arXiv subjects

Chester Holtz

Publications and source records attributed to Chester Holtz.

12 recordsLinked to original sources

arXiv2025

Revisiting Meta-Learning with Noisy Labels: Reweighting Dynamics and Theoretical Guarantees

Learning with noisy labels remains challenging because over-parameterized networks memorize corrupted supervision. Meta-learning-based sample reweighting mitigates this by using a small clean subset to guide training, yet its behavior and training dynamics lack theoretical understanding. We provide a rigorous theoretical analysis of meta-reweighting under label noise and show that its training trajectory unfolds in three phases: (i) an alignment phase that amplifies examples consistent with a clean subset and suppresses conflicting ones; (ii) a filtering phase driving noisy example weights toward zero until the clean subset loss plateaus; and (iii) a post-filtering phase in which noise filtration becomes perturbation-sensitive. The mechanism is a similarity-weighted coupling between training and clean subset signals together with clean subset training loss contraction; in the post-filtering regime where the clean-subset loss is sufficiently small, the coupling term vanishes and meta-reweighting loses discriminatory power. Guided by this analysis, we propose a lightweight surrogate for meta-reweighting that integrates mean-centering, row shifting, and label-signed modulation, yielding more stable performance while avoiding expensive bi-level optimization. Across synthetic and real noisy-label benchmarks, our method consistently outperforms strong reweighting/selection baselines.

cs.LG↗

arXiv2025

Robust Graph-Based Semi-Supervised Learning via $p$-Conductances

We study the problem of semi-supervised learning on graphs in the regime where data labels are scarce or possibly corrupted. We propose an approach called $p$-conductance learning that generalizes the $p$-Laplace and Poisson learning methods by introducing an objective reminiscent of $p$-Laplacian regularization and an affine relaxation of the label constraints. This leads to a family of probability measure mincut programs that balance sparse edge removal with accurate distribution separation. Our theoretical analysis connects these programs to well-known variational and probabilistic problems on graphs (including randomized cuts, effective resistance, and Wasserstein distance) and provides motivation for robustness when labels are diffused via the heat kernel. Computationally, we develop a semismooth Newton-conjugate gradient algorithm and extend it to incorporate class-size estimates when converting the continuous solutions into label assignments. Empirical results on computer vision and citation datasets demonstrate that our approach achieves state-of-the-art accuracy in low label-rate, corrupted-label, and partial-label regimes.

cs.LG↗

arXiv2024

Robust boundary detection and density estimation using doubly stochastic scaling of the Gaussian kernel

This paper addresses the problem of detecting boundary points and estimating the sampling density of a dataset derived from a compact manifold with boundary, potentially in the presence of noise. We extend recent advances in doubly stochastic scaling of the Gaussian heat kernel via Sinkhorn iterations to this setting. Our main contributions are: (a) deriving a characterization of the scaling factors for manifolds with boundary, (b) developing a boundary direction estimator aimed at identifying boundary points followed by a boundary-corrected kernel density estimator based on doubly stochastic kernel and local principal component analysis, and (c) demonstrating through simulations that the resulting estimates of the boundary points and the sampling density outperform the standard Gaussian kernel-based approach, particularly under noisy conditions.

math.ST↗

arXiv2024

Sequential subspace methods on Stiefel manifold optimization

We investigate the minimization of a quadratic function over Stiefel manifolds (the set of all orthogonal $r$- frames in $\mathbf{R}^n$), which has applications in high-dimensional semi-supervised classification tasks. To reduce the computational complexity, we employ sequential subspace methods(SSM) to transform the high-dimensional problem to a series of low-dimensional ones. In this paper, our goal is to achieve an optimal solution of high quality, referred to as a ''qualified critical point". Qualified critical points are defined as those where the associated multiplier matrix meets specific upper-bound conditions. These points exhibit near-global optimality in quadratic optimization problems. In the context of a general quadratic, SSM generates a sequence of qualified critical points through low-dimensional surrogate regularized models. The convergence to a qualified critical point is guaranteed, when each SSM subspace is constructed from the following vectors: (i) a set of orthogonal unit vectors associated with the current iterate, (ii) a set of vectors representing the gradient of the objective, and (iii) a set of eigenvectors links to the smallest $r$ eigenvalues of the system matrix. Furthermore, incorporating Newton direction vectors into the subspaces can significantly accelerate the convergence of SSM.

