitations of the independence assumption, we introduce neurosymbolic diffusion models (NeSyDMs), a new class of NeSy predictors that use discrete diffusion to model dependencies between symbols. Our approach reuses the independence assumption from NeSy predictors at each step of the diffusion process, enabling scalable learning while capturing symbol dependencies and uncertainty quantification. Across both synthetic and real-world benchmarks - including high-dimensional visual path planning and rule-based autonomous driving - NeSyDMs achieve state-of-the-art accuracy among NeSy predictors and demonstrate strong calibration.

Recent advancements in large language models have showcased their remarkable generalizability across various domains. However, their reasoning abilities still have significant room for improvement, especially when confronted with scenarios requiring multi-step reasoning. Although large language models possess extensive knowledge, their behavior, particularly in terms of reasoning, often fails to effectively utilize this knowledge to establish a coherent thinking paradigm. Generative language models sometimes show hallucinations as their reasoning procedures are unconstrained by logical principles. Aiming to improve the zero-shot chain-of-thought reasoning ability of large language models, we propose Logical Chain-of-Thought (LogiCoT), a neurosymbolic framework that leverages principles from symbolic logic to verify and revise the reasoning processes accordingly. Experimental evaluations conducted on language tasks in diverse domains, including arithmetic, commonsense, symbolic, causal inference, and social problems, demonstrate the efficacy of the enhanced reasoning paradigm by logic.

Action quality assessment (AQA) applies computer vision to quantitatively assess the performance or execution of a human action. Current AQA approaches are end-to-end neural models, which lack transparency and tend to be biased because they are trained on subjective human judgements as ground-truth. To address these issues, we introduce a neuro-symbolic paradigm for AQA, which uses neural networks to abstract interpretable symbols from video data and makes quality assessments by applying rules to those symbols. We take diving as the case study. We found that domain experts prefer our system and find it more informative than purely neural approaches to AQA in diving. Our system also achieves state-of-the-art action recognition and temporal segmentation, and automatically generates a detailed report that breaks the dive down into its elements and provides objective scoring with visual evidence. As verified by a group of domain experts, this report may be used to assist judges in scoring, help train judges, and provide feedback to divers. We will open-source all of our annotated training data and code for ease of reproducibility.

Recently, natural language has been the primary medium for human-robot interaction. However, its inherent lack of spatial precision introduces challenges for robotic task definition such as ambiguity and verbosity. Moreover, in some public settings where quiet is required, such as libraries or hospitals, verbal communication with robots is inappropriate. To address these limitations, we introduce the Robotic Visual Instruction (RoVI), a novel paradigm to guide robotic tasks through an object-centric, hand-drawn symbolic representation. RoVI effectively encodes spatial-temporal information into human-interpretable visual instructions through 2D sketches, utilizing arrows, circles, colors, and numbers to direct 3D robotic manipulation. To enable robots to understand RoVI better and generate precise actions based on RoVI, we present Visual Instruction Embodied Workflow (VIEW), a pipeline formulated for RoVI-conditioned policies. This approach leverages Vision-Language Models (VLMs) to interpret RoVI inputs, decode spatial and temporal constraints from 2D pixel space via keypoint extraction, and then transform them into executable 3D action sequences. We additionally curate a specialized dataset of 15K instances to fine-tune small VLMs for edge deployment,enabling them to effectively learn RoVI capabilities. Our approach is rigorously validated across 11 novel tasks in both real and simulated environments, demonstrating significant generalization capability. Notably, VIEW achieves an 87.5% success rate in real-world scenarios involving unseen tasks that feature multi-step actions, with disturbances, and trajectory-following requirements. Project website: https://robotic-visual-instruction.github.io/

The ''pretraining-and-finetuning'' paradigm has become a norm for training domain-specific models in natural language processing and computer vision. In this work, we aim to examine this paradigm for symbolic music generation through leveraging the largest ever symbolic music dataset sourced from the MuseScore forum. We first pretrain a large unconditional transformer model using 1.5 million songs. We then propose a simple technique to equip this pretrained unconditional music transformer model with instrument and genre controls by finetuning the model with additional control tokens. Our proposed representation offers improved high-level controllability and expressiveness against two existing representations. The experimental results show that the proposed model can successfully generate music with user-specified instruments and genre. In a subjective listening test, the proposed model outperforms the pretrained baseline model in terms of coherence, harmony, arrangement and overall quality.

