arXiv subjects

Jonathan Fan

Publications and source records attributed to Jonathan Fan.

5 recordsLinked to original sources

arXiv2026

Language models fail at extended rule following

Large language models are highly capable of answering difficult questions by retrieving, recombining, and attending to information in long contexts. For agentic tasks, an additional capability is required: the preservation of an exact state while repeatedly applying rules. We find that this reliability is absent across language models. To demonstrate, we query 126 leading model variants with the task of counting a long string of repeated characters, and we find they all cannot accurately count above a model-dependent, syntax-sensitive counting capacity threshold. Failures are abrupt and persist even with increasing model size, inference time computation, and external tool. Mechanistic probing indicates that models use a finite number of internal states to mimic counting as a rule and fail once these states are exhausted. Furthermore, such states are the basis for performing complex tasks beyond counting. These results indicate that fundamentally new model architectures are required for autonomous agents to achieve truly reliable rule following capabilities.

cs.CL↗

arXiv2026

Characterizing and Optimizing the Spatial Kernel of Multi Resolution Hash Encodings

Multi-Resolution Hash Encoding (MHE), the foundational technique behind Instant Neural Graphics Primitives, provides a powerful parameterization for neural fields. However, its spatial behavior lacks rigorous understanding from a physical systems perspective, leading to reliance on heuristics for hyperparameter selection. This work introduces a novel analytical approach that characterizes MHE by examining its Point Spread Function (PSF), which is analogous to the Green's function of the system. This methodology enables a quantification of the encoding's spatial resolution and fidelity. We derive a closed-form approximation for the collision-free PSF, uncovering inherent grid-induced anisotropy and a logarithmic spatial profile. We establish that the idealized spatial bandwidth, specifically the Full Width at Half Maximum (FWHM), is determined by the average resolution, $N_{\text{avg}}$. This leads to a counterintuitive finding: the effective resolution of the model is governed by the broadened empirical FWHM (and therefore $N_{\text{avg}}$), rather than the finest resolution $N_{\max}$, a broadening effect we demonstrate arises from optimization dynamics. Furthermore, we analyze the impact of finite hash capacity, demonstrating how collisions introduce speckle noise and degrade the Signal-to-Noise Ratio (SNR). Leveraging these theoretical insights, we propose Rotated MHE (R-MHE), an architecture that applies distinct rotations to the input coordinates at each resolution level. R-MHE mitigates anisotropy while maintaining the efficiency and parameter count of the original MHE. This study establishes a methodology based on physical principles that moves beyond heuristics to characterize and optimize MHE.

cs.CV↗

arXiv2025

Hydrogel-to-Aerogel Transitions in Polymer-Particle Hydrogels Expand the Wildfire Defense Window

The 2025 Los Angeles wildfires caused widespread urban destruction and displacement, and severe economic losses, highlighting the urgent need for better fire retardants. Current fire suppression strategies rely heavily on water, chemical fire retardants, and water-enhancing gels, which use superabsorbent polymers to retain water and adhere to substrates, offering extended fire protection compared to water alone. However, their effectiveness is limited by evaporation and degradation under extreme heat and wind conditions. This study investigates the thermal properties, evaporation dynamics, and fire retardancy mechanisms of a novel polymer-particle (PP) hydrogel with aerogel-forming capabilities. The boiling-induced water vapor expansion and bubble nucleation drive the transformation of the hydrogel into a highly porous, foam-like fire-retardant coating upon rapid heat desiccation, enhancing thermal insulation. By evaluating the retardancy window across different evaporation stages under high heat and wind conditions, this study aims to determine the duration, effectiveness, and governing physical mechanisms of this unique retardant system. These findings provide a framework for designing the next generation of fire retardants with optimized thermal stability and extended protection for wildfire mitigation.

cond-mat.mtrl-sci↗

arXiv2022

FOLIO: Natural Language Reasoning with First-Order Logic

Large language models (LLMs) have achieved remarkable performance on a variety of natural language understanding tasks. However, existing benchmarks are inadequate in measuring the complex logical reasoning capabilities of a model. We present FOLIO, a human-annotated, logically complex and diverse dataset for reasoning in natural language (NL), equipped with first-order logic (FOL) annotations. FOLIO consists of 1,430 examples (unique conclusions), each paired with one of 487 sets of premises used to deductively reason for the validity of each conclusion. The logical correctness of the premises and conclusions is ensured by their FOL annotations, which are automatically verified by an FOL inference engine. In addition to the main NL reasoning task, NL-FOL pairs in FOLIO constitute a new NL-FOL translation dataset. Our experiments on FOLIO systematically evaluate the FOL reasoning ability of supervised fine-tuning on medium-sized language models. For both NL reasoning and NL-FOL translation, we benchmark multiple state-of-the-art language models. Our results show that a subset of FOLIO presents a challenge for one of the most capable {Large Language Model (LLM)} publicly available, GPT-4.

cs.CL↗

arXiv2020

Design space reparameterization enforces hard geometric constraints in inverse-designed nanophotonic devices

Inverse design algorithms are the basis for realizing high-performance, freeform nanophotonic devices. Current methods to enforce geometric constraints, such as practical fabrication constraints, are heuristic and not robust. In this work, we show that hard geometric constraints can be imposed on inverse-designed devices by reparameterizing the design space itself. Instead of evaluating and modifying devices in the physical device space, candidate device layouts are defined in a constraint-free latent space and mathematically transformed to the physical device space, which robustly imposes geometric constraints. Modifications to the physical devices, specified by inverse design algorithms, are made to their latent space representations using backpropagation. As a proof-of-concept demonstration, we apply reparameterization to enforce strict minimum feature size constraints in local and global topology optimizers for metagratings. We anticipate that concepts in reparameterization will provide a general and meaningful platform to incorporate physics and physical constraints in any gradient-based optimizer, including machine learning-enabled global optimizers.

physics.app-ph↗