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Daniel O'Malley

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2 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

Benchmarking Large Language Models with Integer Sequence Generation Tasks

Daniel O'Malley
Manish Bhattarai
Nishath Ranasinghe
Erick Draayer
Javier E. Santos

We present a novel benchmark designed to rigorously evaluate the capabilities of large language models (LLMs) in mathematical reasoning and algorithmic code synthesis tasks. The benchmark comprises integer sequence generation tasks sourced from the Online Encyclopedia of Integer Sequences (OEIS), testing LLMs' abilities to accurately and efficiently generate Python code to compute these sequences without using lookup tables. Our comprehensive evaluation includes leading models from OpenAI (including the specialized reasoning-focused o-series), Anthropic, Meta, and Google across a carefully selected set of 1000 OEIS sequences categorized as easy'' or hard. '' Half of these sequences are classical sequences from the early days of OEIS and half were recently added to avoid contamination with the models' training data. To prevent models from exploiting memorized sequence values, we introduce an automated cheating detection mechanism that flags usage of lookup tables, validated by comparison with human expert evaluations. Experimental results demonstrate that reasoning-specialized models (o3, o3-mini, o4-mini from OpenAI, and Gemini 2. 5-pro from Google) achieve substantial improvements in accuracy over non-reasoning models, especially on more complex tasks. However, overall model performance on the hard sequences is poor, highlighting persistent challenges in algorithmic reasoning. Our benchmark provides important insights into the strengths and limitations of state-of-the-art LLMs, particularly emphasizing the necessity for further advancements to reliably solve complex mathematical reasoning tasks algorithmically.

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ICLR Conference 2025 Conference Paper

Model-Agnostic Knowledge Guided Correction for Improved Neural Surrogate Rollout

Bharat Srikishan
Daniel O'Malley
Mohamed Mehana
Nicholas Lubbers
Nikhil Muralidhar

Modeling the evolution of physical systems is critical to many applications in science and engineering. As the evolution of these systems is governed by partial differential equations (PDEs), there are a number of computational simulations which resolve these systems with high accuracy. However, as these simulations incur high computational costs, they are infeasible to be employed for large-scale analysis. A popular alternative to simulators are neural network surrogates which are trained in a data-driven manner and are much more computationally efficient. However, these surrogate models suffer from high rollout error when used autoregressively, especially when confronted with training data paucity. Existing work proposes to improve surrogate rollout error by either including physical loss terms directly in the optimization of the model or incorporating computational simulators as `differentiable layers' in the neural network. Both of these approaches have their challenges, with physical loss functions suffering from slow convergence for stiff PDEs and simulator layers requiring gradients which are not always available, especially in legacy simulators. We propose the Hybrid PDE Predictor with Reinforcement Learning (HyPER) model: a model-agnostic, RL based, cost-aware model which combines a neural surrogate, RL decision model, and a physics simulator (with or without gradients) to reduce surrogate rollout error significantly. In addition to reducing in-distribution rollout error by **47%-78%**, HyPER learns an intelligent policy that is adaptable to changing physical conditions and resistant to noise corruption. Code available at https://github.com/scailab/HyPER.

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