Training in reverse: How iteration order influences convergence and stability in deep learning
This addresses training instability issues for deep learning practitioners, though it is incremental as it explores a new theoretical avenue without immediate practical application.
The paper tackles the problem of training instability and convergence in neural networks by showing that the order of gradient updates influences stability, demonstrating that backward-SGD converges to a point with improved stability compared to standard forward-SGD.
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.