Related papers: A monotone connection between model class size and…
The discrete distribution of the length of longest increasing subsequences in random permutations of $n$ integers is deeply related to random matrix theory. In a seminal work, Baik, Deift and Johansson provided an asymptotics in terms of…
Maslov's class $\overline{\text{K}}$ is an expressive fragment of First-Order Logic known to have decidable satisfiability problem, whose exact complexity, however, has not been established so far. We show that $\overline{\text{K}}$ has the…
This paper introduces the MCML approach for empirically studying the learnability of relational properties that can be expressed in the well-known software design language Alloy. A key novelty of MCML is quantification of the performance of…
We explore the interlacing between model category structures attained to classes of modules of finite $\mathcal{X}$-dimension, for certain classes of modules $\mathcal{X}$. As an application we give a model structure approach to the…
It is well-known that simple type theory is complete with respect to non-standard set-valued models. Completeness for standard models only holds with respect to certain extended classes of models, e.g., the class of cartesian closed…
We show through theory and experiment that gradient-based explanations of a model quickly reveal the model itself. Our results speak to a tension between the desire to keep a proprietary model secret and the ability to offer model…
Despite their successes, deep learning models struggle with tasks requiring complex reasoning and function composition. We present a theoretical and empirical investigation into the limitations of Structured State Space Models (SSMs) and…
We study the task of learning Generalized Linear models (GLMs) in the agnostic model under the Gaussian distribution. We give the first polynomial-time algorithm that achieves a constant-factor approximation for \textit{any} monotone…
We investigate the asymptotic number of equivalence classes of linear codes with prescribed length and dimension. While the total number of inequivalent codes of a given length has been studied previously, the case where the dimension…
Large language models (LLMs) have achieved remarkable progress in natural language generation, yet they continue to display puzzling behaviors -- such as repetition and incoherence -- even when exhibiting low perplexity. This highlights a…
We investigate the performance of large language models on repetitive deterministic prediction tasks and study how the sequence accuracy rate scales with output length. Each such task involves repeating the same operation n times. Examples…
Deep Boltzmann machines (DBMs), one of the first ``deep'' learning methods ever studied, are multi-layered probabilistic models governed by a pairwise energy function that describes the likelihood of all variables/nodes in the network. In…
Large Language Models (LLMs) are increasingly used in tasks requiring interpretive and inferential accuracy. In this paper, we introduce ExpliCa, a new dataset for evaluating LLMs in explicit causal reasoning. ExpliCa uniquely integrates…
The emergence of Large Language Models (LLMs) has opened new opportunities to automate software engineering activities that traditionally require substantial manual effort. Among these, class diagram generation represents a critical yet…
In this paper, we extend the recent analysis of the new large $D$ limit of matrix models to the cases where the action contains arbitrary multi-trace interaction terms as well as to arbitrary correlation functions. We discuss both the cases…
The Minimum Description Length principle for online sequence estimation/prediction in a proper learning setup is studied. If the underlying model class is discrete, then the total expected square loss is a particularly interesting…
Normative reasoning is a type of reasoning that involves normative or deontic modality, such as obligation and permission. While large language models (LLMs) have demonstrated remarkable performance across various reasoning tasks, their…
Recent advances in reasoning with large language models (LLMs) have demonstrated strong performance on complex mathematical tasks, including combinatorial optimization. Techniques such as Chain-of-Thought and In-Context Learning have…
In generative commonsense reasoning tasks such as CommonGen, generative large language models (LLMs) compose sentences that include all given concepts. However, when focusing on instruction-following capabilities, if a prompt specifies a…
This is a paper in the intersection of time series analysis and complexity theory that presents new results on permutation complexity in general and permutation entropy in particular. In this context, permutation complexity refers to the…