arXiv subjects

Cedar Site Bai

Publications and source records attributed to Cedar Site Bai.

8 recordsLinked to original sources

arXiv2026

Ask to Be Sure: Informative Interactions for Confident Multi-Turn LLM Recommendation

Recent advances in large language models (LLMs) have enabled their use as conversational recommender systems (CRS), demonstrating strong recommendation accuracy and natural dialogue. However, guiding multi-turn interactions to elicit user preferences effectively remains challenging. Existing approaches either use separate reinforcement learning agents with templated interactions or optimize for interactivity judged by another LLM, without measuring how much useful information is actually gained. We propose a new approach that quantifies the effectiveness of each interaction by the reduction in the assistant's uncertainty, measured via entropy over recommendations. We apply this entropy reduction as a reward---without relying on ground-truth recommendations, which are often unavailable in real-world scenarios---to fine-tune the LLM, enabling strategic interaction generation. Empirical results with supervised fine-tuning (SFT) and direct preference optimization (DPO) on the INSPIRED and ReDial datasets show that our method improves both recommendation quality and conversational efficiency.

cs.IR↗

arXiv2026

Spectral Saliency for Machine Unlearning

Machine unlearning (MU) aims to remove the influence of specific training data while preserving model utility. As the name suggests, MU can be viewed as the inverse of learning, using gradient-based updates to reduce the influence of a forget-set by counteracting the previously learned behavior. Recently, Muon, a gradient descent variant, has been introduced. Muon applies spectral magnitude normalization to encourage exploration of rare directions and demonstrates promising performance. Inspired by Muon, we adopt the spectral view for unlearning and propose Spectral Saliency Unlearning (SSU). SSU thresholds weak singular components and updates only those directions supported by a confident unlearning signal. We further provide theoretical justification for this thresholding approach from the perspective of the forgetting-retention trade-off. Experiments across image classifiers, diffusion models, and LLMs demonstrate SSU's effectiveness.

cs.LG↗

arXiv2026

Decoupling Variance and Scale-Invariant Updates in Adaptive Gradient Descent for Unified Vector and Matrix Optimization

Adaptive methods like Adam have become the $\textit{de facto}$ standard for large-scale vector and Euclidean optimization due to their coordinate-wise adaptation with a second-order nature. More recently, matrix-based spectral optimizers like Muon (Jordan et al., 2024b) show the power of treating weight matrices as matrices rather than long vectors. Linking these is hard because many natural generalizations are not feasible to implement, and we also cannot simply move the Adam adaptation to the matrix spectrum. To address this, we reformulate the AdaGrad update and decompose it into a variance adaptation term and a scale-invariant term. This decoupling produces $\textbf{DeVA}$ ($\textbf{De}$coupled $\textbf{V}$ariance $\textbf{A}$daptation), a framework that bridges between vector-based variance adaptation and matrix spectral optimization, enabling a seamless transition from Adam to adaptive spectral descent. Extensive experiments across language modeling and image classification demonstrate that DeVA consistently outperforms state-of-the-art methods such as Muon and SOAP (Vyas et al., 2024), reducing token usage by around 6.6\%. Theoretically, we show that the variance adaptation term effectively improves the blockwise smoothness, facilitating faster convergence. Our implementation is available at https://github.com/Tsedao/Decoupled-Variance-Adaptation

cs.LG↗

arXiv2026

Can Entry-Wise Clipping Give Spectral Control of Stochastic Gradients?

Training instabilities such as loss spikes are frequently the result of stochastic gradient noise. Because of rare expressions in language training data, and multiple layer composition, the noise impact is heavy-tailed and survives mini-batch averaging. Existing remedies trade off structure against cost: vector-norm clipping ignores the matrix structure of weight updates, while spectral normalization (e.g., Muon (Jordan et al., 2024)) respects it at additional cost. We show that this trade-off can be balanced. Real gradient noise appears to be similar to entry-wise heavy-tailed contamination, and a first-order perturbation analysis reveals a localization property of such noise, under which a simple entry-wise method achieves spectral control. Exploiting this, we derive a tractable surrogate for the Bayes-optimal entry-wise estimator under a Gaussian signal prior. We establish $O(ε^{-4})$ convergence guarantee under Cauchy-contaminated noise. Empirically, we find that smooth shrinkage improves Adam on NanoGPT pretraining, saving ${\sim}7\%$ of training tokens. We further find that applying the entry-wise clipping before spectral normalization yields a ${\sim}2\%$ token saving on top of Muon.

