arXiv subjects

Lucas Qingyang Fang

Publications and source records attributed to Lucas Qingyang Fang.

2 recordsLinked to original sources

arXiv2026

Convergence Theory of Knowledge Distillation in Asynchronous P2P Gossip Learning Network

Decentralized, serverless learning increasingly connects devices running different architectures, where the standard tool, decentralized SGD, is undefined as models with different parameter counts cannot be averaged. Knowledge distillation (KD) exchanges soft predictions rather than weights and sidesteps this obstacle, yet convergence theory for fully decentralized, asynchronous peer-to-peer (P2P) KD is lacking. We provide one, relocating consensus from parameter space to function (output) space: a KD event is a geometric contraction operator in logit space on the peers' predictive distributions, which we analyse in the Hilbert space of predictions on a reference measure. Under standard smoothness/variance assumptions and two realizability assumptions, one bridging parameter SGD to the functional step and one controlling restricted task/KD alignment, the time-averaged functional stationarity and function-space disagreement converge at rate $O(1/(ηT))$ to an $O(η)+O(B_f^2)+O(ζ_f^2)$ neighbourhood. Here $B_f$ is the distance from the task optimum to the peers' reachable classes and $ζ_f$ measures persistent local-task heterogeneity. Across homogeneous, width-heterogeneous, and mixed-family networks of the experiments, KD contracts function disagreement by $40-61\times$, while isolated training does not. The sampled stationarity diagnostic has late transient exponents $0.99-1.90$ on the shared-skeleton main runs, and the four-point step-size sweep exhibits the predicted transient: neighbourhood tradeoff.

cs.LG↗

arXiv2026

Predictive Memory Localization: Forecasting Selective Intervention Paths from Internal Signals

Activation steering turns localized representations into control directions, but localization alone does not reveal whether a direction has a selective operating regime. We introduce Predictive Memory Localization (PML), which treats the measured-grid intervention path as the predictive object of memory localization. PML separates random-calibrated target movement from semantic-neighbor and capability damage, and compares static localization and supervised geometry with a strength-disjoint low-dose causal response. Our frozen study covers 3,000 records from nine datasets and fourteen domains, yielding 30,000 distinct record-direction-layer paths and 210,000 distinct path-strength evaluations. At layer 7, the geometry-derived RFM/AGOP direction reaches 13.1% target-any and 12.3% clean-any, exceeding random by 3.6 and 3.4 percentage points under a record-paired bootstrap. Across record-, dataset-, and domain-grouped splits, responses at $|α|=0.1$ are the strongest signal for outcomes at disjoint strengths $|α|\in\{0.25,0.5\}$. On held-out records, a predictor-driven selector chooses a coefficient or abstains, improves utility and reduces semantic-neighbor damage relative to a train-tuned fixed-strength policy, and avoids most evaluations in a dense scan. Across three residual-norm-matched base models, learned directions retain selective-path gains and low-dose responses yield 0.801-0.828 record-held-out macro AUROC. PML therefore turns memory localization into a falsifiable forecast of margin-level selective outcomes and a risk-aware intervention decision.

cs.AI↗