Inference-Time Computations for LLM Reasoning and Planning: A Benchmark and Insights

We examine the reasoning and planning capabilities of large language models (LLMs) in solving complex tasks. Recent advances in inference-time techniques demonstrate the potential to enhance LLM reasoning without additional training by exploring intermediate steps during inference. Notably, OpenAI's o1 model shows promising performance through its novel use of multi-step reasoning and verification. Here, we explore how scaling inference-time techniques can improve reasoning and planning, focusing on understanding the tradeoff between computational cost and performance. To this end, we construct a comprehensive benchmark, known as Sys2Bench, and perform extensive experiments evaluating existing inference-time techniques on eleven diverse tasks across five categories, including arithmetic reasoning, logical reasoning, common sense reasoning, algorithmic reasoning, and planning. Our findings indicate that simply scaling inference-time computation has limitations, as no single inference-time technique consistently performs well across all reasoning and planning tasks.

DiffMS: Diffusion Generation of Molecules Conditioned on Mass Spectra

Mass spectrometry plays a fundamental role in elucidating the structures of unknown molecules and subsequent scientific discoveries. One formulation of the structure elucidation task is the conditional $\textit{de novo}$ generation of molecular structure given a mass spectrum. Toward a more accurate and efficient scientific discovery pipeline for small molecules, we present DiffMS, a formula-restricted encoder-decoder generative network that achieves state-of-the-art performance on this task. The encoder utilizes a transformer architecture and models mass spectra domain knowledge such as peak formulae and neutral losses, and the decoder is a discrete graph diffusion model restricted by the heavy-atom composition of a known chemical formula. To develop a robust decoder that bridges latent embeddings and molecular structures, we pretrain the diffusion decoder with fingerprint-structure pairs, which are available in virtually infinite quantities, compared to structure-spectrum pairs that number in the tens of thousands. Extensive experiments on established benchmarks show that DiffMS outperforms existing models on $\textit{de novo}$ molecule generation. We provide several ablations to demonstrate the effectiveness of our diffusion and pretraining approaches and show consistent performance scaling with increasing pretraining dataset size. DiffMS code is publicly available at https://github.com/coleygroup/DiffMS.

Discovering Physics Laws of Dynamical Systems via Invariant Function Learning

We consider learning underlying laws of dynamical systems governed by ordinary differential equations (ODE). A key challenge is how to discover intrinsic dynamics across multiple environments while circumventing environment-specific mechanisms. Unlike prior work, we tackle more complex environments where changes extend beyond function coefficients to entirely different function forms. For example, we demonstrate the discovery of ideal pendulum's natural motion $\alpha^2 \sin{\theta_t}$ by observing pendulum dynamics in different environments, such as the damped environment $\alpha^2 \sin(\theta_t) - \rho \omega_t$ and powered environment $\alpha^2 \sin(\theta_t) + \rho \frac{\omega_t}{\left|\omega_t\right|}$. Here, we formulate this problem as an \emph{invariant function learning} task and propose a new method, known as \textbf{D}isentanglement of \textbf{I}nvariant \textbf{F}unctions (DIF), that is grounded in causal analysis. We propose a causal graph and design an encoder-decoder hypernetwork that explicitly disentangles invariant functions from environment-specific dynamics. The discovery of invariant functions is guaranteed by our information-based principle that enforces the independence between extracted invariant functions and environments. Quantitative comparisons with meta-learning and invariant learning baselines on three ODE systems demonstrate the effectiveness and efficiency of our method. Furthermore, symbolic regression explanation results highlight the ability of our framework to uncover intrinsic laws.

Reasoning with Graphs: Structuring Implicit Knowledge to Enhance LLMs Reasoning

Large language models (LLMs) have demonstrated remarkable success across a wide range of tasks; however, they still encounter challenges in reasoning tasks that require understanding and inferring relationships between distinct pieces of information within text sequences. This challenge is particularly pronounced in tasks involving multi-step processes, such as logical reasoning and multi-hop question answering, where understanding implicit relationships between entities and leveraging multi-hop connections in the given context are crucial. Graphs, as fundamental data structures, explicitly represent pairwise relationships between entities, thereby offering the potential to enhance LLMs' reasoning capabilities. External graphs have proven effective in supporting LLMs across multiple tasks. However, in many reasoning tasks, no pre-existing graph structure is provided. Can we structure implicit knowledge derived from context into graphs to assist LLMs in reasoning? In this paper, we propose Reasoning with Graphs (RwG) by first constructing explicit graphs from the context and then leveraging these graphs to enhance LLM reasoning performance on reasoning tasks. Extensive experiments demonstrate the effectiveness of the proposed method in improving both logical reasoning and multi-hop question answering tasks.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils

Computational modeling of aerodynamics is a key problem in aerospace engineering, often involving flows interacting with solid objects such as airfoils. Deep surrogate models have emerged as purely data-driven approaches that learn direct mappings from simulation conditions to solutions based on either simulation or experimental data. Here, we consider modeling of incompressible flows over solid objects, wherein geometric structures are a key factor in determining aerodynamics. To effectively incorporate geometries, we propose a message passing scheme that efficiently and expressively integrates the airfoil shape with the mesh representation. Under this framework, we first obtain a representation of the geometry in the form of a latent graph on the airfoil surface. We subsequently propagate this representation to all collocation points through message passing on a directed, bipartite graph. We demonstrate that this framework supports efficient training by downsampling the solution mesh while avoiding distribution shifts at test time when evaluated on the full mesh. To enable our model to be able to distinguish between distinct spatial regimes of dynamics relative to the airfoil, we represent mesh points in both a leading edge and trailing edge coordinate system. We further enhance the expressiveness of our coordinate system representations by embedding our hybrid Polar-Cartesian coordinates using sinusoidal and spherical harmonics bases. We additionally find that a change of basis to canonicalize input representations with respect to inlet velocity substantially improves generalization. Altogether, these design choices lead to a purely data-driven machine learning framework known as GeoMPNN, which won the Best Student Submission award at the NeurIPS 2024 ML4CFD Competition, placing 4th overall. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Political-LLM: Large Language Models in Political Science

