Related papers: Simulating Logspace-Recursion with Logarithmic Qua…

We obtain an equivariant index theorem, or Lefschetz fixed-point formula, for isometries from complete Riemannian manifolds to themselves. The fixed-point set of such an isometry may be noncompact. We build on techniques developed by Roe.…

Ensemble learning remains a cornerstone of machine learning, with stacking used to integrate predictions from multiple base learners through a meta-model. However, deep stacking remains uncommon due to feature redundancy, complexity, and…

We study a class of generalized linear programs (GLP) in a large-scale setting, which includes simple, possibly nonsmooth convex regularizer and simple convex set constraints. By reformulating (GLP) as an equivalent convex-concave min-max…

A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive…

We introduce the notion of an E_k-ring with prelogarithmic structure, define logarithmic topological Hochschild homology and logarithmic topological cyclic homology in this context, and establish localization sequences for these theories.…

Deficiency in expressive power of the first-order logic has led to developing its numerous extensions by fixed point operators, such as Least Fixed-Point (LFP), inflationary fixed-point (IFP), partial fixed-point (PFP), etc. These logics…

While humans naturally learn and adapt from past experiences, large language models (LLMs) and their agentic counterparts struggle to retain reasoning from previous tasks and apply them in future contexts. To address this limitation, we…

We introduce Transductive Local Complexity (TLC) to extend the classical Local Rademacher Complexity (LRC) to the transductive setting, incorporating substantial and novel components. Although LRC has been used to obtain sharp…

In the lattice approach to Loop Quantum Gravity on a fixed graph computations tend to be involved and are rarely analytically manageable. But, when interested in the expectation values of coherent states on the lattice which are sharply…

Large Language Models (LLMs) equipped with external tools have demonstrated enhanced performance on complex reasoning tasks. The widespread adoption of this tool-augmented reasoning is hindered by the scarcity of domain-specific tools. For…

We present a logic for the specification of static analysis problems that goes beyond the logics traditionally used. Its most prominent feature is the direct support for both inductive computations of behaviors as well as co-inductive…

Reliable quantum computation requires systematic identification and correction of errors that occur and accumulate in quantum hardware. To diagnose and correct such errors, standard quantum error-correcting protocols utilize…

We classify graphs and, more generally, finite relational structures that are identified by C2, that is, two-variable first-order logic with counting. Using this classification, we show that it can be decided in almost linear time whether a…

Effective log anomaly detection is critical to sustaining reliability in large-scale IT infrastructures. Transformer-based models require substantial resources and labeled data, exacerbating the cold-start problem in target domains where…

We prove that every triconnected planar graph is definable by a first order sentence that uses at most 15 variables and has quantifier depth at most $11\log_2 n+43$. As a consequence, a canonic form of such graphs is computable in $AC^1$ by…

In this paper, we aim to learn a low-dimensional Euclidean representation from a set of constraints of the form "item j is closer to item i than item k". Existing approaches for this "ordinal embedding" problem require expensive…

Large Reasoning Models (LRMs) demonstrate remarkable problem-solving capabilities through extended Chain-of-Thought (CoT) reasoning but often produce excessively verbose and redundant reasoning traces. This inefficiency incurs high…

Chain-of-Thought (CoT) has substantially empowered Large Language Models (LLMs) to tackle complex reasoning tasks, yet the verbose nature of explicit reasoning steps incurs prohibitive inference latency and computational costs, limiting…

We present Generative Logic (GL), a deterministic architecture that starts from user-supplied axiomatic definitions written in a minimalist Mathematical Programming Language (MPL) and systematically explores a configurable region of their…

Large language models (LLMs) have exhibited remarkable few-shot learning capabilities and unified the paradigm of NLP tasks through the in-context learning (ICL) technique. Despite the success of ICL, the quality of the exemplar…