We propose AnyTOD, an end-to-end, zero-shot task-oriented dialog (TOD) system capable of handling unseen tasks without task-specific training. We view TOD as a program executed by a language model (LM), where program logic and ontology is provided by a designer as a schema. To enable generalization to unseen schemas and programs without prior training, AnyTOD adopts a neuro-symbolic approach. A neural LM keeps track of events occurring during a conversation and a symbolic program implementing the dialog policy is executed to recommend next actions AnyTOD should take. This approach drastically reduces data annotation and model training requirements, addressing the enduring challenge of rapidly adapting a TOD system to unseen tasks and domains. We demonstrate state-of-the-art results on STAR, ABCD and SGD benchmarks. We also demonstrate strong zero-shot transfer ability in low-resource settings, such as zero-shot on MultiWOZ. In addition, we release STARv2, an updated version of the STAR dataset with richer annotations, for benchmarking zero-shot end-to-end TOD models.

We present GeoManip, a framework to enable generalist robots to leverage essential conditions derived from object and part relationships, as geometric constraints, for robot manipulation. For example, cutting the carrot requires adhering to a geometric constraint: the blade of the knife should be perpendicular to the carrot's direction. By interpreting these constraints through symbolic language representations and translating them into low-level actions, GeoManip bridges the gap between natural language and robotic execution, enabling greater generalizability across diverse even unseen tasks, objects, and scenarios. Unlike vision-language-action models that require extensive training, operates training-free by utilizing large foundational models: a constraint generation module that predicts stage-specific geometric constraints and a geometry parser that identifies object parts involved in these constraints. A solver then optimizes trajectories to satisfy inferred constraints from task descriptions and the scene. Furthermore, GeoManip learns in-context and provides five appealing human-robot interaction features: on-the-fly policy adaptation, learning from human demonstrations, learning from failure cases, long-horizon action planning, and efficient data collection for imitation learning. Extensive evaluations on both simulations and real-world scenarios demonstrate GeoManip's state-of-the-art performance, with superior out-of-distribution generalization while avoiding costly model training.

There are two main barriers to using large language models (LLMs) in clinical reasoning. Firstly, while LLMs exhibit significant promise in Natural Language Processing (NLP) tasks, their performance in complex reasoning and planning falls short of expectations. Secondly, LLMs use uninterpretable methods to make clinical decisions that are fundamentally different from the clinician's cognitive processes. This leads to user distrust. In this paper, we present a multi-agent framework called ArgMed-Agents, which aims to enable LLM-based agents to make explainable clinical decision reasoning through interaction. ArgMed-Agents performs self-argumentation iterations via Argumentation Scheme for Clinical Discussion (a reasoning mechanism for modeling cognitive processes in clinical reasoning), and then constructs the argumentation process as a directed graph representing conflicting relationships. Ultimately, use symbolic solver to identify a series of rational and coherent arguments to support decision. We construct a formal model of ArgMed-Agents and present conjectures for theoretical guarantees. ArgMed-Agents enables LLMs to mimic the process of clinical argumentative reasoning by generating explanations of reasoning in a self-directed manner. The setup experiments show that ArgMed-Agents not only improves accuracy in complex clinical decision reasoning problems compared to other prompt methods, but more importantly, it provides users with decision explanations that increase their confidence.

The releases of OpenAI's o1 and o3 mark a significant paradigm shift in Large Language Models towards advanced reasoning capabilities. Notably, o3 outperformed humans in novel problem-solving and skill acquisition on the Abstraction and Reasoning Corpus for Artificial General Intelligence (ARC-AGI). However, this benchmark is limited to symbolic patterns, whereas humans often perceive and reason about multimodal scenarios involving both vision and language data. Thus, there is an urgent need to investigate advanced reasoning capabilities in multimodal tasks. To this end, we track the evolution of the GPT-[n] and o-[n] series models on challenging multimodal puzzles, requiring fine-grained visual perception with abstract or algorithmic reasoning. The superior performance of o1 comes at nearly 750 times the computational cost of GPT-4o, raising concerns about its efficiency. Our results reveal a clear upward trend in reasoning capabilities across model iterations, with notable performance jumps across GPT-series models and subsequently to o1. Nonetheless, we observe that the o1 model still struggles with simple multimodal puzzles requiring abstract reasoning. Furthermore, its performance in algorithmic puzzles remains poor. We plan to continuously track new models in the series and update our results in this paper accordingly. All resources used in this evaluation are openly available https://github.com/declare-lab/LLM-PuzzleTest.

