The Boolean Satisfiability Problem (SAT) plays a crucial role in cryptanalysis, enabling tasks like key recovery and distinguisher construction. Conflict-Driven Clause Learning (CDCL) has emerged as the dominant paradigm in modern SAT solving, and machine learning has been increasingly integrated with CDCL-based SAT solvers to tackle complex cryptographic problems. However, the lack of a unified evaluation framework, inconsistent input formats, and varying modeling approaches hinder fair comparison. Besides, cryptographic SAT instances also differ structurally from standard SAT problems, and the absence of standardized datasets further complicates evaluation. To address these issues, we introduce SAT4CryptoBench, the first comprehensive benchmark for assessing machine learning-based solvers in cryptanalysis.

The VC-dimension is a well-studied and fundamental complexity measure of a set system (or hypergraph) that is central to many areas of machine learning. We establish several new results on the complexity of computing the VC-dimension. In particular, given a hypergraph H = (V,E), we prove that the naive 2O(|V|)-time algorithm is asymptotically tight under the Exponential Time Hypothesis (ETH). We then prove that the problem admits a 1-additive fixed-parameter approximation algorithm when parameterized by the maximum degree of Hand a fixed-parameter algorithm when parameterized by its dimension, and that these are essentially the only such exploitable structural parameters.

Correlated equilibria--and their generalizations known as Φ-equilibria--are a fundamental object of study in game theory, offering a more tractable alternative to Nash equilibria in multi-player settings. While computational aspects of equilibrium computation are well-understood in some settings, fundamental questions are still open in generalized games, that is, games in which the set of strategies allowed to each player depends on the other players' strategies. These classes of games model fundamental settings in economics, and have been a cornerstone of economics research since the seminal paper of Arrow and Debreu [1954]. Recently, there has been growing interest, both in economics and in computer science, in studying correlated equilibria in generalized games. It is known that finding a social welfare maximizing correlated equilibrium in generalized games is NP-hard. However, the existence of efficient algorithms to find any equilibrium remains an important open question.

We consider the graph alignment problem, wherein the objective is to find a vertex correspondence between two graphs that maximizes the edge overlap. The graph alignment problem is an instance of the quadratic assignment problem (QAP), known to be NP-hard in the worst case even to approximately solve. In this paper, we analyze Birkhoff relaxation, a tight convex relaxation of QAP, and present theoretical guarantees on its performance when the inputs follow the Gaussian Wigner Model. More specifically, the weighted adjacency matrices are correlated Gaussian Orthogonal Ensemble with correlation 1/ 1+σ2 .

A certificate that removes outliers sees the data only through its low-degree moments, and an adversary exploits exactly this, hiding corruption where the clean data already looks typical, in the blind spot no bounded-degree test resolves. That blind spot turns out to have an exact size: the Christoffel function of the clean marginal, the very quantity modern data analysis thresholds to detect outliers, here read from the adversary's side as the corruption a bounded-degree certificate cannot remove. We turn this inversion into the organizing principle of the reweighted-hinge approach to robustly learning $γ$-margin halfspaces under malicious noise (Shen, 2025; Zeng and Shen, 2025): the governing resource is the Sum-of-Squares degree of the outlier-removal certificate, and the resolution principle states that the maximal corruption mass which can hide at a center $c$ from a degree-$2t$ certificate is exactly the Christoffel function $λ_{t+1}(c)$ of the clean marginal. Three consequences follow, all against the certificate method (not information-theoretic). A margin-degree tradeoff: certifying the dense pancake to error $ε$ costs SoS degree $Ω(\log(1/ε))$ or margin $Ω(\sqrt{\log(1/ε)}/\sqrt{d})$, explaining why the $\log(1/ε)$ margin Shen (2025) records is forced, with a weighted-Chebyshev reduction making the threshold $2t=Θ((|c|/s)^2)$ tight modulo one classical weighted-extremal estimate. A degree-$2$ outlier barrier: the resolution principle realized as an explicit instance on which degree $2$ is stuck at $η^{1/2}$ while degree $4$ escapes, locating the method's small breakdown rate in the degree, not the analysis. And a degree-$2t$ algorithm tracing the frontier $η^{1-1/2t}$ (recovering Shen (2025) at $t=1$), whose gain is an explicit constant, capped by the pancake density and shown unimprovable by the degree-$2$ barrier.

Learning complex functions that involve multi-step reasoning poses a significant challenge for standard supervised learning from input-output examples. Chainof-thought (CoT) supervision, which augments training data with intermediate reasoning steps to provide a richer learning signal, has driven recent advances in large language model reasoning. This paper develops a statistical theory of learning under CoT supervision. Central to the theory is the CoT information, which measures the additional discriminative power offered by the chain-of-thought for distinguishing hypotheses with different end-to-end behaviors. The main theoretical results demonstrate how CoT supervision can yield significantly faster learning rates compared to standard end-to-end supervision, with both upper bounds and information-theoretic lower bounds characterized by the CoT information.

In contrast, most visual representation learning systems assign fixed-length representations to all inputs, ignoring variations in complexity or familiarity. Recent adaptive tokenization methods address this by allocating variable-length representations but typically require test-time search over multiple hypotheses to identify the most predictive one. Inspired by KC principles, we propose a one-shot adaptive tokenizer, KARL, that predicts the appropriate number of tokens for an image in a single forward pass, halting once its approximate KC is reached. The token count serves as a proxy for the minimum description length. KARL performs comparably to recent adaptive tokenizers while operating in a one-pass manner. Additionally, we present a conceptual study showing a correlation between adaptive tokenization and core ideas from AIT. We demonstrate that adaptive tokenization not only aligns with KC but also reveals empirical signals approximating AIT concepts such as sophistication and logical depth. Finally, we analyze predicted image complexity and interestingness across axes such as structure vs. noise and in-distribution vs. out-of-distribution familiarity, highlighting alignment with human annotations.

Greedy Equivalence Search (GES) is a classic score-based algorithm for causal discovery from observational data. In the sample limit, it recovers the Markov equivalence class of graphs that describe the data. Still, it faces two challenges in practice: computational cost and finite-sample accuracy. In this paper, we develop Less Greedy Equivalence Search (LGES), a variant of GES that retains its theoretical guarantees while partially addressing these limitations. LGES modifies the greedy step; rather than always applying the highest-scoring insertion, it avoids edge insertions between variables for which the score implies some conditional independence.

Agnostic learning of Boolean halfspaces is a fundamental problem in computational learning theory, but it is known to be computationally hard even for weak learning.

Algorithm configuration, which involves selecting algorithm parameters based on sampled problem instances, is a crucial step in applying modern algorithms such as SAT solvers. Although prior work has attempted to understand the theoretical foundations of algorithm configuration, we still lack a comprehensive understanding of why practical algorithm configurators exhibit strong generalization performances in real-world scenarios. In this paper, through the lens of machine learning theory, we provide an algorithm-dependent generalization bound for the widely used model-based algorithm configurators under mild assumptions. Our approach is based on the algorithmic stability framework for generalization bounds. To the best of our knowledge, this is the first generalization bound that applies to a model closely approximating practical model-based algorithm configurators.