Related papers: Constructive Separations and Their Consequences
Despite the vast success of Deep Neural Networks in numerous application domains, it has been shown that such models are not robust i.e., they are vulnerable to small adversarial perturbations of the input. While extensive work has been…
Minimizing the discrepancy of a set system is a fundamental problem in combinatorics. One of the cornerstones in this area is the celebrated six standard deviations result of Spencer (AMS 1985): In any system of n sets in a universe of size…
Trustworthy AI requires reasoning systems that are not only powerful but also transparent and reliable. Automated Theorem Proving (ATP) is central to formal reasoning, yet classical binary resolution remains limited, as each step involves…
Recent research has recognized interpretability and robustness as essential properties of trustworthy classification. Curiously, a connection between robustness and interpretability was empirically observed, but the theoretical reasoning…
We present a new method, the Subdivision Construction, for proving the finite model property (the fmp) for broad classes of modal logics and modal rule systems. The construction builds on the framework of stable canonical rules, and…
Robustness of machine learning models to various adversarial and non-adversarial corruptions continues to be of interest. In this paper, we introduce the notion of the boundary thickness of a classifier, and we describe its connection with…
Counterfactual explanations (CEs) are a powerful means for understanding how decisions made by algorithms can be changed. Researchers have proposed a number of desiderata that CEs should meet to be practically useful, such as requiring…
We examine various categorical structures that can and cannot be constructed. We show that total computable functions can be mimicked by constructible functors. More generally, whatever can be done by a Turing machine can be constructed by…
Contrastive loss has been increasingly used in learning representations from multiple modalities. In the limit, the nature of the contrastive loss encourages modalities to exactly match each other in the latent space. Yet it remains an open…
We prove in Theorem $2.2$ that the multiplicatively closed subset generated by at most two elements in the set of natural numbers $\mathbb{N}$ has arbitrarily large gaps by explicitly constructing large integer intervals with known prime…
Transformer large language models (LLMs) have sparked admiration for their exceptional performance on tasks that demand intricate multi-step reasoning. Yet, these models simultaneously show failures on surprisingly trivial problems. This…
In a previous paper, entitled "Structural Highness Notions," we defined several classes of degrees that are high in senses related to computable structure theory. Each class of degrees is characterized by a structural feature (e.g., an…
The $\textbf{P}$ vs. $\textbf{NP}$ problem is an important problem in contemporary mathematics and theoretical computer science. Many proofs have been proposed to this problem. This paper proposes a theoretic proof for $\textbf{P}$ vs.…
A conservative class of constraint satisfaction problems CSPs is a class for which membership is preserved under arbitrary domain reductions. Many well-known tractable classes of CSPs are conservative. It is well known that lexleader…
A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive…
We study the *refuter* problems for proof complexity lower bounds. Suppose $\varphi$ is a hard tautology that does not admit any length-$s$ proof in some proof system $P$. In the corresponding refuter problem, we are given (query access to)…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
We demonstrate that a dependency parser can be built using a credit assignment compiler which removes the burden of worrying about low-level machine learning details from the parser implementation. The result is a simple parser which…
We tackle the problem of constructive preference elicitation, that is the problem of learning user preferences over very large decision problems, involving a combinatorial space of possible outcomes. In this setting, the suggested…
Constraint Programming (CP) is a powerful declarative programming paradigm where inference and search are interleaved to find feasible and optimal solutions to various type of constraint systems. However, handling logical connectors with…