We present MIPS, a novel method for program synthesis based on automated mechanistic interpretability of neural networks trained to perform the desired task, auto-distilling the learned algorithm into Python code. We test MIPS on a benchmark of 62 algorithmic tasks that can be learned by an RNN and find it highly complementary to GPT-4: MIPS solves 32 of them, including 13 that are not solved by GPT-4 (which also solves 30). MIPS uses an integer autoencoder to convert the RNN into a finite state machine, then applies Boolean or integer symbolic regression to capture the learned algorithm. As opposed to large language models, this program synthesis technique makes no use of (and is therefore not limited by) human training data such as algorithms and code from GitHub. We discuss opportunities and challenges for scaling up this approach to make machine-learned models more interpretable and trustworthy.

We present SongComposer, an innovative LLM designed for song composition. It could understand and generate melodies and lyrics in symbolic song representations, by leveraging the capability of LLM. Existing music-related LLM treated the music as quantized audio signals, while such implicit encoding leads to inefficient encoding and poor flexibility. In contrast, we resort to symbolic song representation, the mature and efficient way humans designed for music, and enable LLM to explicitly compose songs like humans. In practice, we design a novel tuple design to format lyric and three note attributes (pitch, duration, and rest duration) in the melody, which guarantees the correct LLM understanding of musical symbols and realizes precise alignment between lyrics and melody. To impart basic music understanding to LLM, we carefully collected SongCompose-PT, a large-scale song pretraining dataset that includes lyrics, melodies, and paired lyrics-melodies in either Chinese or English. After adequate pre-training, 10K carefully crafted QA pairs are used to empower the LLM with the instruction-following capability and solve diverse tasks. With extensive experiments, SongComposer demonstrates superior performance in lyric-to-melody generation, melody-to-lyric generation, song continuation, and text-to-song creation, outperforming advanced LLMs like GPT-4.

Identifying patient cohorts is fundamental to numerous healthcare tasks, including clinical trial recruitment and retrospective studies. Current cohort retrieval methods in healthcare organizations rely on automated queries of structured data combined with manual curation, which are time-consuming, labor-intensive, and often yield low-quality results. Recent advancements in large language models (LLMs) and information retrieval (IR) offer promising avenues to revolutionize these systems. Major challenges include managing extensive eligibility criteria and handling the longitudinal nature of unstructured Electronic Medical Records (EMRs) while ensuring that the solution remains cost-effective for real-world application. This paper introduces a new task, Automatic Cohort Retrieval (ACR), and evaluates the performance of LLMs and commercial, domain-specific neuro-symbolic approaches. We provide a benchmark task, a query dataset, an EMR dataset, and an evaluation framework. Our findings underscore the necessity for efficient, high-quality ACR systems capable of longitudinal reasoning across extensive patient databases.

This paper explores the integration of two AI subdisciplines employed in the development of artificial agents that exhibit intelligent behavior: Large Language Models (LLMs) and Cognitive Architectures (CAs). We present three integration approaches, each grounded in theoretical models and supported by preliminary empirical evidence. The modular approach, which introduces four models with varying degrees of integration, makes use of chain-of-thought prompting, and draws inspiration from augmented LLMs, the Common Model of Cognition, and the simulation theory of cognition. The agency approach, motivated by the Society of Mind theory and the LIDA cognitive architecture, proposes the formation of agent collections that interact at micro and macro cognitive levels, driven by either LLMs or symbolic components. The neuro-symbolic approach, which takes inspiration from the CLARION cognitive architecture, proposes a model where bottom-up learning extracts symbolic representations from an LLM layer and top-down guidance utilizes symbolic representations to direct prompt engineering in the LLM layer. These approaches aim to harness the strengths of both LLMs and CAs, while mitigating their weaknesses, thereby advancing the development of more robust AI systems. We discuss the tradeoffs and challenges associated with each approach.

Self-supervised learning excels at learning representations from large amounts of data. At the same time, generative models offer the complementary property of learning information about the underlying data generation process. In this study, we aim at establishing a principled connection between these two paradigms and highlight the benefits of their complementarity. In particular, we perform an analysis of self-supervised learning objectives, elucidating the underlying probabilistic graphical models and presenting a standardized methodology for their derivation from first principles. The analysis suggests a natural means of integrating self-supervised learning with likelihood-based generative models. We instantiate this concept within the realm of cluster-based self-supervised learning and energy models, introducing a lower bound proven to reliably penalize the most important failure modes and unlocking full unification. Our theoretical findings are substantiated through experiments on synthetic and real-world data, including SVHN, CIFAR10, and CIFAR100, demonstrating that our objective function allows to jointly train a backbone network in a discriminative and generative fashion, consequently outperforming existing self-supervised learning strategies in terms of clustering, generation and out-of-distribution detection performance by a wide margin. We also demonstrate that the solution can be integrated into a neuro-symbolic framework to tackle a simple yet non-trivial instantiation of the symbol grounding problem. The code is publicly available at https://github.com/emsansone/GEDI.

