Related papers: Robust Reasoning as a Symmetry-Protected Topologic…
The concepts of topology have a profound impact on physics research spanning the fields of condensed matter, photonics and acoustics and predicting topological states that provide unprecedented versatility in routing and control of waves of…
Large language models represent the same reasoning in vastly different surface forms -- English prose, Python code, mathematical notation -- yet whether they share a common internal substrate across these symbolic systems remains unknown.…
Despite remarkable advances, large language models often fail at compositional reasoning tasks, a phenomenon exemplified by the ``curse of two-hop reasoning''. This paper introduces the Identity Bridge, a simple yet powerful mechanism that…
Large Language Models (LLMs) have achieved remarkable success in tasks requiring complex reasoning, such as code generation, mathematical problem solving, and algorithmic synthesis -- especially when aided by reasoning tokens and…
In this lecture for the Nobel symposium, we review previous research on a class of translational-invariant insulators without spin-orbit coupling. These may be realized in intrinsically spinless systems such as photonic crystals and…
LLMs often exhibit Aha moments such as self-correction after tokens like "Wait," yet the underlying mechanism remains unclear. Standard LLMs collapse mainly through silent divergence, where trajectories drift from the correct answer yet…
We elucidate the mechanism for instability of topological Thouless pumping in strongly interacting systems from a viewpoint of symmetry-protected topological phases. If the protecting symmetries of the underlying topological phases change…
We present an exactly solvable model for one-dimensional symmetry-protected topological phases with $\mathbb{Z}_N\times\mathbb{Z}_N$ symmetry. The model works by binding point topological defects (domain walls) of one symmetry to charges of…
We investigate the stability of the topological phase of the toric code model in the presence of a uniform magnetic field by means of variational and high-order series expansion approaches. We find that when this perturbation is strong…
Multi-agent language systems can exhibit a failure mode where a shared dominant context progressively absorbs individual semantics, yielding near-uniform behavior across agents. We study this effect under the name Asymptotic Semantic…
We study the robustness of conformal prediction, a powerful tool for uncertainty quantification, to label noise. Our analysis tackles both regression and classification problems, characterizing when and how it is possible to construct…
Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…
Complex problems, whether in math, logic, or planning, are solved by humans through a sequence of steps where the result of one step informs the next. In this work, we adopt the perspective that the reasoning power of Transformers is…
Transformer LMs show emergent reasoning that resists mechanistic understanding. We offer a statistical physics framework for continuous-time chain-of-thought reasoning dynamics. We model sentence-level hidden state trajectories as a…
Causal discovery through experimentation and intervention is fundamental to robust problem solving. It requires not just updating beliefs within a fixed framework but revising the hypothesis space itself, a capacity current AI agents lack…
This paper proposes the External Hippocampus framework, which models language model reasoning from a cognitive dynamics perspective as the flow of information energy in semantic space. Unlike traditional weight-space optimization methods,…
We use low-depth quantum circuits, a specific type of tensor networks, to classify two-dimensional symmetry-protected topological many-body localized phases. For (anti-)unitary on-site symmetries we show that the (generalized) third…
While large language models (LLMs) excel in mathematical and code reasoning, we observe they struggle with social reasoning tasks, exhibiting cognitive confusion, logical inconsistencies, and conflation between objective world states and…
The prevailing assumption of an exponential decay in large language model (LLM) reliability with sequence length, predicated on independent per-token error probabilities, posits an inherent limitation for long autoregressive outputs. Our…
Higher-order topological insulators are established as topological crystalline insulators protected by crystalline symmetries. One celebrated example is the second-order topological insulator in three dimensions that hosts chiral hinge…