Implicit bias produces neural scaling laws in learning curves, from perceptrons to deep networks

Scaling laws in deep learning - empirical power-law relationships linking model performance to resource growth - have emerged as simple yet striking regularities across architectures, datasets, and tasks. These laws are particularly impactful in guiding the design of state-of-the-art models, since they quantify the benefits of increasing data or model size, and hint at the foundations of interpretability in machine learning. However, most studies focus on asymptotic behavior at the end of training or on the optimal training time given the model size. In this work, we uncover a richer picture by analyzing the entire training dynamics through the lens of spectral complexity norms. We identify two novel dynamical scaling laws that govern how performance evolves during training. These laws together recover the well-known test error scaling at convergence, offering a mechanistic explanation of generalization emergence. Our findings are consistent across CNNs, ResNets, and Vision Transformers trained on MNIST, CIFAR-10 and CIFAR-100. Furthermore, we provide analytical support using a solvable model: a single-layer perceptron trained with binary cross-entropy. In this setting, we show that the growth of spectral complexity driven by the implicit bias mirrors the generalization behavior observed at fixed norm, allowing us to connect the performance dynamics to classical learning rules in the perceptron.

The role of data partitioning on the performance of EEG-based deep learning models in supervised cross-subject analysis: a preliminary study

Deep learning is significantly advancing the analysis of electroencephalography (EEG) data by effectively discovering highly nonlinear patterns within the signals. Data partitioning and cross-validation are crucial for assessing model performance and ensuring study comparability, as they can produce varied results and data leakage due to specific signal properties (e.g., biometric). Such variability leads to incomparable studies and, increasingly, overestimated performance claims, which are detrimental to the field. Nevertheless, no comprehensive guidelines for proper data partitioning and cross-validation exist in the domain, nor is there a quantitative evaluation of their impact on model accuracy, reliability, and generalizability. To assist researchers in identifying optimal experimental strategies, this paper thoroughly investigates the role of data partitioning and cross-validation in evaluating EEG deep learning models. Five cross-validation settings are compared across three supervised cross-subject classification tasks (BCI, Parkinson's, and Alzheimer's disease detection) and four established architectures of increasing complexity (ShallowConvNet, EEGNet, DeepConvNet, and Temporal-based ResNet). The comparison of over 100,000 trained models underscores, first, the importance of using subject-based cross-validation strategies for evaluating EEG deep learning models, except when within-subject analyses are acceptable (e.g., BCI). Second, it highlights the greater reliability of nested approaches (N-LNSO) compared to non-nested counterparts, which are prone to data leakage and favor larger models overfitting to validation data. In conclusion, this work provides EEG deep learning researchers with an analysis of data partitioning and cross-validation and offers guidelines to avoid data leakage, currently undermining the domain with potentially overestimated performance claims.

Automatic Complementary Separation Pruning Toward Lightweight CNNs

In this paper, we present Automatic Complementary Separation Pruning (ACSP), a novel and fully automated pruning method for convolutional neural networks. ACSP integrates the strengths of both structured pruning and activation-based pruning, enabling the efficient removal of entire components such as neurons and channels while leveraging activations to identify and retain the most relevant components. Our approach is designed specifically for supervised learning tasks, where we construct a graph space that encodes the separation capabilities of each component with respect to all class pairs. By employing complementary selection principles and utilizing a clustering algorithm, ACSP ensures that the selected components maintain diverse and complementary separation capabilities, reducing redundancy and maintaining high network performance. The method automatically determines the optimal subset of components in each layer, utilizing a knee-finding algorithm to select the minimal subset that preserves performance without requiring user-defined pruning volumes. Extensive experiments on multiple architectures, including VGG-16, ResNet-50, and MobileNet-V2, across datasets like CIFAR-10, CIFAR-100, and ImageNet-1K, demonstrate that ACSP achieves competitive accuracy compared to other methods while significantly reducing computational costs. This fully automated approach not only enhances scalability but also makes ACSP especially practical for real-world deployment by eliminating the need for manually defining the pruning volume.

Guiding Diffusion with Deep Geometric Moments: Balancing Fidelity and Variation

Text-to-image generation models have achieved remarkable capabilities in synthesizing images, but often struggle to provide fine-grained control over the output. Existing guidance approaches, such as segmentation maps and depth maps, introduce spatial rigidity that restricts the inherent diversity of diffusion models. In this work, we introduce Deep Geometric Moments (DGM) as a novel form of guidance that encapsulates the subject's visual features and nuances through a learned geometric prior. DGMs focus specifically on the subject itself compared to DINO or CLIP features, which suffer from overemphasis on global image features or semantics. Unlike ResNets, which are sensitive to pixel-wise perturbations, DGMs rely on robust geometric moments. Our experiments demonstrate that DGM effectively balance control and diversity in diffusion-based image generation, allowing a flexible control mechanism for steering the diffusion process.

Parameter Efficient Continual Learning with Dynamic Low-Rank Adaptation

Catastrophic forgetting has remained a critical challenge for deep neural networks in Continual Learning (CL) as it undermines consolidated knowledge when learning new tasks. Parameter efficient fine tuning CL techniques are gaining traction for their effectiveness in addressing catastrophic forgetting with a lightweight training schedule while avoiding degradation of consolidated knowledge in pre-trained models. However, low rank adapters (LoRA) in these approaches are highly sensitive to rank selection which can lead to sub-optimal resource allocation and performance. To this end, we introduce PEARL, a rehearsal-free CL framework that entails dynamic rank allocation for LoRA components during CL training. Specifically, PEARL leverages reference task weights and adaptively determines the rank of task-specific LoRA components based on the current tasks' proximity to reference task weights in parameter space. To demonstrate the versatility of PEARL, we evaluate it across three vision architectures (ResNet, Separable Convolutional Network and Vision Transformer) and a multitude of CL scenarios, and show that PEARL outperforms all considered baselines by a large margin.