We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and the Navier-Stokes equations with incompressible and compressible flow, regular and complex geometries, and different buoyancy settings. This work presents a new transformer-based multi-operator learning approach that fuses symbolic information to perform operator-based data prediction, i.e. non-autoregressive. By incorporating multiple modalities in the inputs, the PDE foundation model builds in a pathway for including mathematical descriptions of the physical behavior. We pre-train our foundation model on 6 parametric families of equations collected from 13 datasets, including over 60K trajectories. Our model outperforms popular operator learning, computer vision, and multi-physics models, in benchmark forward prediction tasks. We test our architecture choices with ablation studies.

We present VISPROG, a neuro-symbolic approach to solving complex and compositional visual tasks given natural language instructions. VISPROG avoids the need for any task-specific training. Instead, it uses the in-context learning ability of large language models to generate python-like modular programs, which are then executed to get both the solution and a comprehensive and interpretable rationale. Each line of the generated program may invoke one of several off-the-shelf computer vision models, image processing routines, or python functions to produce intermediate outputs that may be consumed by subsequent parts of the program. We demonstrate the flexibility of VISPROG on 4 diverse tasks - compositional visual question answering, zero-shot reasoning on image pairs, factual knowledge object tagging, and language-guided image editing. We believe neuro-symbolic approaches like VISPROG are an exciting avenue to easily and effectively expand the scope of AI systems to serve the long tail of complex tasks that people may wish to perform.

We present a framework for the unsupervised learning of neurosymbolic encoders, which are encoders obtained by composing neural networks with symbolic programs from a domain-specific language. Our framework naturally incorporates symbolic expert knowledge into the learning process, which leads to more interpretable and factorized latent representations compared to fully neural encoders. We integrate modern program synthesis techniques with the variational autoencoding (VAE) framework, in order to learn a neurosymbolic encoder in conjunction with a standard decoder. The programmatic descriptions from our encoders can benefit many analysis workflows, such as in behavior modeling where interpreting agent actions and movements is important. We evaluate our method on learning latent representations for real-world trajectory data from animal biology and sports analytics. We show that our approach offers significantly better separation of meaningful categories than standard VAEs and leads to practical gains on downstream analysis tasks, such as for behavior classification.

Legal reasoning requires both precise interpretation of statutory language and consistent application of complex rules, presenting significant challenges for AI systems. This paper introduces a modular multi-agent framework that decomposes legal reasoning into distinct knowledge acquisition and application stages. In the first stage, specialized agents extract legal concepts and formalize rules to create verifiable intermediate representations of statutes. The second stage applies this knowledge to specific cases through three steps: analyzing queries to map case facts onto the ontology schema, performing symbolic inference to derive logically entailed conclusions, and generating final answers using a programmatic implementation that operationalizes the ontological knowledge. This bridging of natural language understanding with symbolic reasoning provides explicit and verifiable inspection points, significantly enhancing transparency compared to end-to-end approaches. Evaluation on statutory tax calculation tasks demonstrates substantial improvements, with foundational models achieving 76.4\% accuracy compared to 18.8\% baseline performance, effectively narrowing the performance gap between reasoning and foundational models. These findings suggest that modular architectures with formalized knowledge representations can make sophisticated legal reasoning more accessible through computationally efficient models while enhancing consistency and explainability in AI legal reasoning, establishing a foundation for future research into more transparent, trustworthy, and effective AI systems for legal domain.

Retrieval-augmented generation (RAG) framework has shown promising potential in knowledge-intensive question answering (QA) by retrieving external corpus and generating based on augmented context. However, existing approaches only consider the query itself, neither specifying the retrieval preferences for the retrievers nor informing the generators of how to refer to the retrieved documents for the answers, which poses a significant challenge to the QA performance. To address these issues, we propose Rule-Guided Retrieval-Augmented Generation with LMs, which explicitly introduces symbolic rules as demonstrations for in-context learning (RuleRAG-ICL) to guide retrievers to retrieve logically related documents in the directions of rules and uniformly guide generators to generate answers attributed by the guidance of the same set of rules. Moreover, the combination of queries and rules can be further used as supervised fine-tuning data to update retrievers and generators (RuleRAG-FT) to achieve better rule-based instruction following capability, leading to retrieve more supportive results and generate more acceptable answers. To emphasize the attribution of rules, we construct five rule-aware QA benchmarks, including three temporal and two static scenarios, and equip RuleRAG with several kinds of retrievers and generators. Experiments demonstrate that training-free RuleRAG-ICL effectively improves the retrieval quality of +89.2% in Recall@10 scores and generation accuracy of +103.1% in exact match scores over standard RAG on average across the five benchmarks, and further fine-tuned RuleRAG-FT consistently yields more significant performance enhancement. Extensive analyses indicate that RuleRAG scales well with increasing numbers of retrieved documents and exhibits generalization ability for untrained rules.

