arXiv subjects

Guan-Ju Peng

Publications and source records attributed to Guan-Ju Peng.

3 recordsLinked to original sources

arXiv2026

Beyond Client Averaging: A Client-Independent Second-Order Stationary-Bias Component in Stochastic SCAFFOLD

Existing constant-step analysis of stochastic \Scaf{} identifies a leading $O(γ/N)$ stationary mean bias and shows that higher-order bias can persist as the client count increases, but does not identify the first client-independent contribution at coefficient level. For full-participation stochastic \Scaf{} with one-dimensional homogeneous clients, fixed local-step count $H$, and bounded additive gradient noise, we prove, uniformly over $N\ge2$, $$ \begin{aligned} \mathbb{E}_{π_{γ,N,H}}[x]-x^\star ={}& -\frac{f'''(x^\star)σ^2}{4f''(x^\star)^2}\fracγ{N}\\ &- \frac{f'''(x^\star)σ^2}{12f''(x^\star)} \frac{(H-1)(5H-1)}{H}γ^2 +O_H\!\left(\frac{γ^2}{N}+γ^3\right). \end{aligned} $$ Hence client averaging suppresses the leading $O(γ/N)$ bias but does not remove the client-independent $O(γ^2)$ component when its coefficient is nonzero. The mechanism is indirect: although the direct control contribution cancels pathwise in the linear global average, the controls still alter within-round local trajectories and their second moments. Fresh gradient noise and persistent control fluctuations therefore generate local second-moment corrections that nonquadratic curvature converts into stationary mean bias. The coefficient vanishes for quadratic objectives. Numerical experiments are consistent with the predicted coefficient, its persistence as client count increases, and the stated joint remainder. The result is restricted to the one-dimensional homogeneous fixed-$H$ setting.

cs.LG↗

arXiv2026

Physical-Support Confidence Sets for Highly Coherent Dictionaries

Sparse pursuit after dictionary learning can yield a precise atom support even when its physical interpretation is not justified by the calibration data, especially for highly coherent dictionaries where alternative calibration-compatible dictionaries may assign different physical meanings to the same selected support. We develop resolution-aware physical-support inference that jointly accounts for uncertainty in the learned dictionary and in the representation of a deployment signal. Our cross-dictionary confidence correspondence retains calibration-compatible dictionaries and deployment-compatible sparse representations, then projects the surviving explanations onto physical-support space. For local coherent-atom classes with separation scale s, once the deployment data resolve the coherent-block explanation and its atom support, the minimax physical resolution from N calibration signals satisfies $δ_{\mathrm{opt}}(N,s)\asymp\min\{s,\frac{1}{\sqrt{N}s^2}\}$, with relative resolution governed by the orientation-information scale $Ns^6$. Deployment replication improves physical localization only when orientation changes cannot be absorbed by adjusting the active coefficients. For computation, we introduce active endpoint bracketing (AEB), an adaptive finite-bank procedure that evaluates only candidates that can still affect the physical report and otherwise safely coarsens or abstains. Finite-bank experiments, including a four-region synthetic application, show that a point-valued plug-in selector can be physically overprecise, whereas AEB avoids unsupported refinement with fewer candidate evaluations.

cs.LG↗

arXiv2026

Honest Physical-Support Inference after Latent Dictionary Learning: Collision Singularities and Minimax Resolution

Sparse-support uncertainty is usually quantified by treating the dictionary as known, an assumption that can produce overconfident, label-dependent conclusions when the dictionary is learned from latent sparse mixtures. Near collisions of coherent atoms, a test signal may identify the active physical group even though the training data cannot distinguish the physical rays within it. We develop inference for active physical rays, unit atoms modulo sign, after latent dictionary learning. In a fixed-dimensional Gaussian train-test experiment, we retain all dictionaries compatible with a robust training-moment region, profile the test representation over them, and project surviving configurations onto a permutation-invariant support space. The resulting confidence correspondence can report cross-sheet inconclusiveness, group resolution with child ambiguity, or fine-support resolution. We characterize both its statistical cost and decision-theoretic benefit. Residual block orientation first affects the latent training density at cubic order, yielding information of order $s^6$, where $s$ is the within-block collision scale. The correspondence provides high-probability-over-training conditional test coverage, with resolution governed separately by parent detectability, test-time support separation, and learned-dictionary orientation. In the resolved fixed-shell regime, its projective Hausdorff diameter contracts at the minimax-optimal rate $s \wedge (\sqrt{N}s^2)^{-1}$, up to constants. A restricted-task theorem further determines when coefficient asymmetry allows test replication to supplement training information and when calibration uncertainty remains irreducible. The framework thus yields honest, resolution-adaptive support statements and guides the allocation of training versus test measurements.

cs.LG↗