All publications

Characterizes, across 188 controlled runs, when a representational prior accelerates grokking: the prior must be built from the right feature family, label-free invariances outperform supervised signals, and the benefit is concentrated in a narrow critical window early in training.

Controlled experiments showing the grokking delay is causally the time to form task-structured representations. Injecting the right structure through a contrastive representational prior collapses the delay — up to 22× faster generalization — while structure-agnostic interventions do not.

Treats a Coconut-style latent reasoner's chain of continuous thoughts as a discrete-time dynamical system and pre-registers spectral predictions with kill conditions. The kill condition fired: the dynamics are contracting and non-normal, but spectral invariants are not the mechanism of latent reasoning.

When are two neural networks the same computation? A process-level equivalence metric from ergodic theory that separates what representation-geometry tools (CKA, SVCCA) and linearized-dynamics tools (DSA) conflate — such as a model versus its pruned, distilled, or noise-injected twin.

Casts per-synapse memory consolidation as a Doob h-transform: condition each weight's stochastic dynamics on never crossing a memory barrier, and intrinsic device noise becomes a consolidation resource instead of an accuracy tax. Confirmed on real BrainScaleS-2 analog neuromorphic hardware, with +15.6 points retention.

Training data is routinely collected by a selection process the model never sees — loans observed only when granted, outcomes only when a test was ordered. When selection acts on unobservables, importance weighting and covariate-shift corrections fail; adapting Heckman's econometric selection model to deep networks restores calibrated uncertainty.

Learning-curve surrogates for hyperparameter optimization are fit on curves that survived earlier rungs of successive halving — a censoring mechanism no method in that line models. The paper quantifies the resulting survivor bias and treats it with selection-aware corrections.

Learns Koopman/transfer-operator spectra on small domains of chaotic PDEs and extrapolates to domains up to 64× larger. The finite-size-scaling pipeline works in absolute terms — but never beats simple interpolation. An honest negative, shipped with a practical convergence diagnostic.

A delta-network event is, definitionally, a level crossing of an activation time series — so Rice's formula predicts event rates from activation statistics. This yields closed-form threshold allocation and a differentiable handle on temporal sparsity, with a pre-registered negative on end-to-end budget training reported alongside.

Builds a one-sided Kac–Rice level-crossing budget for PINNs on stiff PDEs and validates its mechanism — then reports that the widely-cited catastrophic high-frequency divergence it was designed to prevent does not appear in a careful reproduction of the benchmark.

Smooth Monte-Carlo estimators for the complete integral-geometric description of a neural field's level sets — area, boundary measure, and Euler characteristic — enabling topology repair roughly 250× faster than persistent-homology pipelines, with validated design rules and a documented adversarial failure mode.

Generative surrogates of chaotic systems — including diffusion-based weather and climate emulators — are evaluated on extreme events but never trained on their timing. Adding a temporal-point-process likelihood over event times corrects long-horizon extreme-event statistics on a two-scale Lorenz-96 testbed.

Coordinate-MLP neural fields exhibit spectral bias: low frequencies fit quickly, high frequencies slowly or never. The Kac–Rice level-crossing density gives a mesh-free, FFT-free auxiliary loss that acts directly on scattered data in the spatial domain — where frequency-domain remedies require grids.

Two chaotic systems can share an invariant measure yet compute different dynamics — a failure Wasserstein-style evaluation cannot see. Ornstein's d̄-distance from ergodic isomorphism theory catches it, validated on Lorenz-63 and Kuramoto–Sivashinsky surrogates.

Positional signals tied to absolute indices saturate over long spans and generalize poorly beyond training length. Semantic reference frames measure position relative to learned semantic anchors — a frame-conditioned attention bias that generalizes ALiBi and improves length extrapolation on recall tasks and enwik8.