numerical stability
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Implementing Stable Softmax in Deep Learning
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Softmax is a crucial activation function in deep learning for transforming neural network outputs into a probability distribution, allowing for interpretable predictions in multi-class classification tasks. However, a naive implementation of Softmax can lead to numerical instability due to exponential overflow and underflow, especially with extreme logit values, resulting in NaN values and infinite losses that disrupt training. To address this, a stable implementation involves shifting logits before exponentiation and using the LogSumExp trick to maintain numerical stability, preventing overflow and underflow issues. This approach ensures reliable gradient computations and successful backpropagation, highlighting the importance of understanding and implementing numerically stable methods in deep learning models. Why this matters: Ensuring numerical stability in Softmax implementations is critical for preventing training failures and maintaining the integrity of deep learning models.
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Stabilizing Hyper Connections in AI Models
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DeepSeek researchers have addressed instability issues in large language model training by applying a 1967 matrix normalization algorithm to hyper connections. Hyper connections, which enhance the expressivity of models by widening the residual stream, were found to cause instability at scale due to excessive amplification of signals. The new method, Manifold Constrained Hyper Connections (mHC), projects residual mixing matrices onto the manifold of doubly stochastic matrices using the Sinkhorn-Knopp algorithm, ensuring numerical stability by maintaining controlled signal propagation. This approach significantly reduces amplification in the model, leading to improved performance and stability with only a modest increase in training time, demonstrating a new axis for scaling large language models. This matters because it offers a practical solution to enhance the stability and performance of large AI models, paving the way for more efficient and reliable AI systems.
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Visualizing DeepSeek’s mHC Training Fix
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DeepSeek's recent paper introduces Manifold-Constrained Hyper-Connections (mHC) to address training instability in deep learning models with many layers. When stacking over 60 layers of learned mixing matrices, small amplifications can compound, leading to explosive growth in training gains. By projecting these matrices onto a "doubly stochastic" manifold using the Sinkhorn-Knopp algorithm, gains remain bounded regardless of depth, with just one iteration significantly reducing gain from 1016 to approximately 1. An interactive demo and PyTorch implementation are available for experimentation, illustrating how this approach effectively stabilizes training. This matters because it offers a solution to a critical challenge in scaling deep learning models safely and efficiently.