Formal verification (FV) has witnessed growing significance with current emerging program synthesis by the evolving large language models (LLMs). However, current formal verification mainly resorts to symbolic verifiers or hand-craft rules, resulting in limitations for extensive and flexible verification. On the other hand, formal languages for automated theorem proving, such as Isabelle, as another line of rigorous verification, are maintained with comprehensive rules and theorems. In this paper, we propose FVEL, an interactive Formal Verification Environment with LLMs. Specifically, FVEL transforms a given code to be verified into Isabelle, and then conducts verification via neural automated theorem proving with an LLM. The joined paradigm leverages the rigorous yet abundant formulated and organized rules in Isabelle and is also convenient for introducing and adjusting cutting-edge LLMs. To achieve this goal, we extract a large-scale FVELER3. The FVELER dataset includes code dependencies and verification processes that are formulated in Isabelle, containing 758 theories, 29,125 lemmas, and 200,646 proof steps in total with in-depth dependencies. We benchmark FVELER in the FVEL environment by first fine-tuning LLMs with FVELER and then evaluating them on Code2Inv and SV-COMP. The results show that FVEL with FVELER fine-tuned Llama3- 8B solves 17.39% (69 -> 81) more problems, and Mistral-7B 12% (75 -> 84) more problems in SV-COMP. And the proportion of proof errors is reduced. Project page: https://fveler.github.io/.

The derivation of mathematical results in specialised fields using Large Language Models (LLMs) is an emerging research direction that can help identify models' limitations, and potentially support mathematical discovery. In this paper, we leverage a symbolic engine to generate derivations of equations at scale, and investigate the capabilities of LLMs when deriving goal equations from premises. Specifically, we employ in-context learning for GPT and fine-tune a range of T5 models to compare the robustness and generalisation of pre-training strategies to specialised models. Empirical results show that fine-tuned FLAN-T5-large (MathT5) outperforms GPT models on all static and out-of-distribution test sets in terms of absolute performance. However, an in-depth analysis reveals that the fine-tuned models are more sensitive to perturbations involving unseen symbols and (to a lesser extent) changes to equation structure. In addition, we analyse 1.7K equations and over 200 derivations to highlight common reasoning errors such as the inclusion of incorrect, irrelevant, and redundant equations, along with the tendency to skip derivation steps. Finally, we explore the suitability of existing metrics for evaluating mathematical derivations finding evidence that, while they capture general properties such as sensitivity to perturbations, they fail to highlight fine-grained reasoning errors and essential differences between models. Overall, this work demonstrates that training models on synthetic data can improve their mathematical capabilities beyond larger architectures.

Recent directions in automatic speech recognition (ASR) research have shown that applying deep learning models from image recognition challenges in computer vision is beneficial. As automatic music transcription (AMT) is superficially similar to ASR, in the sense that methods often rely on transforming spectrograms to symbolic sequences of events (e.g. words or notes), deep learning should benefit AMT as well. In this work, we outline an online polyphonic pitch detection system that streams audio to MIDI by ConvLSTMs. Our system achieves state-of-the-art results on the 2007 MIREX multi-F0 development set, with an F-measure of 83\% on the bassoon, clarinet, flute, horn and oboe ensemble recording without requiring any musical language modelling or assumptions of instrument timbre.

