Kevin Zhu

Ben Zelenskiy, Saibilila Abudukelimu, George Flint et al.

We introduce the Sumudu Neural Operator (SNO), a neural operator rooted in the properties of the Sumudu Transform. We leverage the relationship between the polynomial expansions of transform pairs to decompose the input space as coefficients, which are then transformed into the Sumudu Space, where the neural operator is parameterized. We evaluate the operator in ODEs (Duffing Oscillator, Lorenz System, and Driven Pendulum) and PDEs (Euler-Bernoulli Beam, Burger's Equation, Diffusion, Diffusion-Reaction, and Brusselator). SNO achieves superior performance to FNO on PDEs and demonstrates competitive accuracy with LNO on several PDE tasks, including the lowest error on the Euler-Bernoulli Beam and Diffusion Equation. Additionally, we apply zero-shot super-resolution to the PDE tasks to observe the model's capability of obtaining higher quality data from low-quality samples. These preliminary findings suggest promise for the Sumudu Transform as a neural operator design, particularly for certain classes of PDEs.

Anthony Cui, Pranav Nandyalam, Andrew Rufail et al.

Momentum-Aided Prompt Optimization (MAPO) enhances the efficiency and efficacy of prompt optimization for Large Language Models (LLMs). Building on ProTeGi, MAPO uses positive natural language "gradients" and a momentum-based extension to refine prompts effectively. By tracking gradient history, MAPO avoids local minima and oscillations. It also utilizes beam search and an Upper Confidence Bound (UCB) algorithm for balanced candidate expansion and selection. Benchmark testing shows that MAPO achieves faster convergence time with fewer API calls and higher F1 scores than ProTeGi, proving it as a robust and scalable solution for automated prompt engineering in LLMs.

Chris Su, Harrison Li, Matheus Marques et al.

Recent work reports that Large Reasoning Models (LRMs) undergo a collapse in performance on solving puzzles beyond certain perplexity thresholds. In subsequent discourse, questions have arisen as to whether the nature of the task muddles an evaluation of true reasoning. One potential confound is the requirement that the model keep track of the state space on its own. We provide a large language model (LLM) with an environment interface for Tower of Hanoi problems, allowing it to make a move with a tool call, provide written justification, observe the resulting state space, and reprompt itself for the next move. We observe that access to an environment interface does not delay or eradicate performance collapse. Furthermore, LLM-parameterized policy analysis reveals increasing divergence from both optimal policies and uniformly random policies, suggesting that the model exhibits mode-like collapse at each level of complexity, and that performance is dependent upon whether the mode reflects the correct solution for the problem. We suggest that a similar phenomena might take place in LRMs.