Facial Recognition Leveraging Generative Adversarial Networks

Face recognition performance based on deep learning heavily relies on large-scale training data, which is often difficult to acquire in practical applications. To address this challenge, this paper proposes a GAN-based data augmentation method with three key contributions: (1) a residual-embedded generator to alleviate gradient vanishing/exploding problems, (2) an Inception ResNet-V1 based FaceNet discriminator for improved adversarial training, and (3) an end-to-end framework that jointly optimizes data generation and recognition performance. Experimental results demonstrate that our approach achieves stable training dynamics and significantly improves face recognition accuracy by 12.7% on the LFW benchmark compared to baseline methods, while maintaining good generalization capability with limited training samples.

Approximation theory for 1-Lipschitz ResNets

1-Lipschitz neural networks are fundamental for generative modelling, inverse problems, and robust classifiers. In this paper, we focus on 1-Lipschitz residual networks (ResNets) based on explicit Euler steps of negative gradient flows and study their approximation capabilities. Leveraging the Restricted Stone-Weierstrass Theorem, we first show that these 1-Lipschitz ResNets are dense in the set of scalar 1-Lipschitz functions on any compact domain when width and depth are allowed to grow. We also show that these networks can exactly represent scalar piecewise affine 1-Lipschitz functions. We then prove a stronger statement: by inserting norm-constrained linear maps between the residual blocks, the same density holds when the hidden width is fixed. Because every layer obeys simple norm constraints, the resulting models can be trained with off-the-shelf optimisers. This paper provides the first universal approximation guarantees for 1-Lipschitz ResNets, laying a rigorous foundation for their practical use.

Towards Adaptive Deep Learning: Model Elasticity via Prune-and-Grow CNN Architectures

Deploying deep convolutional neural networks (CNNs) on resource-constrained devices presents significant challenges due to their high computational demands and rigid, static architectures. To overcome these limitations, this thesis explores methods for enabling CNNs to dynamically adjust their computational complexity based on available hardware resources. We introduce adaptive CNN architectures capable of scaling their capacity at runtime, thus efficiently balancing performance and resource utilization. To achieve this adaptability, we propose a structured pruning and dynamic re-construction approach that creates nested subnetworks within a single CNN model. This approach allows the network to dynamically switch between compact and full-sized configurations without retraining, making it suitable for deployment across varying hardware platforms. Experiments conducted across multiple CNN architectures including VGG-16, AlexNet, ResNet-20, and ResNet-56 on CIFAR-10 and Imagenette datasets demonstrate that adaptive models effectively maintain or even enhance performance under varying computational constraints. Our results highlight that embedding adaptability directly into CNN architectures significantly improves their robustness and flexibility, paving the way for efficient real-world deployment in diverse computational environments.

PhiNet v2: A Mask-Free Brain-Inspired Vision Foundation Model from Video

Recent advances in self-supervised learning (SSL) have revolutionized computer vision through innovative architectures and learning objectives, yet they have not fully leveraged insights from biological visual processing systems. Recently, a brain-inspired SSL model named PhiNet was proposed; it is based on a ResNet backbone and operates on static image inputs with strong augmentation. In this paper, we introduce PhiNet v2, a novel Transformer-based architecture that processes temporal visual input (that is, sequences of images) without relying on strong augmentation. Our model leverages variational inference to learn robust visual representations from continuous input streams, similar to human visual processing. Through extensive experimentation, we demonstrate that PhiNet v2 achieves competitive performance compared to state-of-the-art vision foundation models, while maintaining the ability to learn from sequential input without strong data augmentation. This work represents a significant step toward more biologically plausible computer vision systems that process visual information in a manner more closely aligned with human cognitive processes.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks

By replacing standard non-linearities with polynomial activations, Polynomial Neural Networks (PNNs) are pivotal for applications such as privacy-preserving inference via Homomorphic Encryption (HE). However, training PNNs effectively presents a significant challenge: low-degree polynomials can limit model expressivity, while higher-degree polynomials, crucial for capturing complex functions, often suffer from numerical instability and gradient explosion. We introduce a robust and versatile training framework featuring two synergistic innovations: 1) a novel Boundary Loss that exponentially penalizes activation inputs outside a predefined stable range, and 2) Selective Gradient Clipping that effectively tames gradient magnitudes while preserving essential Batch Normalization statistics. We demonstrate our framework's broad efficacy by training PNNs within deep architectures composed of HE-compatible layers (e.g., linear layers, average pooling, batch normalization, as used in ResNet variants) across diverse image, audio, and human activity recognition datasets. These models consistently achieve high accuracy with low-degree polynomial activations (such as degree 2) and, critically, exhibit stable training and strong performance with polynomial degrees up to 22, where standard methods typically fail or suffer severe degradation. Furthermore, the performance of these PNNs achieves a remarkable parity, closely approaching that of their original ReLU-based counterparts. Extensive ablation studies validate the contributions of our techniques and guide hyperparameter selection. We confirm the HE-compatibility of the trained models, advancing the practical deployment of accurate, stable, and secure deep learning inference.