Maintaining legacy software requires many software and systems engineering hours. Assembly code programs, which demand low-level control over the computer machine state and have no variable names, are particularly difficult for humans to analyze. Existing conventional program translators guarantee correctness, but are hand-engineered for the source and target programming languages in question. Learned transpilation, i.e. automatic translation of code, offers an alternative to manual re-writing and engineering efforts. Automated symbolic program translation approaches guarantee correctness but struggle to scale to longer programs due to the exponentially large search space. Their rigid rule-based systems also limit their expressivity, so they can only reason about a reduced space of programs. Probabilistic neural language models (LMs) produce plausible outputs for every input, but do so at the cost of guaranteed correctness. In this work, we leverage the strengths of LMs and symbolic solvers in a neurosymbolic approach to learned transpilation for assembly code. Assembly code is an appropriate setting for a neurosymbolic approach, since assembly code can be divided into shorter non-branching basic blocks amenable to the use of symbolic methods. Guess & Sketch extracts alignment and confidence information from features of the LM then passes it to a symbolic solver to resolve semantic equivalence of the transpilation input and output. We test Guess & Sketch on three different test sets of assembly transpilation tasks, varying in difficulty, and show that it successfully transpiles 57.6% more examples than GPT-4 and 39.6% more examples than an engineered transpiler. We also share a training and evaluation dataset for this task.

Automated discovery of physical laws from observational data in the real world is a grand challenge in AI. Current methods, relying on symbolic regression or LLMs, are limited to uni-modal data and overlook the rich, visual phenomenological representations of motion that are indispensable to physicists. This "sensory deprivation" severely weakens their ability to interpret the inherent spatio-temporal patterns within dynamic phenomena. To address this gap, we propose VIPER-R1, a multimodal model that performs Visual Induction for Physics-based Equation Reasoning to discover fundamental symbolic formulas. It integrates visual perception, trajectory data, and symbolic reasoning to emulate the scientific discovery process. The model is trained via a curriculum of Motion Structure Induction (MSI), using supervised fine-tuning to interpret kinematic phase portraits and to construct hypotheses guided by a Causal Chain of Thought (C-CoT), followed by Reward-Guided Symbolic Calibration (RGSC) to refine the formula structure with reinforcement learning. During inference, the trained VIPER-R1 acts as an agent: it first posits a high-confidence symbolic ansatz, then proactively invokes an external symbolic regression tool to perform Symbolic Residual Realignment (SR^2). This final step, analogous to a physicist's perturbation analysis, reconciles the theoretical model with empirical data. To support this research, we introduce PhysSymbol, a new 5,000-instance multimodal corpus. Experiments show that VIPER-R1 consistently outperforms state-of-the-art VLM baselines in accuracy and interpretability, enabling more precise discovery of physical laws. Project page: https://jiaaqiliu.github.io/VIPER-R1/

Radiology report generation (RRG) is a challenging task, as it requires a thorough understanding of medical images, integration of multiple temporal inputs, and accurate report generation. Effective interpretation of medical images, such as chest X-rays (CXRs), demands sophisticated visual-language reasoning to map visual findings to structured reports. Recent studies have shown that multimodal large language models (MLLMs) can acquire multimodal capabilities by aligning with pre-trained vision encoders. However, current approaches predominantly focus on single-image analysis or utilise rule-based symbolic processing to handle multiple images, thereby overlooking the essential temporal information derived from comparing current images with prior ones. To overcome this critical limitation, we introduce Libra, a temporal-aware MLLM tailored for CXR report generation using temporal images. Libra integrates a radiology-specific image encoder with a MLLM and utilises a novel Temporal Alignment Connector to capture and synthesise temporal information of images across different time points with unprecedented precision. Extensive experiments show that Libra achieves new state-of-the-art performance among the same parameter scale MLLMs for RRG tasks on the MIMIC-CXR. Specifically, Libra improves the RadCliQ metric by 12.9% and makes substantial gains across all lexical metrics compared to previous models.

Question answering over visually rich documents (VRDs) requires reasoning not only over isolated content but also over documents' structural organization and cross-page dependencies. However, conventional retrieval-augmented generation (RAG) methods encode content in isolated chunks during ingestion, losing structural and cross-page dependencies, and retrieve a fixed number of pages at inference, regardless of the specific demands of the question or context. This often results in incomplete evidence retrieval and degraded answer quality for multi-page reasoning tasks. To address these limitations, we propose LAD-RAG, a novel Layout-Aware Dynamic RAG framework. During ingestion, LAD-RAG constructs a symbolic document graph that captures layout structure and cross-page dependencies, adding it alongside standard neural embeddings to yield a more holistic representation of the document. During inference, an LLM agent dynamically interacts with the neural and symbolic indices to adaptively retrieve the necessary evidence based on the query. Experiments on MMLongBench-Doc, LongDocURL, DUDE, and MP-DocVQA demonstrate that LAD-RAG improves retrieval, achieving over 90% perfect recall on average without any top-k tuning, and outperforming baseline retrievers by up to 20% in recall at comparable noise levels, yielding higher QA accuracy with minimal latency.