cs.LG↗

arXiv2025

Faster Acceleration for Steepest Descent

Recent advances (Sherman, 2017; Sidford and Tian, 2018; Cohen et al., 2021) have overcome the fundamental barrier of dimension dependence in the iteration complexity of solving $\ell_\infty$ regression with first-order methods. Yet it remains unclear to what extent such acceleration can be achieved for general $\ell_p$ smooth functions. In this paper, we propose a new accelerated first-order method for convex optimization under non-Euclidean smoothness assumptions. In contrast to standard acceleration techniques, our approach uses primal-dual iterate sequences taken with respect to $\textit{differing}$ norms, which are then coupled using an $\textit{implicitly}$ determined interpolation parameter. For $\ell_p$ norm smooth problems in $d$ dimensions, our method provides an iteration complexity improvement of up to $O(d^{1-\frac{2}{p}})$ in terms of calls to a first-order oracle, thereby allowing us to circumvent long-standing barriers in accelerated non-Euclidean steepest descent.

math.OC↗

arXiv2025

Tight Lower Bounds under Asymmetric High-Order Hölder Smoothness and Uniform Convexity

In this paper, we provide tight lower bounds for the oracle complexity of minimizing high-order Hölder smooth and uniformly convex functions. Specifically, for a function whose $p^{th}$-order derivatives are Hölder continuous with degree $ν$ and parameter $H$, and that is uniformly convex with degree $q$ and parameter $σ$, we focus on two asymmetric cases: (1) $q > p + ν$, and (2) $q < p+ν$. Given up to $p^{th}$-order oracle access, we establish worst-case oracle complexities of $Ω\left( \left( \frac{H}σ\right)^\frac{2}{3(p+ν)-2}\left( \fracσε\right)^\frac{2(q-p-ν)}{q(3(p+ν)-2)}\right)$ in the first case with an $\ell_\infty$-ball-truncated-Gaussian smoothed hard function and $Ω\left(\left(\frac{H}σ\right)^\frac{2}{3(p+ν)-2}+ \log\log\left(\left(\frac{σ^{p+ν}}{H^q}\right)^\frac{1}{p+ν-q}\frac{1}ε\right)\right)$ in the second case, for reaching an $ε$-approximate solution in terms of the optimality gap. Our analysis generalizes previous lower bounds for functions under first- and second-order smoothness as well as those for uniformly convex functions, and furthermore our results match the corresponding upper bounds in this general setting.

math.OC↗

arXiv2025

Stacey: Promoting Stochastic Steepest Descent via Accelerated $\ell_p$-Smooth Nonconvex Optimization

While popular optimization methods such as SGD, AdamW, and Lion depend on steepest descent updates in either $\ell_2$ or $\ell_\infty$ norms, there remains a critical gap in handling the non-Euclidean structure observed in modern deep networks training. In this work, we address this need by introducing a new accelerated $\ell_p$ steepest descent algorithm, called Stacey, which uses interpolated primal-dual iterate sequences to effectively navigate non-Euclidean smooth optimization tasks. In addition to providing novel theoretical guarantees for the foundations of our algorithm, we empirically compare our approach against these popular methods on tasks including image classification and language model (LLM) pretraining, demonstrating both faster convergence and higher final accuracy. We further evaluate different values of $p$ across various models and datasets, underscoring the importance and efficiency of non-Euclidean approaches over standard Euclidean methods. Code can be found at https://github.com/xinyuluo8561/Stacey .

cs.LG↗

arXiv2025

Model Immunization from a Condition Number Perspective

Model immunization aims to pre-train models that are difficult to fine-tune on harmful tasks while retaining their utility on other non-harmful tasks. Though prior work has shown empirical evidence for immunizing text-to-image models, the key understanding of when immunization is possible and a precise definition of an immunized model remain unclear. In this work, we propose a framework, based on the condition number of a Hessian matrix, to analyze model immunization for linear models. Building on this framework, we design an algorithm with regularization terms to control the resulting condition numbers after pre-training. Empirical results on linear models and non-linear deep-nets demonstrate the effectiveness of the proposed algorithm on model immunization. The code is available at https://github.com/amberyzheng/model-immunization-cond-num.

cs.LG↗