VQV Signal
According to a post on X by @Memoirs, Ruijia Zhang and Soufiane Hayou prove results for linear residual networks using Depth-μP and μP scaling. With gradient clipping, the network output converges along every joint width-and-depth growth path for any fixed number of gradient-descent steps. Without clipping, the authors show a weaker convergence in probability. The headline indicates the result covers training, not only initialization.
According to a post on X by @Memoirs, Ruijia Zhang and Soufiane Hayou prove results for linear residual networks using Depth-μP and μP scaling. With gradient clipping, the network output converges along every joint width-and-depth growth path for any fixed number of gradient-descent steps. Without clipping, the authors show a weaker convergence in probability. The headline indicates the result covers training, not only initialization.
AI-assisted summary based on the listed source.
Ruijia Zhang and Soufiane Hayou prove that for linear residual networks using Depth-μP and μP scaling, the network output converges along every joint width-and-depth growth path for any fixed number of gradient-descent steps with gradient clipping. Without clipping they show a weaker convergence in probability. It...
Researchers who scale width and depth when designing large models may find this theory supports using those scaling rules during training as well as at setup. The stronger guarantee depends on gradient clipping, so training setups without it fall under the weaker result. The analysis covers linear residual networks, so the next thing to watch is whether follow-up work extends it to more realistic architectures.
Hardware and robotics watchers may want to track whether this becomes a product, benchmark, or deployment signal.
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