TraversalBench: Challenging Paths to Follow for Vision Language Models

Vision-language models (VLMs) perform strongly on many multimodal benchmarks. However, the ability to follow complex visual paths -- a task that human observers typically find straightforward -- remains under-tested. We introduce TraversalBench, a controlled benchmark for exact visual path traversal. Each instance contains a single continuous polyline, a unique start marker, and markers placed at path vertices; the task is to recover the exact ordered sequence encountered when traversing the path from start to finish. The benchmark explicitly balances key path-structural factors including self-intersection count, tortuosity, vertex count, and nearby confounding lines, while minimizing reliance on OCR, world knowledge, and open-ended planning. We find that self-intersections are the dominant source of difficulty. A first-crossing analysis shows that errors are sharply localized: performance is relatively stable immediately before the first crossing, then drops steeply when the model must resolve the correct continuation. By contrast, nearby confounding lines produce a weaker persistent degradation that compounds with repeated exposure. These analyses make TraversalBench a useful diagnostic for identifying whether models suffer from human-like failures or other breakdowns in sustained visual processing. An auxiliary reading-order benchmark further reveals a consistent preference for layouts compatible with left-to-right serialization, while not explaining away the main effects of path complexity. Together, these results position TraversalBench as a controlled diagnostic of path-faithful visual reasoning and as a useful testbed for studying multimodal spatial reasoning under ambiguity, clutter, and distractor structure. More broadly, we position TraversalBench as a contribution to the still-limited area of sustained visual grounding benchmarks for VLMs.

A Framework for Closed-Loop Robotic Assembly, Alignment and Self-Recovery of Precision Optical Systems

Robotic automation has transformed scientific workflows in domains such as chemistry and materials science, yet free-space optics, which is a high precision domain, remains largely manual. Optical systems impose strict spatial and angular tolerances, and their performance is governed by tightly coupled physical parameters, making generalizable automation particularly challenging. In this work, we present a robotics framework for the autonomous construction, alignment, and maintenance of precision optical systems. Our approach integrates hierarchical computer vision systems, optimization routines, and custom-built tools to achieve this functionality. As a representative demonstration, we perform the fully autonomous construction of a tabletop laser cavity from randomly distributed components. The system performs several tasks such as laser beam centering, spatial alignment of multiple beams, resonator alignment, laser mode selection, and self-recovery from induced misalignment and disturbances. By achieving closed-loop autonomy for highly sensitive optical systems, this work establishes a foundation for autonomous optical experiments for applications across technical domains.

Unsupervised Decomposition and Recombination with Discriminator-Driven Diffusion Models

Decomposing complex data into factorized representations can reveal reusable components and enable synthesizing new samples via component recombination. We investigate this in the context of diffusion-based models that learn factorized latent spaces without factor-level supervision. In images, factors can capture background, illumination, and object attributes; in robotic videos, they can capture reusable motion components. To improve both latent factor discovery and quality of compositional generation, we introduce an adversarial training signal via a discriminator trained to distinguish between single-source samples and those generated by recombining factors across sources. By optimizing the generator to fool this discriminator, we encourage physical and semantic consistency in the resulting recombinations. Our method outperforms implementations of prior baselines on CelebA-HQ, Virtual KITTI, CLEVR, and Falcor3D, achieving lower FID scores and better disentanglement as measured by MIG and MCC. Furthermore, we demonstrate a novel application to robotic video trajectories: by recombining learned action components, we generate diverse sequences that significantly increase state-space coverage for exploration on the LIBERO benchmark.

Active learning for photonics

Active learning for photonic crystals explores the integration of analytic approximate Bayesian last layer neural networks (LL-BNNs) with uncertainty-driven sample selection to accelerate photonic band gap prediction. We employ an analytic LL-BNN formulation, corresponding to the infinite Monte Carlo sample limit, to obtain uncertainty estimates that are strongly correlated with the true predictive error on unlabeled candidate structures. These uncertainty scores drive an active learning strategy that prioritizes the most informative simulations during training. Applied to the task of predicting band gap sizes in two-dimensional, two-tone photonic crystals, our approach achieves up to a 2.6x reduction in required training data compared to a random sampling baseline while maintaining predictive accuracy. The efficiency gains arise from concentrating computational resources on high uncertainty regions of the design space rather than sampling uniformly. Given the substantial cost of full band structure simulations, especially in three dimensions, this data efficiency enables rapid and scalable surrogate modeling. Our results suggest that analytic LL-BNN based active learning can substantially accelerate topological optimization and inverse design workflows for photonic crystals, and more broadly, offers a general framework for data efficient regression across scientific machine learning domains.

Learning simple heuristic rules for classifying materials based on chemical composition

In the past decade, there has been a significant interest in the use of machine learning approaches in materials science research. Conventional deep learning approaches that rely on complex, nonlinear models have become increasingly important in computational materials science due to their high predictive accuracy. In contrast to these approaches, we have shown in a recent work that a remarkably simple learned heuristic rule -- based on the concept of topogivity -- can classify whether a material is topological using only its chemical composition. In this paper, we go beyond the topology classification scenario by also studying the use of machine learning to develop simple heuristic rules for classifying whether a material is a metal based on chemical composition. Moreover, we present a framework for incorporating chemistry-informed inductive bias based on the structure of the periodic table. For both the topology classification and the metallicity classification tasks, we empirically characterize the performance of simple heuristic rules fit with and without chemistry-informed inductive bias across a wide range of training set sizes. We find evidence that incorporating chemistry-informed inductive bias can reduce the amount of training data required to reach a given level of test accuracy.

