arXiv subjects

Kennon Stewart

Publications and source records attributed to Kennon Stewart.

4 recordsLinked to original sources

arXiv2026

Geometric Factorization of Sufficient Harmonic Representations

For tasks of likelihood families invariant under the action of a lie group, the quotient is the minimal sufficient invariant representation. On compact homogeneous spaces, this quotient representation admits a harmonic realization through spherical Fourier coefficients; for finite-band harmonic exponential families, the empirical harmonic coefficients are minimal sufficient statistics. The partition function can be expressed algebraically by extracting the trivial representation component through Clebsch-Gordan decomposition.

math.RT↗

arXiv2026

Form and Function: Machine Unlearning as a Problem of Misaligned States

We formulate machine unlearning for online L-BFGS as a counterfactual state-alignment problem. Given an actual event stream and a deletion-edited counterfactual stream, the target of unlearning is the optimizer state that would have arisen had the deleted samples never been processed. We introduce state-aware metrics that separately measure parameter error, memory-operator error, combined state error, and update-direction error. The memory metric compares the inverse-Hessian actions induced by the o-L-BFGS memory, rather than treating curvature pairs as of finite influence. Under convexity assumptions, we derive a recursive bound on counterfactual state deviation. We then evaluate a state-aware benchmark of deletion interventions, including memory-only and parameter-only corrections, against an counterfactual oracle model. These results show that unlearning for online L-BFGS is not merely a parameter-correction problem: it requires alignment with a realizable counterfactual optimizer state.

cs.LG↗

arXiv2026

Shape of Memory: a Geometric Analysis of Machine Unlearning in Second-Order Optimizers

We argue that current definitions of machine unlearning are underspecified for second-order optimizers. We compare first-order and second-order learners for their ability to handle the data deletion task with varying degrees of eigendecomposition to mimic the loss model memory. While both first and second-order methods realign with the ideal counterfactul in terms of performance and gradient, the second-order optimizer shows significant volatility in the optimizer state. This indicates residual information, supposedly deleted, that isn't detectable by first-order analysis. Various eigendecay treatments show that stability and information loss is regained only under controlled state pertubation where geometric information (or memory) is erased.

cs.LG↗

arXiv2025

Mo' Memory, Mo' Problems: Stream-Native Machine Unlearning

Machine unlearning work assumes a static, i.i.d training environment that doesn't truly exist. Modern ML pipelines need to learn, unlearn, and predict continuously on production streams of data. We translate batch unlearning to the online setting using notions of regret, sample complexity, and deletion capacity. We tighten regret bounds to a logarithmic $\mathcal{O}(\ln{T})$, a first for a certified unlearning algorithm. When fitted with an online variant of L-BFGS optimization, the algorithm achieves state of the art regret with a constant memory footprint. Such changes extend the lifespan of an ML model before expensive retraining, making for a more efficient unlearning process.

stat.ML↗