The paper demonstrates that neural networks can maintain perfect training accuracy while their training cross‑entropy remains nearly flat at a positive level, a phenomenon observed on modular addition tasks. Using ReLU networks with supported‑Polar hidden updates, normalized output‑layer updates, and weight decay, the authors show that hidden features evolve and held‑out accuracy can rise from zero to above 90% even as cross‑entropy stays flat. Theoretical results for one‑hidden‑layer networks and empirical evidence from deeper networks and transformers confirm that correct classification need not coincide with minimal cross‑entropy, challenging conventional assumptions about loss plateaus.
arXiv:2606. 05863v1 Announce Type: new Abstract: Grokking suggests that fitting the training data and learning a simple underlying rule may occur on different time scales.
arXiv:2605.06240v2 Announce Type: replace-cross Abstract: Forward-Forward (FF) training lets each layer learn from a local goodness criterion. In cumulative-goodness variants, later layers can inheri...
LayerRoPE introduces a depth‑wise magnitude and angular superposition mechanism that replaces per‑layer normalization gains with a single shared vector and depth‑conditioned scalars, reducing parameters and computational cost. Across 16 pre‑trained large language models and a 100B+ token model ladder, LayerRoPE outperforms traditional Pre‑, Post‑, and Peri‑Norm schemes, achieving comparable or better performance with significantly less compute and improved convergence up to 512 layers. The method demonstrates that widening the residual stream, rather than shrinking it, enhances depth stability and learning‑rate sensitivity, and it transfers effectively to latent and vision transformer architectures.
Deep neural networks can exhibit periodic loss spikes known as the "Slingshot Mechanism" during long‑term training. This paper shows that such spikes arise from finite‑precision floating‑point arithmetic: when the correct‑class logit becomes much larger than the others, the gradient for that class is rounded to zero while others remain nonzero, breaking the zero‑sum constraint and creating a positive feedback loop that inflates feature and classifier norms. The authors term this Numerical Feature Inflation (NFI) and demonstrate that it explains the rapid norm growth, reappearance of gradients, and loss spikes, while also showing that partial absorption can still cause hidden norm growth without visible spikes.
arXiv:2608. 06177v1 Announce Type: new Abstract: Binary neural networks are very attractive for constrained deployment, enabling small footprint and low-power inference.
arXiv:2505. 22578v2 Announce Type: replace Abstract: The optimization of neural networks under weight decay remains poorly understood from a theoretical standpoint.
The paper presents a spectral theory explaining the phenomenon of grokking, where an initial fit to training data is followed by a delayed improvement in generalization. It shows that for homogeneous networks trained with squared loss and L₂ weight decay, residuals after memorization influence the neural tangent kernel (NTK) dynamics, leading to a transition from lazy to rich learning. The theory predicts that grokking timescales depend on the product of learning rate and weight decay, and that stronger decay can halt fitting, with empirical validation on modular addition tasks using MLPs and Transformers.
arXiv:2610. 31663v1 Announce Type: cross Abstract: Constructing accurate and computationally tractable approximation spaces is a fundamental task in scientific computing.
The paper investigates whether flatter loss landscapes drive better generalization in the context of Grokking. It shows that sharpness‑aware minimization (SAM) alone does not reliably induce the transition to generalization, but when combined with weight decay, SAM can accelerate this transition up to four times faster. The authors provide a theoretical analysis using a minimal two‑layer ReLU model, demonstrating that flatness alone cannot distinguish memorizing from generalizing solutions, while weight decay favors generalization and a local stability window explains SAM’s effect.
The paper investigates a negative weight drift that arises from the interaction between standard loss functions (MSE or cross‑entropy) and positively biased activation functions. This drift, which is inherent to the optimization process rather than the data, pushes downstream weights toward negative values during early training and leads to high activation sparsity—up to nearly 90% in GPT‑nano when using ReLU. The authors also examine the impact of this sparsity, noting that model performance degrades sharply when activation sparsity exceeds about 70%, and study sparsity‑inducing activation functions that produce spikes in intermediate transformer layers.
arXiv:2411. 16073v4 Announce Type: replace-cross Abstract: Inspired by the Well-initialized Lottery Ticket Hypothesis (WLTH), we introduce Soft-TransFormers (Soft-TF), a continual learning framework that adapts a frozen pre-trained Transformer through task-specific soft subnetworks: real-valued multiplicative masks over the query, key, value, and output projections of selected self-attention layers.
arXiv:2606. 27759v1 Announce Type: new Abstract: Training binary neural networks (BNNs) from scratch is dominated by the straight-through estimator (STE), whose forward/backward mismatch produces severe accuracy degradation as networks deepen.