Related papers: Nonlowness independent from frequent mind changes
Given a level set $E$ of an arbitrary multiplicative function $f$, we establish, by building on the fundamental work of Frantzikinakis and Host [13,14], a structure theorem which gives a decomposition of $\mathbb{1}_E$ into an almost…
Adversarial robustness is a key desirable property of neural networks. It has been empirically shown to be affected by their sizes, with larger networks being typically more robust. Recently, Bubeck and Sellke proved a lower bound on the…
We explore the interaction between Lebesgue measure and dominating functions. We show, via both a priority construction and a forcing construction, that there is a function of incomplete degree that dominates almost all degrees. This…
Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…
In recent decades, a number of centrality metrics describing network properties of nodes have been proposed to rank the importance of nodes. In order to understand the correlations between centrality metrics and to approximate a…
Chain-of-thought (CoT) outputs let us read a model's step-by-step reasoning. Since any long, serial reasoning process must pass through this textual trace, the quality of the CoT is a direct window into what the model is thinking. This…
The deployment of deep neural networks (DNNs) in safety-critical edge environments necessitates robustness against hardware-induced bit-flip errors. While empirical studies indicate that reducing numerical precision can improve fault…
Large Language Models (LLMs) have demonstrated impressive performance across various tasks, with different models excelling in distinct domains and specific abilities. Effectively combining the predictions of multiple LLMs is crucial for…
We consider the evaluation of first-order queries over classes of databases that have bounded degree and low degree. More precisely, given a query and a database, we want to efficiently test whether there is a solution, count how many…
This paper explores the intricate relationship between interpretability and robustness in deep learning models. Despite their remarkable performance across various tasks, deep learning models often exhibit critical vulnerabilities,…
We provide a theoretical framework to understand how widely used measures of choice difficulty relate. In a binary-option Bayesian expected-utility framework, we show that three measures of difficulty, (i) understanding (ex-ante value),…
Training large language models (LLMs) with open-domain instruction data has yielded remarkable success in aligning to end tasks and human preferences. Extensive research has highlighted the importance of the quality and diversity of…
In this paper we criticize the robustness measure traditionally employed to assess the performance of machine learning models deployed in adversarial settings. To mitigate the limitations of robustness, we introduce a new measure called…
While significant progress has been made in specifying neural networks capable of representing uncertainty, deep networks still often suffer from overconfidence and misaligned predictive distributions. Existing approaches for measuring this…
There is a growing literature on reasoning by large language models (LLMs), but the discussion on the uncertainty in their responses is still lacking. Our aim is to assess the extent of confidence that LLMs have in their answers and how it…
While deep learning has led to remarkable results on a number of challenging problems, researchers have discovered a vulnerability of neural networks in adversarial settings, where small but carefully chosen perturbations to the input can…
Learning performed over finite time is inherently irreversible. In Part~I of this series, we modeled learning as a transport process in the space of parameter distributions and derived the Epistemic Speed Limit (ESL), which lower-bounds…
Computably enumerable equivalence relations (ceers) received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility $\leq_c$. This gives rise to a rich degree-structure. In this…
For a long time, designing neural architectures that exhibit high performance was considered a dark art that required expert hand-tuning. One of the few well-known guidelines for architecture design is the avoidance of exploding gradients,…
Data structure has a dramatic impact on the properties of neural networks, yet its significance in the established theoretical frameworks is poorly understood. Here we compute the Vapnik-Chervonenkis entropy of a kernel machine operating on…