Related papers: A Qualitative Analysis of Kernel Extension for Hig…
In signal analysis and synthesis, linear approximation theory considers a linear decomposition of any given signal in a set of atoms, collected into a so-called dictionary. Relevant sparse representations are obtained by relaxing the…
In-context learning (ICL) has emerged as an effective solution for few-shot learning with large language models (LLMs). However, how LLMs leverage demonstrations to specify a task and learn a corresponding computational function through ICL…
In this paper we present new algorithms for training reduced-size nonlinear representations in the Kernel Dictionary Learning (KDL) problem. Standard KDL has the drawback of a large size of the kernel matrix when the data set is large.…
Accurately evaluating machine-translated text remains a long-standing challenge, particularly for long documents. Recent work has shown that large language models (LLMs) can serve as reliable and interpretable sentence-level translation…
Uncertainty quantification for LLMs is a key research direction towards addressing hallucination and other issues that limit their reliable deployment. In this work, we show that reasoning trace length is a simple and useful confidence…
Proof-theoretic semantics (P-tS) is the approach to meaning in logic based on 'proof' (as opposed to 'truth'). There are two major approaches to P-tS: proof-theoretic validity (P-tV) and base-extension semantics (B-eS). The former is a…
Large language models have achieved remarkable success on final-answer mathematical problems, largely due to the ease of applying reinforcement learning with verifiable rewards. However, the reasoning underlying these solutions is often…
We analytically study proximity and distance properties of various kernels and similarity measures on graphs. This helps to understand the mathematical nature of such measures and can potentially be useful for recommending the adoption of…
Neural kernels have drastically increased performance on diverse and nonstandard data modalities but require significantly more compute, which previously limited their application to smaller datasets. In this work, we address this by…
In recent work, we formalized the theory of optimal-size sorting networks with the goal of extracting a verified checker for the large-scale computer-generated proof that 25 comparisons are optimal when sorting 9 inputs, which required more…
The use of topological persistence in contemporary data analysis has provided considerable impetus for investigations into the geometric and functional-analytic structure of the space of persistence modules. In this paper, we isolate a…
Eliciting "chain of thought" (CoT) rationales -- sequences of token that convey a "reasoning" process -- has been shown to consistently improve LLM performance on tasks like question answering. More recent efforts have shown that such…
In ontology-mediated query answering, access to incomplete data sources is mediated by a conceptual layer constituted by an ontology. To correctly compute answers to queries, it is necessary to perform complex reasoning over the constraints…
At this point in time there is a need for a new representation of different information, to identify and organize descending its characteristics. Today, science is a powerful tool for the description of reality - the numbers. Why the most…
Search-augmented large language models (LLMs) excel at knowledge-intensive tasks by integrating external retrieval. However, they often over-search -- unnecessarily invoking search tool even when it does not improve response quality, which…
The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their…
The syntactic structures of sentences can be readily read-out from the activations of large language models (LLMs). However, the ``structural probes'' that have been developed to reveal this phenomenon are typically evaluated on an…
Ideally, the time that an incremental algorithm uses to process a change should be a function of the size of the change rather than, say, the size of the entire current input. Based on a formalization of ``the set of things changed'' by an…
Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…
Reasoning in Large Language Models incurs significant inference-time compute, yet the token-level information structure of reasoning traces remains underexplored. We observe that reasoning tokens split into two functional types: low-entropy…