L$^2$M: Mutual Information Scaling Law for Long-Context Language Modeling

We rigorously establish a bipartite mutual information scaling law in natural language that governs long-range dependencies. This scaling law, which we show is distinct from and scales independently of the conventional two-point mutual information, is the key to understanding long-context language modeling. Using this scaling law, we formulate the Long-context Language Modeling (L$^2$M) condition, which relates a model's capacity for effective long context length modeling to the scaling of its latent state size for storing past information. Our results are validated through experiments on both transformers and state space models. This work establishes a theoretical foundation that guides the development of large language models toward longer context lengths.

Predicting band gap from chemical composition: A simple learned model for a material property with atypical statistics

In solid-state materials science, substantial efforts have been devoted to the calculation and modeling of the electronic band gap. While a wide range of ab initio methods and machine learning algorithms have been created that can predict this quantity, the development of new computational approaches for studying the band gap remains an active area of research. Here we introduce a simple machine learning model for predicting the band gap using only the chemical composition of the crystalline material. To motivate the form of the model, we first analyze the empirical distribution of the band gap, which sheds new light on its atypical statistics. Specifically, our analysis enables us to frame band gap prediction as a task of modeling a mixed random variable, and we design our model accordingly. Our model formulation incorporates thematic ideas from chemical heuristic models for other material properties in a manner that is suited towards the band gap modeling task. The model has exactly one parameter corresponding to each element, which is fit using data. To predict the band gap for a given material, the model computes a weighted average of the parameters associated with its constituent elements and then takes the maximum of this quantity and zero. The model provides heuristic chemical interpretability by intuitively capturing the associations between the band gap and individual chemical elements.

OccamLLM: Fast and Exact Language Model Arithmetic in a Single Step

Despite significant advancements in text generation and reasoning, Large Language Models (LLMs) still face challenges in accurately performing complex arithmetic operations. To achieve accurate calculations, language model systems often enable LLMs to generate code for arithmetic operations. However, this approach compromises speed and security and, if finetuning is involved, risks the language model losing prior capabilities. We propose a framework that enables exact arithmetic in \textit{a single autoregressive step}, providing faster, more secure, and more interpretable LLM systems with arithmetic capabilities. We use the hidden states of an LLM to control a symbolic architecture which performs arithmetic. Our implementation using Llama 3 8B Instruct with OccamNet as a symbolic model (OccamLlama) achieves 100\% accuracy on single arithmetic operations ($+,-,\times,\div,\sin{},\cos{},\log{},\exp{},\sqrt{}$), outperforming GPT 4o and on par with GPT 4o using a code interpreter. OccamLlama also outperforms both Llama 3 8B Instruct and GPT 3.5 Turbo on multistep reasoning problems involving challenging arithmetic, thus enabling small LLMs to match the arithmetic performance of even much larger models. We will make our code public shortly.

QuanTA: Efficient High-Rank Fine-Tuning of LLMs with Quantum-Informed Tensor Adaptation

We propose Quantum-informed Tensor Adaptation (QuanTA), a novel, easy-to-implement, fine-tuning method with no inference overhead for large-scale pre-trained language models. By leveraging quantum-inspired methods derived from quantum circuit structures, QuanTA enables efficient high-rank fine-tuning, surpassing the limitations of Low-Rank Adaptation (LoRA)--low-rank approximation may fail for complicated downstream tasks. Our approach is theoretically supported by the universality theorem and the rank representation theorem to achieve efficient high-rank adaptations. Experiments demonstrate that QuanTA significantly enhances commonsense reasoning, arithmetic reasoning, and scalability compared to traditional methods. Furthermore, QuanTA shows superior performance with fewer trainable parameters compared to other approaches and can be designed to integrate with existing fine-tuning algorithms for further improvement, providing a scalable and efficient solution for fine-tuning large language models and advancing state-of-the-art in natural language processing.

KAN: Kolmogorov-Arnold Networks

Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have learnable activation functions on edges ("weights"). KANs have no linear weights at all -- every weight parameter is replaced by a univariate function parametrized as a spline. We show that this seemingly simple change makes KANs outperform MLPs in terms of accuracy and interpretability. For accuracy, much smaller KANs can achieve comparable or better accuracy than much larger MLPs in data fitting and PDE solving. Theoretically and empirically, KANs possess faster neural scaling laws than MLPs. For interpretability, KANs can be intuitively visualized and can easily interact with human users. Through two examples in mathematics and physics, KANs are shown to be useful collaborators helping scientists (re)discover mathematical and physical laws. In summary, KANs are promising alternatives for MLPs, opening opportunities for further improving today's deep learning models which rely heavily on MLPs.