math.OC↗

arXiv2024

On Robustness and Generalization of ML-Based Congestion Predictors to Valid and Imperceptible Perturbations

There is substantial interest in the use of machine learning (ML)-based techniques throughout the electronic computer-aided design (CAD) flow, particularly methods based on deep learning. However, while deep learning methods have achieved state-of-the-art performance in several applications, recent work has demonstrated that neural networks are generally vulnerable to small, carefully chosen perturbations of their input (e.g. a single pixel change in an image). In this work, we investigate robustness in the context of ML-based EDA tools -- particularly for congestion prediction. As far as we are aware, we are the first to explore this concept in the context of ML-based EDA. We first describe a novel notion of imperceptibility designed specifically for VLSI layout problems defined on netlists and cell placements. Our definition of imperceptibility is characterized by a guarantee that a perturbation to a layout will not alter its global routing. We then demonstrate that state-of-the-art CNN and GNN-based congestion models exhibit brittleness to imperceptible perturbations. Namely, we show that when a small number of cells (e.g. 1%-5% of cells) have their positions shifted such that a measure of global congestion is guaranteed to remain unaffected (e.g. 1% of the design adversarially shifted by 0.001% of the layout space results in a predicted decrease in congestion of up to 90%, while no change in congestion is implied by the perturbation). In other words, the quality of a predictor can be made arbitrarily poor (i.e. can be made to predict that a design is "congestion-free") for an arbitrary input layout. Next, we describe a simple technique to train predictors that improves robustness to these perturbations. Our work indicates that CAD engineers should be cautious when integrating neural network-based mechanisms in EDA flows to ensure robust and high-quality results.

cs.LG↗

arXiv2023

Semi-Supervised Laplace Learning on Stiefel Manifolds

Motivated by the need to address the degeneracy of canonical Laplace learning algorithms in low label rates, we propose to reformulate graph-based semi-supervised learning as a nonconvex generalization of a \emph{Trust-Region Subproblem} (TRS). This reformulation is motivated by the well-posedness of Laplacian eigenvectors in the limit of infinite unlabeled data. To solve this problem, we first show that a first-order condition implies the solution of a manifold alignment problem and that solutions to the classical \emph{Orthogonal Procrustes} problem can be used to efficiently find good classifiers that are amenable to further refinement. To tackle refinement, we develop the framework of Sequential Subspace Optimization for graph-based SSL. Next, we address the criticality of selecting supervised samples at low-label rates. We characterize informative samples with a novel measure of centrality derived from the principal eigenvectors of a certain submatrix of the graph Laplacian. We demonstrate that our framework achieves lower classification error compared to recent state-of-the-art and classical semi-supervised learning methods at extremely low, medium, and high label rates.

cs.LG↗

arXiv2022

Net Separation-Oriented Printed Circuit Board Placement via Margin Maximization

Packaging has become a crucial process due to the paradigm shift of More than Moore. Addressing manufacturing and yield issues is a significant challenge for modern layout algorithms. We propose to use printed circuit board (PCB) placement as a benchmark for the packaging problem. A maximum-margin formulation is devised to improve the separation between nets. Our framework includes seed layout proposals, a coordinate descent-based procedure to optimize routability, and a mixed-integer linear programming method to legalize the layout. We perform an extensive study with 14 PCB designs and an open-source router. We show that the placements produced by NS-place improve routed wirelength by up to 25\%, reduce the number of vias by up to 50\%, and reduce the number of DRVs by 79\% compared to manual and wirelength-minimal placements.

