This work proposes an NC-inspired training framework for simplifying deep networks during training, monitoring representation dynamics through the Inverse Fisher Criterion to identify both the split point between feature extraction and classification and the training stage at which simplification becomes viable.
Abstract
Understanding and exploiting the training dynamics of overparameterized deep neural networks remains a central challenge in modern machine learning. Recent evidence on Neural Collapse (NC) shows that class representations and classifiers exhibit highly structured geometry, while the Tunnel Effect suggests that only a subset of layers is essential for feature extraction. We combine these two perspectives and propose an NC-inspired training framework for simplifying deep networks during training. Our method monitors representation dynamics through the Inverse Fisher Criterion, a stable and efficient proxy for the variability collapse behavior, to identify both the split point between feature extraction and classification and the training stage at which simplification becomes viable. We then replace the trailing layers with a lightweight classification head and continue training the reduced model. Experiments on image-classification benchmarks across MLP, VGG, and ResNet architectures show that the proposed method achieves substantial parameter reductions while maintaining accuracy comparable to that of the full model. Code to reproduce the experiments can be found at: https://github.com/LorenzoSciandra/NNS.
The symmetries of a learning task have become an important factor in designing modern deep learning solutions. Data augmentation is a straightforward and effective way of incorporating symmetries into a generic neural network. Recent results show that infinitely large deep ensembles show perfect symmetry when trained on augmented data. However, since training ensembles requires repeating the training process many times, this method is costly. In this work, we study stochastic weight averaging (SWA) as an alternative ensembling technique that does not require repeated training runs. We analyze SWA by approximating the stochastic training trajectory at the end of training with an Ornstein--Uhlenbeck process. We show that in the infinite-width limit, SWA on augmented data provides an equiviariance boost that goes beyond what could be expected from the performance increase due to SWA alone. We verify our results with extensive numerical experiments on numerous models spanning computer vision and graph classification with both discrete and continuous symmetries.
Longde Huang, Axel Flinth, Jan E. Gerken· 0 citations
It is demonstrated that network architecture and its coeficients can be learned together by unifying concepts of evolutionary search within a population based traditional training process.
Backpropagation (BP) dominates deep learning training, but its reliance on gradients brings inherent troubles -- vanishing and exploding gradients. The pursuit of gradient-free methods has long been a goal in the field of artificial intelligence. This paper shows that indeed the simplest Monte Carlo algorithm implemented on a single GPU -- randomly mutate a parameter, keep it if the loss decreases, otherwise retry -- can practically train deep networks. This gradient-free method does not even need common techniques such as batch normalization or residual connections to directly train sufficiently deep networks. More remarkably, its flexibility extends to several nontrivial scenarios: it enables pure pruning training, supports discrete weights, accommodates unconventional transfer functions such as Gaussian, and reveals the substantial redundancy of deep networks. We have demonstrated its feasibility on deep networks with more than 20 layers, single-hidden-layer wide networks with up to 16,384 hidden neurons, and even a simple Transformer architecture trained on both image classification (MNIST) and character-level language modeling (Tiny Shakespeare). This simple gradient-free method may offer a complementary perspective for understanding the self-organization and learning mechanisms of neural networks, and also provides an alternative route for building physically inspired deep learning systems.
An Embedded One-Class Classification (EOCC) framework for monitoring task-informed neural network representations andComparisons with depth-based, density-based, covariance-based, isolation-based, and end-to-end deep one-class methods show that EOCC is competitive and frequently achieves low Type II error while maintaining the nominal in-control acceptance probability.
Edgard M. Maboudou-Tchao, Poorna Sandamini Senaratne, Randyll Pandohie et al.· Mathematics· 0 citations
Randomized neural networks enable fast and analytically tractable training by fixing the input to hidden layer parameters at random and learning the output weights in closed form; however, their performance critically depends on a single uninformed draw of hidden units. This one shot and task uninformed feature construction often leads to redundant representations and suboptimal utilization of model capacity. To address this limitation, we propose a simple and broadly applicable residual guided procedure that greedily constructs the hidden layer using a closed form residual decrease criterion. At each stage, we (i) generate a pool of random candidate units, (ii) score each candidate by the exact reduction it induces in the ridge regularized objective, (iii) select the top k units, and (iv) refit the readout in closed form using the standard design with direct input links. This procedure yields a progressive training process with a guaranteed monotonic decrease of the training objective. The method is model agnostic: only the candidate generation is architecture specific, while the scoring selection refitting loop is shared across models. Extensive experiments on 71 benchmark datasets from the UCI repository, covering both binary and multiclass classification tasks, demonstrate that the proposed residual-guided models consistently outperform their baseline counterparts in terms of accuracy, stability, and overall ranking performance.
We present a novel view on feature evolution in Vision Transformers (ViTs) by visualizing the training process over two dimensions -- network depth (layer) and training time (epochs). We employ Sparse Autoencoders (SAEs) to extract candidate sparse features from CLS-token representations and compare their activation profiles across epoch--layer pairs. This allows us to study feature-level dynamics that are not directly visible from representation-level similarity measures. Furthermore, we demonstrate how this framework of feature evolution allows us to describe feature migration, the change in the layer where a feature is most detectable during training. Our experiments show that migration is concentrated early in training, occurs more often toward earlier layers than toward deeper layers, and declines as feature organization stabilizes. We further find that deeper layers stabilize earlier and more strongly than shallow layers. The results show that our approach can be employed as a tool for understanding how ViTs learn and evolve.
Joonas Järve, Halil Ibrahim Aysel, Tarun Khajuria et al.· 0 citations