arXiv:2602.19169v1 Announce Type: cross Abstract: I introduce Virtual Parameter Sharpening (VPS), an inference-time technique that augments frozen transformer linear layers with dynamic, activation-conditioned low-rank perturbations. Unlike parameter-efficient fine-tuning methods such as LoRA, which learn static low-rank adapters, VPS constructs its perturbation factors on the fly from batch activation statistics and optional gradient signals, enabling test-time adaptation without persistent parameter updates. The perturbation takes the form Delta W = gamma * W^T V U^T W, where selector matrices U and V are constructed via sparse activation-guided selection or Sylvester-coupled regression. We provide a theoretical analysis of the perturbation's spectral properties and describe an adaptive policy system that modulates perturbation magnitude based on activation energy and token-level entropy. This system incorporates multi-objective verification with iterative refinement for tasks with ground-truth supervision. We present the complete algorithmic framework, analyze its mathematical foundations, and discuss the mechanisms by which activation-conditioned computation may enhance reasoning capabilities in large language models. Implementation and experimental code are available at https://github.com/Saba-Kublashvili/vps-virtual-parameter-synthesis .

arXiv:2602.19964v1 Announce Type: cross Abstract: Uncertainty quantification is central to safe and efficient deployments of deep learning models, yet many computationally practical methods lack lacking rigorous theoretical motivation. Random network distillation (RND) is a lightweight technique that measures novelty via prediction errors against a fixed random target. While empirically effective, it has remained unclear what uncertainties RND measures and how its estimates relate to other approaches, e.g. Bayesian inference or deep ensembles. This paper establishes these missing theoretical connections by analyzing RND within the neural tangent kernel framework in the limit of infinite network width. Our analysis reveals two central findings in this limit: (1) The uncertainty signal from RND -- its squared self-predictive error -- is equivalent to the predictive variance of a deep ensemble. (2) By constructing a specific RND target function, we show that the RND error distribution can be made to mirror the centered posterior predictive distribution of Bayesian inference with wide neural networks. Based on this equivalence, we moreover devise a posterior sampling algorithm that generates i.i.d. samples from an exact Bayesian posterior predictive distribution using this modified \textit{Bayesian RND} model. Collectively, our findings provide a unified theoretical perspective that places RND within the principled frameworks of deep ensembles and Bayesian inference, and offer new avenues for efficient yet theoretically grounded uncertainty quantification methods.

arXiv:2505.06595v3 Announce Type: replace-cross Abstract: In this paper, we propose a method for transferring feature representation to lightweight student models from larger teacher models. We mathematically define a new notion called \textit{perception coherence}. Based on this notion, we propose a loss function, which takes into account the dissimilarities between data points in feature space through their ranking. At a high level, by minimizing this loss function, the student model learns to mimic how the teacher model \textit{perceives} inputs. More precisely, our method is motivated by the fact that the representational capacity of the student model is weaker than the teacher model. Hence, we aim to develop a new method allowing for a better relaxation. This means that, the student model does not need to preserve the absolute geometry of the teacher one, while preserving global coherence through dissimilarity ranking. Importantly, while rankings are defined only on finite sets, our notion of \textit{perception coherence} extends them into a probabilistic form. This formulation depends on the input distribution and applies to general dissimilarity metrics. Our theoretical insights provide a probabilistic perspective on the process of feature representation transfer. Our experiments results show that our method outperforms or achieves on-par performance compared to strong baseline methods for representation transferring.