cs.CG↗

arXiv2022

Learning Sample Reweighting for Accuracy and Adversarial Robustness

There has been great interest in enhancing the robustness of neural network classifiers to defend against adversarial perturbations through adversarial training, while balancing the trade-off between robust accuracy and standard accuracy. We propose a novel adversarial training framework that learns to reweight the loss associated with individual training samples based on a notion of class-conditioned margin, with the goal of improving robust generalization. We formulate weighted adversarial training as a bilevel optimization problem with the upper-level problem corresponding to learning a robust classifier, and the lower-level problem corresponding to learning a parametric function that maps from a sample's \textit{multi-class margin} to an importance weight. Extensive experiments demonstrate that our approach consistently improves both clean and robust accuracy compared to related methods and state-of-the-art baselines.

cs.LG↗

arXiv2022

Evaluating Disentanglement in Generative Models Without Knowledge of Latent Factors

Probabilistic generative models provide a flexible and systematic framework for learning the underlying geometry of data. However, model selection in this setting is challenging, particularly when selecting for ill-defined qualities such as disentanglement or interpretability. In this work, we address this gap by introducing a method for ranking generative models based on the training dynamics exhibited during learning. Inspired by recent theoretical characterizations of disentanglement, our method does not require supervision of the underlying latent factors. We evaluate our approach by demonstrating the need for disentanglement metrics which do not require labels\textemdash the underlying generative factors. We additionally demonstrate that our approach correlates with baseline supervised methods for evaluating disentanglement. Finally, we show that our method can be used as an unsupervised indicator for downstream performance on reinforcement learning and fairness-classification problems.

cs.LG↗

arXiv2021

Online Adversarial Purification based on Self-Supervision

Deep neural networks are known to be vulnerable to adversarial examples, where a perturbation in the input space leads to an amplified shift in the latent network representation. In this paper, we combine canonical supervised learning with self-supervised representation learning, and present Self-supervised Online Adversarial Purification (SOAP), a novel defense strategy that uses a self-supervised loss to purify adversarial examples at test-time. Our approach leverages the label-independent nature of self-supervised signals and counters the adversarial perturbation with respect to the self-supervised tasks. SOAP yields competitive robust accuracy against state-of-the-art adversarial training and purification methods, with considerably less training complexity. In addition, our approach is robust even when adversaries are given knowledge of the purification defense strategy. To the best of our knowledge, our paper is the first that generalizes the idea of using self-supervised signals to perform online test-time purification.

cs.LG↗

arXiv2015

Comparative Analysis of Classic Garbage-Collection Algorithms for a Lisp-like Language

In this paper, we demonstrate the effectiveness of Cheney's Copy Algorithm for a Lisp-like system and experimentally show the infeasability of developing an optimal garbage collector for general use. We summarize and compare several garbage-collection algorithms including Cheney's Algorithm, the canonical Mark and Sweep Algorithm, and Knuth's Classical Lisp 2 Algorithm. We implement and analyze these three algorithms in the context of a custom MicroLisp environment. We conclude and present the core considerations behind the development of a garbage collector---specifically for Lisp---and make an attempt to investigate these issues in depth. We also discuss experimental results that imply the effectiveness of Cheney's algorithm over Mark-Sweep for Lisp-like languages.

cs.PL↗

arXiv2015

A Refutation of the Clique-Based P=NP Proofs of LaPlante and Tamta-Pande-Dhami

In this work, we critique two papers, "A Polynomial-Time Solution to the Clique Problem" by Tamta, Pande, and Dhami, and "A Polynomial-Time Algorithm For Solving Clique Problems" by LaPlante. We summarize and analyze both papers, noting that the algorithms presented in both papers are flawed. We conclude that neither author has successfully established that P = NP.

cs.CC↗