Dynamics

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Contents

• Sharp multiple testing boundary for sparse sequences
• Pattern avoidance in compositions and powers of permutations
• Poisson Approximation and the Chen-Stein Method
• Finite-support Bellman envelopes
• Terminal and discounted Bellman contracts
• Sparse Uniformity Testing
• The Chebyshev–Edgeworth correction in the central limit theorem for integer-valued independent summands
• Approximation of rejective sampling inclusion probabilities and application to high order correlations
• Negative dependence and the geometry of polynomials
• Zeta functions of restrictions of the shift transformation
• Variable selection with Hamming loss
• Variable selection, monotone likelihood ratio and group sparsity
• Optimal Detection of Sparse Mixtures Against a Given Null Distribution
• Kakutani–Fibonacci partition supplier
• Optimal detection of multi-sample aligned sparse signals
• On the Measure of Intelligence
• Counterexample-Guided Abstraction Refinement
• Regularization of Inverse Problems
• Information Processing Capacity of Dynamical Systems
• Testing Symmetric Markov Chains From a Single Trajectory
• Detectability of nonparametric signals: higher criticism versus likelihood ratio
• Gradient Descent Provably Optimizes Over-parameterized Neural Networks
• Historical origin of the Dyson terminology
• Growing-count local empirical Gaussian limits
• Regularization of Inverse Problems
• Directional limits and exact-capacity selection
• Length of Time’s Arrow
• Global and local empirical limits
• Limit theorems for stationary Markov processes with L2-spectral gap
• Fundamental limits of exact support recovery in high dimensions
• Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability
• Projective compact Hausdorff covers and dynamics
• Shared stationary initialization and coherent absorption
• Scalar entropy extremum supplier
• Inverse limits and finite-cover shadowing
• Linear elimination and memory
• Beyond Progress Measures: Theoretical Insights into the Mechanism of Grokking
• Innovated higher criticism for detecting sparse signals in correlated noise
• On Pairs of f-divergences and their Joint Range
• The Elements of Statistical Learning: Data Mining, Inference, and Prediction
• Ridge Regression: Biased Estimation for Nonorthogonal Problems
• Training Two-Layer ReLU Networks with Gradient Descent is Inconsistent
• Time-uniform Chernoff bounds via nonnegative supermartingales
• A collapsed posterior noise measure and its group variation
• Neural Tangent Kernel: Convergence and Generalization in Neural Networks
• A central limit theorem for m-dependent variables
• Limiting Distributions for Sums of Independent Random Products
• OEIS A331859
• Grokking on the Weight-Decay Clock: A Rate Hierarchy from Softly Broken Symmetries
• Statistical limits of sparse mixture detection
• Grokking as the Transition from Lazy to Rich Training Dynamics
• Symmetric tridiagonal recurrence
• Grokking in Linear Estimators – A Solvable Model that Groks without Understanding
• Omnigrok: Grokking Beyond Algorithmic Data
• What Happens after SGD Reaches Zero Loss? A Mathematical Framework
• Dichotomy of Early and Late Phase Implicit Biases Can Provably Induce Grokking
• Calibrated linear memory and noise
• Arithmetic isolation of a posterior score atom
• Neighborhood two-shadowing beyond quasi-finite type
• Why Do You Grok? A Theoretical Analysis of Grokking Modular Addition
• Hypothesis testing for high-dimensional sparse binary regression
• The Geometry of Grokking: Norm Minimization on the Zero-Loss Manifold
• Progress Measures for Grokking via Mechanistic Interpretability
• Optimal detection of planted stars via a random energy model
• Diagonal bases and diagonal periods of elementary cellular automata
• Gaussian convergence in a fixed Wiener chaos
• Oscillations for order statistics of some discrete processes
• Exact realization as an intermediate input
• Compact Hausdorff shadowing and zero-dimensional extensions
• Neural Networks are Convex Regularizers
• Discrete-time balanced truncation: ordered cuts and strict stability
• Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets
• Grokking at the Edge of Numerical Stability
• Profinite Groups
• Decision Making in the Arrow of Time
• Exact solutions to the nonlinear dynamics of learning in deep linear neural networks
• Network theory of microscopic and macroscopic behavior of master equation systems
• Linear Models
• Computational Mechanics: Pattern and Prediction, Structure and Simplicity
• On the absolute constants in the Berry–Esseen type inequalities for identically distributed summands
• Local Bernoulli probabilities and a growing posterior interval
• On local and ratio limit theorems
• The Non-Linear Representation Dilemma: Is Causal Abstraction Enough for Mechanistic Interpretability?
• Half-line endpoint response
• The Slingshot Mechanism: An Empirical Study of Adaptive Optimizers and the Grokking Phenomenon
• The information bottleneck method
• visomirskigriffin2026spatial
• wallner2026passbucket
• False discovery rate control with e-values
• Martingale limits and a posterior rank process
• Minimax Testing of Identity to a Reference Ergodic Markov Chain
• Information Geometry of Reversible Markov Chains
• To Grok Grokking: Provable Grokking in Ridge Regression
• Benign Overfitting and Grokking in ReLU Networks for XOR Cluster Data
• System aliasing for sampled matrix exponentials
• One-deletion Lonely Runner bounds and equality cases