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Apr 15

Bounded Hyperbolic Tangent: A Stable and Efficient Alternative to Pre-Layer Normalization in Large Language Models

Pre-Layer Normalization (Pre-LN) is the de facto choice for large language models (LLMs) and is crucial for stable pretraining and effective transfer learning. However, Pre-LN is inefficient due to repeated statistical calculations and suffers from the curse of depth. As layers grow, the magnitude and variance of the hidden state escalate, destabilizing training. Efficiency-oriented normalization-free methods such as Dynamic Tanh (DyT) improve speed but remain fragile at depth. To jointly address stability and efficiency, we propose Bounded Hyperbolic Tanh (BHyT), a drop-in replacement for Pre-LN. BHyT couples a tanh nonlinearity with explicit, data-driven input bounding to keep activations within a non-saturating range. It prevents depth-wise growth in activation magnitude and variance and comes with a theoretical stability guarantee. For efficiency, BHyT computes exact statistics once per block and replaces a second normalization with a lightweight variance approximation, enhancing efficiency. Empirically, BHyT demonstrates improved stability and efficiency during pretraining, achieving an average of 15.8% faster training and an average of 4.2% higher token generation throughput compared to RMSNorm., while matching or surpassing its inference performance and robustness across language understanding and reasoning benchmarks. Our code is available at: https://anonymous.4open.science/r/BHyT

  • 5 authors
·
Dec 26, 2025

True 4-Bit Quantized Convolutional Neural Network Training on CPU: Achieving Full-Precision Parity

Low-precision neural network training has emerged as a promising direction for reducing computational costs and democratizing access to deep learning research. However, existing 4-bit quantization methods either rely on expensive GPU infrastructure or suffer from significant accuracy degradation. In this work, we present a practical method for training convolutional neural networks at true 4-bit precision using standard PyTorch operations on commodity CPUs. We introduce a novel tanh-based soft weight clipping technique that, combined with symmetric quantization, dynamic per-layer scaling, and straight-through estimators, achieves stable convergence and competitive accuracy. Training a VGG-style architecture with 3.25 million parameters from scratch on CIFAR-10, our method achieves 92.34% test accuracy on Google Colab's free CPU tier -- matching full-precision baseline performance (92.5%) with only a 0.16% gap. We further validate on CIFAR-100, achieving 70.94% test accuracy across 100 classes with the same architecture and training procedure, demonstrating that 4-bit training from scratch generalizes to harder classification tasks. Both experiments achieve 8x memory compression over FP32 while maintaining exactly 15 unique weight values per layer throughout training. We additionally validate hardware independence by demonstrating rapid convergence on a consumer mobile device (OnePlus 9R), achieving 83.16% accuracy in only 6 epochs. To the best of our knowledge, no prior work has demonstrated 4-bit quantization-aware training achieving full-precision parity on standard CPU hardware without specialized kernels or post-training quantization.

  • 1 authors
·
Mar 14