When faced with novel situations, people are able to marshal relevant considerations from a wide range of background knowledge and put these to use in inferences and predictions. What permits us to draw in globally relevant information and reason over it coherently? Here, we explore the hypothesis that people use a combination of distributed and symbolic representations to construct bespoke mental models tailored to novel situations. We propose a computational implementation of this idea -- a ``Model Synthesis Architecture'' (MSA) -- using language models to implement global relevance-based retrieval and model synthesis and probabilistic programs to implement bespoke, coherent world models. We evaluate our MSA as a model of human judgments on a novel reasoning dataset. The dataset -- built around a `Model Olympics` domain of sports vignettes -- tests models' capacity for human-like, open-ended reasoning by requiring (i) judgments about novel causal structures described in language; (ii) drawing on large bodies of background knowledge; and (iii) doing both in light of observations that introduce arbitrary novel variables. Our MSA approach captures human judgments better than language model-only baselines, under both direct and chain-of-thought generations from the LM that supports model synthesis. These results suggest that MSAs can be implemented in a way that mirrors people's ability to deliver locally coherent reasoning over globally relevant variables, offering a path to understanding and replicating human reasoning in open-ended domains.

As Large Language Models (LLMs) become more integrated into our daily lives, it is crucial to identify and mitigate their risks, especially when the risks can have profound impacts on human users and societies. Guardrails, which filter the inputs or outputs of LLMs, have emerged as a core safeguarding technology. This position paper takes a deep look at current open-source solutions (Llama Guard, Nvidia NeMo, Guardrails AI), and discusses the challenges and the road towards building more complete solutions. Drawing on robust evidence from previous research, we advocate for a systematic approach to construct guardrails for LLMs, based on comprehensive consideration of diverse contexts across various LLMs applications. We propose employing socio-technical methods through collaboration with a multi-disciplinary team to pinpoint precise technical requirements, exploring advanced neural-symbolic implementations to embrace the complexity of the requirements, and developing verification and testing to ensure the utmost quality of the final product.

As a seemingly self-explanatory task, problem-solving has been a significant component of science and engineering. However, a general yet concrete formulation of problem-solving itself is missing. With the recent development of AI-based problem-solving agents, the demand for process-level verifiability is rapidly increasing yet underexplored. To fill these gaps, we present a principled formulation of problem-solving as a deterministic Markov decision process; a novel framework, FPS (Formal Problem-Solving), which utilizes existing FTP (formal theorem proving) environments to perform process-verified problem-solving; and D-FPS (Deductive FPS), decoupling solving and answer verification for better human-alignment. The expressiveness, soundness and completeness of the frameworks are proven. We construct three benchmarks on problem-solving: FormalMath500, a formalization of a subset of the MATH500 benchmark; MiniF2F-Solving and PutnamBench-Solving, adaptations of FTP benchmarks MiniF2F and PutnamBench. For faithful, interpretable, and human-aligned evaluation, we propose RPE (Restricted Propositional Equivalence), a symbolic approach to determine the correctness of answers by formal verification. We evaluate four prevalent FTP models and two prompting methods as baselines, solving at most 23.77% of FormalMath500, 27.47% of MiniF2F-Solving, and 0.31% of PutnamBench-Solving.

We introduce SLR, an end-to-end framework for systematic evaluation and training of Large Language Models (LLMs) via Scalable Logical Reasoning. Given a user's task specification, SLR enables scalable, automated synthesis of inductive reasoning tasks with precisely controlled difficulty. For each task, SLR synthesizes (i) a latent ground-truth rule, (ii) an executable validation program used by a symbolic judge to deterministically verify model outputs, and (iii) an instruction prompt for the reasoning task. Using SLR, we create SLR-Bench, a benchmark comprising over 19k prompts spanning 20 curriculum levels that progressively increase in relational, arithmetic, and recursive complexity. Large-scale evaluation reveals that contemporary LLMs readily produce syntactically valid rules, yet often fail at correct logical inference. Recent reasoning LLMs do somewhat better, but incur substantial increases in test-time compute, sometimes exceeding 15k completion tokens. Finally, logic-tuning via SLR doubles Llama-3-8B accuracy on SLR-Bench, achieving parity with Gemini-Flash-Thinking at a fraction of computational cost. SLR is fully automated, requires no human annotation, ensures dataset novelty, and offers a scalable environment for probing and advancing LLMs' reasoning capabilities.

