Alex Cloninger

Noreen Jamil, Xuemei Chen, Alex Cloninger

The Hildreth's algorithm is a row action method for solving large systems of inequalities. This algorithm is efficient for problems with sparse matrices, as opposed to direct methods such as Gaussian elimination or QR-factorization. We apply the Hildreth's algorithm, as well as a randomized version, along with prioritized selection of the inequalities, to efficiently detect the highest priority feasible subsystem of equations. We prove convergence results and feasibility criteria for both cyclic and randomized Hildreth's algorithm, as well as a mixed algorithm which uses Hildreth's algorithm for inequalities and Kaczmarz algorithm for equalities. These prioritized, sparse systems of inequalities commonly appear in constraint-based user interface (UI) layout specifications. The performance and convergence of these proposed algorithms are evaluated empirically using randomly generated UI layout specifications of various sizes. The results show that these methods offer improvements in performance over standard methods like Matlab's LINPROG, a well-known efficient linear programming solver, and the recent developed Kaczmarz algorithm with prioritized IIS detection.

Yiming Zhang, Sitong Liu, Alex Cloninger

We address the computational and theoretical limitations of current distributional alignment methods for source-free unsupervised domain adaptation (SFUDA) using source class-mean features. In particular, we focus on estimating classification performance and confidence in the absence of target labels. Current theoretical frameworks for these methods often yield computationally intractable quantities and fail to adequately reflect the properties of the alignment algorithms employed. To overcome these challenges, we introduce the Optimal Transport (OT) score, a confidence metric derived from a novel theoretical analysis that exploits the flexibility of decision boundaries induced by Semi-Discrete Optimal Transport alignment. The proposed OT score is intuitively interpretable and theoretically rigorous. It provides principled uncertainty estimates for any given set of target pseudo-labels. Experimental results demonstrate that OT score outperforms existing confidence scores. Moreover, it improves SFUDA performance through training-time reweighting and provides a reliable, label-free proxy for model performance.

Joshua Lentz, Nicholas Karris, Alex Cloninger et al.

Hyperspectral images capture vast amounts of high-dimensional spectral information about a scene, making labeling an intensive task that is resistant to out-of-the-box statistical methods. Unsupervised learning of clusters allows for automated segmentation of the scene, enabling a more rapid understanding of the image. Partitioning the spectral information contained within the data via dictionary learning in Wasserstein space has proven an effective method for unsupervised clustering. However, this approach requires balancing the spectral profiles of the data, blurring the classes, and sacrificing robustness to outliers and noise. In this paper, we suggest improving this approach by utilizing unbalanced Wasserstein barycenters to learn a lower-dimensional representation of the underlying data. The deployment of spectral clustering on the learned representation results in an effective approach for the unsupervised learning of labels.

Yiming Zhang, Chester Holtz, Gal Mishne et al.

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.

Robi Bhattacharjee, Alex Cloninger, Yoav Freund et al.

Effective resistance (ER) is an attractive way to interrogate the structure of graphs. It is an alternative to computing the eigen-vectors of the graph Laplacian. Graph laplacians are used to find low dimensional structures in high dimensional data. Here too, ER based analysis has advantages over eign-vector based methods. Unfortunately Von Luxburg et al. (2010) show that, when vertices correspond to a sample from a distribution over a metric space, the limit of the ER between distant points converges to a trivial quantity that holds no information about the structure of the graph. We show that by using scaling resistances in a graph with $n$ vertices by $n^2$, one gets a meaningful limit of the voltages and of effective resistances. We also show that by adding a "ground" node to a metric graph one gets a simple and natural way to compute all of the distances from a chosen point to all other points.

Scott Mahan, Emily King, Alex Cloninger

We examine the closedness of sets of realized neural networks of a fixed architecture in Sobolev spaces. For an exactly $m$-times differentiable activation function $ρ$, we construct a sequence of neural networks $(Φ_n)_{n \in \mathbb{N}}$ whose realizations converge in order-$(m-1)$ Sobolev norm to a function that cannot be realized exactly by a neural network. Thus, sets of realized neural networks are not closed in order-$(m-1)$ Sobolev spaces $W^{m-1,p}$ for $p \in [1,\infty]$. We further show that these sets are not closed in $W^{m,p}$ under slightly stronger conditions on the $m$-th derivative of $ρ$. For a real analytic activation function, we show that sets of realized neural networks are not closed in $W^{k,p}$ for any $k \in \mathbb{N}$. The nonclosedness allows for approximation of non-network target functions with unbounded parameter growth. We partially characterize the rate of parameter growth for most activation functions by showing that a specific sequence of realized neural networks can approximate the activation function's derivative with weights increasing inversely proportional to the $L^p$ approximation error. Finally, we present experimental results showing that networks are capable of closely approximating non-network target functions with increasing parameters via training.

Ahmed T. Elthakeb, Prannoy Pilligundla, Alex Cloninger et al.

The deep layers of modern neural networks extract a rather rich set of features as an input propagates through the network. This paper sets out to harvest these rich intermediate representations for quantization with minimal accuracy loss while significantly reducing the memory footprint and compute intensity of the DNN. This paper utilizes knowledge distillation through teacher-student paradigm (Hinton et al., 2015) in a novel setting that exploits the feature extraction capability of DNNs for higher-accuracy quantization. As such, our algorithm logically divides a pretrained full-precision DNN to multiple sections, each of which exposes intermediate features to train a team of students independently in the quantized domain. This divide and conquer strategy, in fact, makes the training of each student section possible in isolation while all these independently trained sections are later stitched together to form the equivalent fully quantized network. Our algorithm is a sectional approach towards knowledge distillation and is not treating the intermediate representation as a hint for pretraining before one knowledge distillation pass over the entire network (Romero et al., 2015). Experiments on various DNNs (AlexNet, LeNet, MobileNet, ResNet-18, ResNet-20, SVHN and VGG-11) show that, this approach -- called DCQ (Divide and Conquer Quantization) -- on average, improves the performance of a state-of-the-art quantized training technique, DoReFa-Net (Zhou et al., 2016) by 21.6% and 9.3% for binary and ternary quantization, respectively. Additionally, we show that incorporating DCQ to existing quantized training methods leads to improved accuracies as compared to previously reported by multiple state-of-the-art quantized training methods.

Uri Shaham, James Garritano, Yutaro Yamada et al.

We study the effectiveness of various approaches that defend against adversarial attacks on deep networks via manipulations based on basis function representations of images. Specifically, we experiment with low-pass filtering, PCA, JPEG compression, low resolution wavelet approximation, and soft-thresholding. We evaluate these defense techniques using three types of popular attacks in black, gray and white-box settings. Our results show JPEG compression tends to outperform the other tested defenses in most of the settings considered, in addition to soft-thresholding, which performs well in specific cases, and yields a more mild decrease in accuracy on benign examples. In addition, we also mathematically derive a novel white-box attack in which the adversarial perturbation is composed only of terms corresponding a to pre-determined subset of the basis functions, of which a "low frequency attack" is a special case.