Training Deep Visual Networks Beyond Loss and Accuracy Through a Dynamical Systems Approach

Deep visual recognition models are usually trained and evaluated using metrics such as loss and accuracy. While these measures show whether a model is improving, they reveal very little about how its internal representations change during training. This paper introduces a complementary way to study that process by examining training through the lens of dynamical systems. Drawing on ideas from signal analysis originally used to study biological neural activity, we define three measures from layer activations collected across training epochs: an integration score that reflects long-range coordination across layers, a metastability score that captures how flexibly the network shifts between more and less synchronised states, and a combined dynamical stability index. We apply this framework to nine combinations of model architecture and dataset, including several ResNet variants, DenseNet-121, MobileNetV2, VGG-16, and a pretrained Vision Transformer on CIFAR-10 and CIFAR-100. The results suggest three main patterns. First, the integration measure consistently distinguishes the easier CIFAR-10 setting from the more difficult CIFAR-100 setting. Second, changes in the volatility of the stability index may provide an early sign of convergence before accuracy fully plateaus. Third, the relationship between integration and metastability appears to reflect different styles of training behaviour. Overall, this study offers an exploratory but promising new way to understand deep visual training beyond loss and accuracy.

A Neural Tension Operator for Curve Subdivision across Constant Curvature Geometries

Interpolatory subdivision schemes generate smooth curves from piecewise-linear control polygons by repeatedly inserting new vertices. Classical schemes rely on a single global tension parameter and typically require separate formulations in Euclidean, spherical, and hyperbolic geometries. We introduce a shared learned tension predictor that replaces the global parameter with per-edge insertion angles predicted by a single 140K-parameter network. The network takes local intrinsic features and a trainable geometry embedding as input, and the predicted angles drive geometry-specific insertion operators across all three spaces without architectural modification. A constrained sigmoid output head enforces a structural safety bound, guaranteeing that every inserted vertex lies within a valid angular range for any finite weight configuration. Three theoretical results accompany the method: a structural guarantee of tangent-safe insertions; a heuristic motivation for per-edge adaptivity; and a conditional convergence certificate for continuously differentiable limit curves, subject to an explicit Lipschitz constraint verified post hoc. On 240 held-out validation curves, the learned predictor occupies a distinct position on the fidelity--smoothness Pareto frontier, achieving markedly lower bending energy and angular roughness than all fixed-tension and manifold-lift baselines. Riemannian manifold lifts retain a pointwise-fidelity advantage, which this study quantifies directly. On the out-of-distribution ISS orbital ground-track example, bending energy falls by 41% and angular roughness by 68% with only a modest increase in Hausdorff distance, suggesting that the predictor generalises beyond its synthetic training distribution.

Handcrafted Feature-Assisted One-Class Learning for Artist Authentication in Historical Drawings

Authentication and attribution of works on paper remain persistent challenges in cultural heritage, particularly when the available reference corpus is small and stylistic cues are primarily expressed through line and limited tonal variation. We present a verification-based computational framework for historical drawing authentication using one-class autoencoders trained on a compact set of interpretable handcrafted features. Ten artist-specific verifiers are trained using authenticated sketches from the Metropolitan Museum of Art open-access collection, the Ashmolean Collections Catalogue, the Morgan Library and Museum, the Royal Collection Trust (UK), the Victoria and Albert Museum Collections, and an online catalogue of the Casa Buonarroti collection and evaluated under a biometric-style protocol with genuine and impostor trials. Feature vectors comprise Fourier-domain energy, Shannon entropy, global contrast, GLCM-based homogeneity, and a box-counting estimate of fractal complexity. Across 900 verification decisions (90 genuine and 810 impostor trials), the pooled system achieves a True Acceptance Rate of 83.3% with a False Acceptance Rate of 9.5% at the chosen operating point. Performance varies substantially by artist, with near-zero false acceptance for some verifiers and elevated confusability for others. A pairwise attribution of false accepts indicates structured error pathways consistent with stylistic proximity and shared drawing conventions, whilst also motivating tighter control of digitisation artefacts and threshold calibration. The proposed methodology is designed to complement, rather than replace, connoisseurship by providing reproducible, quantitative evidence suitable for data-scarce settings common in historical sketch attribution.

Dynamical Systems Analysis Reveals Functional Regimes in Large Language Models

Large language models perform text generation through high-dimensional internal dynamics, yet the temporal organisation of these dynamics remains poorly understood. Most interpretability approaches emphasise static representations or causal interventions, leaving temporal structure largely unexplored. Drawing on neuroscience, where temporal integration and metastability are core markers of neural organisation, we adapt these concepts to transformer models and discuss a composite dynamical metric, computed from activation time-series during autoregressive generation. We evaluate this metric in GPT-2-medium across five conditions: structured reasoning, forced repetition, high-temperature noisy sampling, attention-head pruning, and weight-noise injection. Structured reasoning consistently exhibits elevated metric relative to repetitive, noisy, and perturbed regimes, with statistically significant differences confirmed by one-way ANOVA and large effect sizes in key comparisons. These results are robust to layer selection, channel subsampling, and random seeds. Our findings demonstrate that neuroscience-inspired dynamical metrics can reliably characterise differences in computational organisation across functional regimes in large language models. We stress that the proposed metric captures formal dynamical properties and does not imply subjective experience.

DFA-CON: A Contrastive Learning Approach for Detecting Copyright Infringement in DeepFake Art

Recent proliferation of generative AI tools for visual content creation-particularly in the context of visual artworks-has raised serious concerns about copyright infringement and forgery. The large-scale datasets used to train these models often contain a mixture of copyrighted and non-copyrighted artworks. Given the tendency of generative models to memorize training patterns, they are susceptible to varying degrees of copyright violation. Building on the recently proposed DeepfakeArt Challenge benchmark, this work introduces DFA-CON, a contrastive learning framework designed to detect copyright-infringing or forged AI-generated art. DFA-CON learns a discriminative representation space, posing affinity among original artworks and their forged counterparts within a contrastive learning framework. The model is trained across multiple attack types, including inpainting, style transfer, adversarial perturbation, and cutmix. Evaluation results demonstrate robust detection performance across most attack types, outperforming recent pretrained foundation models. Code and model checkpoints will be released publicly upon acceptance.