For vision-language models (VLMs), understanding the dynamic properties of objects and their interactions in 3D scenes from videos is crucial for effective reasoning about high-level temporal and action semantics. Although humans are adept at understanding these properties by constructing 3D and temporal (4D) representations of the world, current video understanding models struggle to extract these dynamic semantics, arguably because these models use cross-frame reasoning without underlying knowledge of the 3D/4D scenes. In this work, we introduce DynSuperCLEVR, the first video question answering dataset that focuses on language understanding of the dynamic properties of 3D objects. We concentrate on three physical concepts -- velocity, acceleration, and collisions within 4D scenes. We further generate three types of questions, including factual queries, future predictions, and counterfactual reasoning that involve different aspects of reasoning about these 4D dynamic properties. To further demonstrate the importance of explicit scene representations in answering these 4D dynamics questions, we propose NS-4DPhysics, a Neural-Symbolic VideoQA model integrating Physics prior for 4D dynamic properties with explicit scene representation of videos. Instead of answering the questions directly from the video text input, our method first estimates the 4D world states with a 3D generative model powered by physical priors, and then uses neural symbolic reasoning to answer the questions based on the 4D world states. Our evaluation on all three types of questions in DynSuperCLEVR shows that previous video question answering models and large multimodal models struggle with questions about 4D dynamics, while our NS-4DPhysics significantly outperforms previous state-of-the-art models. Our code and data are released in https://xingruiwang.github.io/projects/DynSuperCLEVR/.

We present BYOKG, a universal question-answering (QA) system that can operate on any knowledge graph (KG), requires no human-annotated training data, and can be ready to use within a day -- attributes that are out-of-scope for current KGQA systems. BYOKG draws inspiration from the remarkable ability of humans to comprehend information present in an unseen KG through exploration -- starting at random nodes, inspecting the labels of adjacent nodes and edges, and combining them with their prior world knowledge. In BYOKG, exploration leverages an LLM-backed symbolic agent that generates a diverse set of query-program exemplars, which are then used to ground a retrieval-augmented reasoning procedure to predict programs for arbitrary questions. BYOKG is effective over both small- and large-scale graphs, showing dramatic gains in QA accuracy over a zero-shot baseline of 27.89 and 58.02 F1 on GrailQA and MetaQA, respectively. On GrailQA, we further show that our unsupervised BYOKG outperforms a supervised in-context learning method, demonstrating the effectiveness of exploration. Lastly, we find that performance of BYOKG reliably improves with continued exploration as well as improvements in the base LLM, notably outperforming a state-of-the-art fine-tuned model by 7.08 F1 on a sub-sampled zero-shot split of GrailQA.

We present JASCO, a temporally controlled text-to-music generation model utilizing both symbolic and audio-based conditions. JASCO can generate high-quality music samples conditioned on global text descriptions along with fine-grained local controls. JASCO is based on the Flow Matching modeling paradigm together with a novel conditioning method. This allows music generation controlled both locally (e.g., chords) and globally (text description). Specifically, we apply information bottleneck layers in conjunction with temporal blurring to extract relevant information with respect to specific controls. This allows the incorporation of both symbolic and audio-based conditions in the same text-to-music model. We experiment with various symbolic control signals (e.g., chords, melody), as well as with audio representations (e.g., separated drum tracks, full-mix). We evaluate JASCO considering both generation quality and condition adherence, using both objective metrics and human studies. Results suggest that JASCO is comparable to the evaluated baselines considering generation quality while allowing significantly better and more versatile controls over the generated music. Samples are available on our demo page https://pages.cs.huji.ac.il/adiyoss-lab/JASCO.

Fine-tuning language models on tasks with instructions has demonstrated potential in facilitating zero-shot generalization to unseen tasks. In this paper, we introduce a straightforward yet effective method for enhancing instruction tuning by employing symbolic tasks. Compared to crowdsourced human tasks or model-generated tasks, symbolic tasks present a unique advantage as they can be easily generated in vast quantities, theoretically providing an infinite supply of high-quality training instances. To explore the potential of symbolic tasks, we carry out an extensive case study on the representative symbolic task of SQL execution. Empirical results on various benchmarks validate that the integration of SQL execution leads to significant improvements in zero-shot scenarios, particularly in table reasoning. Notably, our 3B model surpasses both the 175B GPT-3 and ChatGPT in zero-shot table reasoning across four benchmarks. Furthermore, experimental results on BBH (27 tasks) and MMLU (57 tasks) reveal that language models can be enhanced through symbolic tasks without compromising their generality. We hope that our paper serves as a catalyst, inspiring increased efforts to incorporate symbolic tasks in instruction tuning.