arXiv subjects

Parniyan Farvardin

Publications and source records attributed to Parniyan Farvardin.

3 recordsLinked to original sources

arXiv2026

Why CNN Features Are not Gaussian: A Statistical Anatomy of Deep Representations

Deep convolutional neural networks (CNNs) are commonly analyzed through geometric and linear-algebraic perspectives, yet the statistical distribution of their internal feature activations remains poorly understood. In many applications, deep features are implicitly treated as Gaussian when modeling densities. In this work, we empirically examine this assumption and show that it does not accurately describe the distribution of CNN feature activations. Through a systematic study across multiple architectures and datasets, we find that the feature activations deviate substantially from Gaussian and are better characterized by Weibull and related long-tailed distributions. We further introduce a novel Discretized Characteristic Function Copula (DCF-Copula) method to model multivariate feature dependencies. We find that tail-length increases with network depth and that upper-tail dependence emerges between feature pairs. These statistical findings are not consistent with the Central Limit Theorem, and are instead indicative of a Matthew process that progressively concentrates semantic signal within the tails. These statistical findings suggest that CNNs are excellent at noise reduction, yet poor at outlier removal tasks. We recommend the use of long-tailed upper-tail-dependent priors as opposed to Gaussian priors for accurately CNN deep feature density. Code available at https://github.com/dchapman-prof/DCF-Copula

cs.CV↗

arXiv2026

End-to-end Feature Alignment: A Simple CNN with Intrinsic Class Attribution

We present Feature-Align CNN (FA-CNN), a prototype CNN architecture with intrinsic class attribution through end-to-end feature alignment. Our intuition is that the use of unordered operations such as Linear and Conv2D layers cause unnecessary shuffling and mixing of semantic concepts, thereby making raw feature maps difficult to understand. We introduce two new order preserving layers, the dampened skip connection, and the global average pooling classifier head. These layers force the model to maintain an end-to-end feature alignment from the raw input pixels all the way to final class logits. This end-to-end alignment enhances the interpretability of the model by allowing the raw feature maps to intrinsically exhibit class attribution. We prove theoretically that FA-CNN penultimate feature maps are identical to Grad-CAM saliency maps. Moreover, we prove that these feature maps slowly morph layer-by-layer over network depth, showing the evolution of features through network depth toward penultimate class activations. FA-CNN performs well on benchmark image classification datasets. Moreover, we compare the averaged FA-CNN raw feature maps against Grad-CAM and permutation methods in a percent pixels removed interpretability task. We conclude this work with a discussion and future, including limitations and extensions toward hybrid models.

cs.CV↗

arXiv2024

A Method of Moments Embedding Constraint and its Application to Semi-Supervised Learning

Discriminative deep learning models with a linear+softmax final layer have a problem: the latent space only predicts the conditional probabilities $p(Y|X)$ but not the full joint distribution $p(Y,X)$, which necessitates a generative approach. The conditional probability cannot detect outliers, causing outlier sensitivity in softmax networks. This exacerbates model over-confidence impacting many problems, such as hallucinations, confounding biases, and dependence on large datasets. To address this we introduce a novel embedding constraint based on the Method of Moments (MoM). We investigate the use of polynomial moments ranging from 1st through 4th order hyper-covariance matrices. Furthermore, we use this embedding constraint to train an Axis-Aligned Gaussian Mixture Model (AAGMM) final layer, which learns not only the conditional, but also the joint distribution of the latent space. We apply this method to the domain of semi-supervised image classification by extending FlexMatch with our technique. We find our MoM constraint with the AAGMM layer is able to match the reported FlexMatch accuracy, while also modeling the joint distribution, thereby reducing outlier sensitivity. We also present a preliminary outlier detection strategy based on Mahalanobis distance and discuss future improvements to this strategy. Code is available at: \url{https://github.com/mmajurski/ssl-gmm}

cs.CV↗