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Recent progress has been made in understanding optimisation dynamics in neural networks trained with full-batch gradient descent with momentum with the uncovering of the edge of stability phenomenon in supervised learning. The edge of…
We present a unified information-theoretic framework elucidating the interplay between stability, privacy, and the generalization performance of quantum learning algorithms. We establish a bound on the expected generalization error in terms…
A fundamental question in the theory of reinforcement learning is: suppose the optimal $Q$-function lies in the linear span of a given $d$ dimensional feature mapping, is sample-efficient reinforcement learning (RL) possible? The recent and…
We study the continuity property of the generalized entropy as a function of the underlying probability distribution, defined with an action space and a loss function, and use this property to answer the basic questions in statistical…
Recently there are a considerable amount of work devoted to the study of the algorithmic stability and generalization for stochastic gradient descent (SGD). However, the existing stability analysis requires to impose restrictive assumptions…
The prevailing assumption of an exponential decay in large language model (LLM) reliability with sequence length, predicated on independent per-token error probabilities, posits an inherent limitation for long autoregressive outputs. Our…
Recently, some mixture algorithms of pointwise and pairwise learning (PPL) have been formulated by employing the hybrid error metric of "pointwise loss + pairwise loss" and have shown empirical effectiveness on feature selection, ranking…
Existing reinforcement learning (RL)-based post-training methods for large language models have advanced rapidly, yet their design has largely been guided by heuristics rather than systematic theoretical principles. This gap limits our…
We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…
We analyze neural scaling laws in a solvable model of last-layer fine-tuning where targets have intrinsic, instance-heterogeneous difficulty. In our Latent Instance Difficulty (LID) model, each input's target variance is governed by a…
We study the problem of imitating an expert demonstrator in a discrete-time, continuous state-and-action control system. We show that, even if the dynamics satisfy a control-theoretic property called exponential stability (i.e. the effects…
We show that the average stability notion introduced by \cite{kearns1999algorithmic, bousquet2002stability} is invariant to data preconditioning, for a wide class of generalized linear models that includes most of the known exp-concave…
Generalization analyses of deep learning typically assume that the training converges to a fixed point. But, recent results indicate that in practice, the weights of deep neural networks optimized with stochastic gradient descent often…
This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…
An explicit upper bound on the tail probabilities for the normalized Rademacher sums is given. This bound, which is best possible in a certain sense, is asymptotically equivalent to the corresponding tail probability of the standard normal…
Algorithmic stability is a classical approach to understanding and analysis of the generalization error of learning algorithms. A notable weakness of most stability-based generalization bounds is that they hold only in expectation.…
This work studies the learning ability of consensus and diffusion distributed learners from continuous streams of data arising from different but related statistical distributions. Four distinctive features for diffusion learners are…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
Many machine learning tasks can be formulated as Regularized Empirical Risk Minimization (R-ERM), and solved by optimization algorithms such as gradient descent (GD), stochastic gradient descent (SGD), and stochastic variance reduction…
We analyze the behavior of stochastic approximation algorithms where iterates, in expectation, progress towards an objective at each step. When progress is proportional to the step size of the algorithm, we prove exponential concentration…