Related papers: Robust Reasoning as a Symmetry-Protected Topologic…

Reasoning in large language models is predominantly evaluated through labeled benchmarks, conflating task performance with the quality of internal inference. Here we study reasoning as an intrinsic dynamical process by examining the…

Large Language Models (LLMs) are increasingly described as possessing strong reasoning capabilities, supported by high performance on mathematical, logical, and planning benchmarks. However, most existing evaluations rely on aggregate…

Topological insulators, which allow edge or interface waves but forbid bulk waves, have revolutionized our scientific cognition of acoustic/elastic systems. Due to their nontrivial topological characteristics, edge (interface)waves are…

Despite their impressive performance, contemporary neural networks often lack structural safeguards that promote stable learning and interpretable behavior. In this work, we introduce a reformulation of layer-level transformations that…

Mathematical reasoning models are widely deployed in education, automated tutoring, and decision support systems despite exhibiting fundamental computational instabilities. We demonstrate that state-of-the-art models (Qwen2.5-Math-7B)…

Transformers have been shown to be able to perform deductive reasoning on a logical rulebase containing rules and statements written in English natural language. While the progress is promising, it is currently unclear if these models…

This paper proposes a novel approach to analyzing multi-hop reasoning in language models through Hamiltonian mechanics. We map reasoning chains in embedding spaces to Hamiltonian systems, defining a function that balances reasoning…

We discover that large language models exhibit \emph{spectral phase transitions} in their hidden activation spaces when engaging in reasoning versus factual recall. Through systematic spectral analysis across \textbf{11 models} spanning…

Multimodal Large Language Models struggle to maintain reliable performance under extreme real-world visual degradations, which impede their practical robustness. Existing robust MLLMs predominantly rely on implicit training/adaptation that…

Two global symmetries are holo-equivalent if their algebras of local symmetric operators are isomorphic. Holo-equivalent classes of global symmetries are classified by gappable-boundary topological orders (TO) in one higher dimension…

As large language models (LLMs) become integrated into everyday and high-stakes decision-making, they inherit the ambiguity and biases of human language. While they produce fluent and coherent outputs, they rely on statistical pattern…

Transformer architectures have achieved great success in solving natural language tasks, which learn strong language representations from large-scale unlabeled texts. In this paper, we seek to go further beyond and explore a new logical…

Prompt injection attacks pose significant risks to language model safety, yet existing defenses are typically evaluated using classification performance. We show that high detection performance does not imply representational robustness.…

One of the hallmarks of bulk topology is the existence of robust boundary localized states. For instance, a conventional $d$ dimensional topological system hosts $d{-}1$ dimensional surface modes, which are protected by non-spatial…

We study the stability of topological crystalline superconductors in the symmetry class DIIIR and in two-dimensional space when perturbed by quartic contact interactions. It is known that no less than eight copies of helical pairs of…

Standard Transformers have a fixed computational depth, fundamentally limiting their ability to generalize to tasks requiring variable-depth reasoning, such as multi-hop graph traversal or nested logic. We propose a depth-recurrent…

Reasoning failures in large language models (LLMs) are typically measured only at the end of a generation, yet many failures manifest as a process-level breakdown: the model "loses the thread" mid-reasoning. We study whether such breakdowns…

The topological classification of gapped band structures depends on the particular definition of topological equivalence. For translation-invariant systems, stable equivalence is defined by a lack of restrictions on the numbers of occupied…

Maintaining the safety of large language models (LLMs) is crucial as they are increasingly deployed in real-world applications. Existing safety guardrails typically rely on single-pass classification or, more recently, distilled reasoning.…

We study the non-adiabatic dynamics of a typical symmetry-protected topological phase-the Haldane insulator phase with broken bond-centered inversion. By continuously breaking the middle chain, we find the gap closes at a critical point in…