Training in reverse: How iteration order influences convergence and stability in deep learning

• URL: http://arxiv.org/abs/2502.01557v1
• Date: Mon, 03 Feb 2025 17:40:03 GMT
• Title: Training in reverse: How iteration order influences convergence and stability in deep learning
• Authors: Benoit Dherin, Benny Avelin, Anders Karlsson, Hanna Mazzawi, Javier Gonzalvo, Michael Munn,
• Abstract summary: Training neural networks remains computationally expensive and is often plagued by instabilities that can degrade convergence. This work explores theoretical issues concerning training stability in the constant-learning-rate (i.e., without schedule) and small-batch-size regime. We show that the order of gradient updates affects stability and convergence in gradient-based iterations. We illustrate this new line of thinking using backward-SGD, which processes batch gradient updates like SGD but in reverse order.
• Score: 7.702226188904773
• License:
• Abstract: Despite exceptional achievements, training neural networks remains computationally expensive and is often plagued by instabilities that can degrade convergence. While learning rate schedules can help mitigate these issues, finding optimal schedules is time-consuming and resource-intensive. This work explores theoretical issues concerning training stability in the constant-learning-rate (i.e., without schedule) and small-batch-size regime. Surprisingly, we show that the order of gradient updates affects stability and convergence in gradient-based optimizers. We illustrate this new line of thinking using backward-SGD, which processes batch gradient updates like SGD but in reverse order. Our theoretical analysis shows that in contractive regions (e.g., around minima) backward-SGD converges to a point while the standard forward-SGD generally only converges to a distribution. This leads to improved stability and convergence which we demonstrate experimentally. While full backward-SGD is computationally intensive in practice, it highlights opportunities to exploit reverse training dynamics (or more generally alternate iteration orders) to improve training. To our knowledge, this represents a new and unexplored avenue in deep learning optimization.

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