George Pavlidis

Vasileios Arampatzakis, George Pavlidis, Nikolaos Mitianoudis et al.

Vision Transformers (ViTs) have achieved state-of-the-art performance in image classification, yet their attention mechanisms often remain opaque and exhibit dense, non-structured behaviors. In this work, we adapt our previously proposed SVD-Inspired Attention (SVDA) mechanism to the ViT architecture, introducing a geometrically grounded formulation that enhances interpretability, sparsity, and spectral structure. We apply the use of interpretability indicators -- originally proposed with SVDA -- to monitor attention dynamics during training and assess structural properties of the learned representations. Experimental evaluations on four widely used benchmarks -- CIFAR-10, FashionMNIST, CIFAR-100, and ImageNet-100 -- demonstrate that SVDA consistently yields more interpretable attention patterns without sacrificing classification accuracy. While the current framework offers descriptive insights rather than prescriptive guidance, our results establish SVDA as a comprehensive and informative tool for analyzing and developing structured attention models in computer vision. This work lays the foundation for future advances in explainable AI, spectral diagnostics, and attention-based model compression.

Vasileios Sevetlidis, George Pavlidis

Deep networks learn internal representations whose geometry--how features bend, rotate, and evolve--affects both generalization and robustness. Existing similarity measures such as CKA or SVCCA capture pointwise overlap between activation sets, but miss how representations change along input paths. Two models may appear nearly identical under these metrics yet respond very differently to perturbations or adversarial stress. We introduce representation holonomy, a gauge-invariant statistic that measures this path dependence. Conceptually, holonomy quantifies the "twist" accumulated when features are parallel-transported around a small loop in input space: flat representations yield zero holonomy, while nonzero values reveal hidden curvature. Our estimator fixes gauge through global whitening, aligns neighborhoods using shared subspaces and rotation-only Procrustes, and embeds the result back to the full feature space. We prove invariance to orthogonal (and affine, post-whitening) transformations, establish a linear null for affine layers, and show that holonomy vanishes at small radii. Empirically, holonomy increases with loop radius, separates models that appear similar under CKA, and correlates with adversarial and corruption robustness. It also tracks training dynamics as features form and stabilize. Together, these results position representation holonomy as a practical and scalable diagnostic for probing the geometric structure of learned representations beyond pointwise similarity.

Vasileios Sevetlidis, George Pavlidis

This work proposes neural training as a \emph{process tensor}: a multi-time map that takes a sequence of controllable instruments (batch choices, augmentations, optimizer micro-steps) and returns an observable of the trained model. Building on this operational lens, we introduce a simple, model-agnostic witness of training memory based on \emph{back-flow of distinguishability}. In a controlled two-step protocol, we compare outcome distributions after one intervention versus two; the increase $Δ_{\mathrm{BF}} = D_2 - D_1>0$ (with $D\in\{\mathrm{TV}, \mathrm{JS}, \mathrm{H}\}$ measured on softmax predictions over a fixed probe set) certifies non-Markovianity. We observe consistent positive back-flow with tight bootstrap confidence intervals, amplification under higher momentum, larger batch overlap, and more micro-steps, and collapse under a \emph{causal break} (resetting optimizer state), directly attributing the effect to optimizer/data-state memory. The witness is robust across TV/JS/Hellinger, inexpensive to compute, and requires no architectural changes. We position this as a \emph{measurement} contribution: a principled diagnostic and empirical evidence that practical SGD deviates from the Markov idealization. An exploratory case study illustrates how the micro-level signal can inform curriculum orderings. "Data order matters" turns into a testable operator with confidence bounds, our framework offers a common stage to compare optimizers, curricula, and schedules through their induced training memory.

Vasileios Sevetlidis, George Pavlidis

Modern deep-learning training is not memoryless. Updates depend on optimizer moments and averaging, data-order policies (random reshuffling vs with-replacement, staged augmentations and replay), the nonconvex path, and auxiliary state (teacher EMA/SWA, contrastive queues, BatchNorm statistics). This survey organizes mechanisms by source, lifetime, and visibility. It introduces seed-paired, function-space causal estimands; portable perturbation primitives (carry/reset of momentum/Adam/EMA/BN, order-window swaps, queue/teacher tweaks); and a reporting checklist with audit artifacts (order hashes, buffer/BN checksums, RNG contracts). The conclusion is a protocol for portable, causal, uncertainty-aware measurement that attributes how much training history matters across models, data, and regimes.