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

We show that sharply defined topological quantum phase transitions are not limited to states of matter with gapped electronic spectra. Such transitions may also occur between two gapless metallic states both with extended Fermi surfaces.…

One dimensional topological insulators are characterized by edge states with exponentially small energies. According to one generalization of topological phases to non-Hermitian systems, a finite system in a non-trivial topological phase…

Despite excellent performance on many tasks, NLP systems are easily fooled by small adversarial perturbations of inputs. Existing procedures to defend against such perturbations are either (i) heuristic in nature and susceptible to stronger…

We investigate mathematical structures that provide natural semantics for families of (quantified) non-classical logics featuring special unary connectives, known as recovery operators, that allow us to 'recover' the properties of classical…

Robust edge states and non-Abelian excitations are the trademark of topological states of matter, with promising applications such as "topologically protected" quantum memory and computing. While so far topological phases have been…

Large language models often produce unsupported claims. We frame this as a misclassification error at the output boundary, where internally generated completions are emitted as if they were grounded in evidence. This motivates a composite…

In current Large Language Models we can trust the production of smoothly flowing prose on the basis of the principles of machine learning. However, there is no comparably principled basis to justify trust in the content of the text…

Quantum spin Hall insulators, which possess a non-trivial $\mathbb{Z}_2$ topological phase, have attracted great attention for two decades. It is generally believed that when an even number of layers of the quantum spin Hall insulators are…

Prediction and discovery of new materials with desired properties are at the forefront of quantum science and technology research. A major bottleneck in this field is the computational resources and time complexity related to finding new…

Benchmarks measure whether a model is correct. They do not measure whether a model is reliable. This distinction is largely academic for single-shot inference, but becomes critical for agentic AI systems, where a single rephrased prompt can…

We document an empirical phenomenon in chain-of-thought and ReAct agents driven by ten large language models from seven architecture families: meaning-bearing perturbations (e.g., paraphrase, synonym) alter final answers more often than…

The non-Abelian geometric phase possesses the capability of enabling robust and fault-resilient unitary transformations, making it a cornerstone of holonomic quantum computation. This "all-geometric" approach has successfully advanced the…

Continuous latent-space reasoning offers a compact alternative to textual chain-of-thought for multimodal models, enabling high-dimensional visual evidence to be integrated without explicit reasoning tokens. However, we identify a…

Semantic segmentation networks (SSNs) are central to safety-critical applications such as medical imaging and autonomous driving, where robustness under uncertainty is essential. However, existing probabilistic verification methods often…

Holonomic gates for quantum computation are commonly considered to be robust against certain kinds of parametric noise, the very motivation of this robustness being the geometric character of the transformation achieved in the adiabatic…

Large Language Models (LLMs) show remarkable capabilities, yet their stochastic next-token prediction creates logical inconsistencies and reward hacking that formal symbolic systems avoid. To bridge this gap, we introduce a formal logic…

We study topological stability of nodes in nonsymmorphic superconductors (SCs). In particular, we demonstrate that line nodes in nonsymmirphic odd-parity SCs are protected by the interplay between topology and nonsymmorphic symmetry. As an…

The ``holography of information'' (HoI) principle argues that gravity can encode information redundantly in asymptotic observables. Although HoI is ultimately a nonperturbative claim, its standard motivation uses semiclassical gravitational…

Given a graded $E_1$-module over an $E_2$-algebra in spaces, we construct an augmented semi-simplicial space up to higher coherent homotopy over it, called its canonical resolution, whose graded connectivity yields homological stability for…

While quasi-two-dimensional (layered) materials can be highly anisotropic, their asymptotic long-distance behavior generally reflects the properties of a fully three dimensional phase of matter. However, certain topologically ordered…