In recent years, large language models (LLMs) have been widely adopted in political science tasks such as election prediction, sentiment analysis, policy impact assessment, and misinformation detection. Meanwhile, the need to systematically understand how LLMs can further revolutionize the field also becomes urgent. In this work, we--a multidisciplinary team of researchers spanning computer science and political science--present the first principled framework termed Political-LLM to advance the comprehensive understanding of integrating LLMs into computational political science. Specifically, we first introduce a fundamental taxonomy classifying the existing explorations into two perspectives: political science and computational methodologies. In particular, from the political science perspective, we highlight the role of LLMs in automating predictive and generative tasks, simulating behavior dynamics, and improving causal inference through tools like counterfactual generation; from a computational perspective, we introduce advancements in data preparation, fine-tuning, and evaluation methods for LLMs that are tailored to political contexts. We identify key challenges and future directions, emphasizing the development of domain-specific datasets, addressing issues of bias and fairness, incorporating human expertise, and redefining evaluation criteria to align with the unique requirements of computational political science. Political-LLM seeks to serve as a guidebook for researchers to foster an informed, ethical, and impactful use of Artificial Intelligence in political science. Our online resource is available at: http://political-llm.org/.

Equivariant Graph Network Approximations of High-Degree Polynomials for Force Field Prediction

Recent advancements in equivariant deep models have shown promise in accurately predicting atomic potentials and force fields in molecular dynamics simulations. Using spherical harmonics (SH) and tensor products (TP), these equivariant networks gain enhanced physical understanding, like symmetries and many-body interactions. Beyond encoding physical insights, SH and TP are also crucial to represent equivariant polynomial functions. In this work, we analyze the equivariant polynomial functions for the equivariant architecture, and introduce a novel equivariant network, named PACE. The proposed PACE utilizes edge booster and the Atomic Cluster Expansion (ACE) technique to approximate a greater number of $SE(3) \times S_n$ equivariant polynomial functions with enhanced degrees. As experimented in commonly used benchmarks, PACE demonstrates state-of-the-art performance in predicting atomic energy and force fields, with robust generalization capability across various geometric distributions under molecular dynamics (MD) across different temperature conditions. Our code is publicly available as part of the AIRS library https://github.com/divelab/AIRS/.

A Hierarchical Language Model For Interpretable Graph Reasoning

Large language models (LLMs) are being increasingly explored for graph tasks. Despite their remarkable success in text-based tasks, LLMs' capabilities in understanding explicit graph structures remain limited, particularly with large graphs. In this work, we introduce Hierarchical Language Model for Graph (HLM-G), which employs a two-block architecture to capture node-centric local information and interaction-centric global structure, effectively enhancing graph structure understanding abilities. The proposed scheme allows LLMs to address various graph queries with high efficacy, efficiency, and robustness, while reducing computational costs on large-scale graph tasks. Furthermore, we demonstrate the interpretability of our model using intrinsic attention weights and established explainers. Comprehensive evaluations across diverse graph reasoning and real-world tasks of node, link, and graph-levels highlight the superiority of our method, marking a significant advancement in the application of LLMs to graph understanding.

Geometry Informed Tokenization of Molecules for Language Model Generation

We consider molecule generation in 3D space using language models (LMs), which requires discrete tokenization of 3D molecular geometries. Although tokenization of molecular graphs exists, that for 3D geometries is largely unexplored. Here, we attempt to bridge this gap by proposing the Geo2Seq, which converts molecular geometries into $SE(3)$-invariant 1D discrete sequences. Geo2Seq consists of canonical labeling and invariant spherical representation steps, which together maintain geometric and atomic fidelity in a format conducive to LMs. Our experiments show that, when coupled with Geo2Seq, various LMs excel in molecular geometry generation, especially in controlled generation tasks.

Eliminating Position Bias of Language Models: A Mechanistic Approach

Position bias has proven to be a prevalent issue of modern language models (LMs), where the models prioritize content based on its position within the given context. This bias often leads to unexpected model failures and hurts performance, robustness, and reliability across various applications. Our mechanistic analysis attributes the position bias to two components employed in nearly all state-of-the-art LMs: causal attention and relative positional encodings. Specifically, we find that causal attention generally causes models to favor distant content, while relative positional encodings like RoPE prefer nearby ones based on the analysis of retrieval-augmented question answering (QA). Further, our empirical study on object detection reveals that position bias is also present in vision-language models (VLMs). Based on the above analyses, we propose to ELIMINATE position bias caused by different input segment orders (e.g., options in LM-as-a-judge, retrieved documents in QA) in a TRAINING-FREE ZERO-SHOT manner. Our method changes the causal attention to bidirectional attention between segments and utilizes model attention values to decide the relative orders of segments instead of using the order provided in input prompts, therefore enabling Position-INvariant inferencE (PINE) at the segment level. By eliminating position bias, models achieve better performance and reliability in downstream tasks where position bias widely exists, such as LM-as-a-judge and retrieval-augmented QA. Notably, PINE is especially useful when adapting LMs for evaluating reasoning pairs: it consistently provides 8 to 10 percentage points performance gains in most cases, and makes Llama-3-70B-Instruct perform even better than GPT-4-0125-preview on the RewardBench reasoning subset.