Yiming Dong

Yiming Dong, Huan Li, Zhouchen Lin

The LION (evoLved sIgn mOmeNtum) optimizer for deep neural network training was found by Google via program search, with the simple sign update yet showing impressive performance in training large scale networks. Although previous studies have investigated its convergence properties, a comprehensive analysis, especially the convergence rate, is still desirable. Recognizing that LION can be regarded as solving a specific constrained problem, this paper focuses on demonstrating its convergence to the Karush-Kuhn-Tucker (KKT) point at the rate of $\cal O(\sqrt{d}K^{-1/4})$ measured by gradient $\ell_1$ norm, where $d$ is the problem dimension and $K$ is the number of iteration steps. Step further, we remove the constraint and establish that LION converges to the critical point of the general unconstrained problem at the same rate. This rate not only delivers the currently optimal dependence on the problem dimension $d$ but also tightly matches the theoretical lower bound for nonconvex stochastic optimization algorithms, which is typically measured using the gradient $\ell_2$ norm, with respect to the number of iterations $K$. Through extensive experiments, we not only demonstrate that LION achieves lower loss and higher performance compared to standard SGD, but also empirically confirm that the gradient $\ell_1/\ell_2$ norm ratio aligns with $Θ(\sqrt{d})$, thus proving that our convergence rate matches the theoretical lower bound with respect to $d$ in the empirical sense.

Yibo Jin, Yixu Xu, Yue Chen et al.

Serving disaggregated large language models has been widely adopted in industrial practice for enhanced performance. However, too many tokens generated in decoding phase, i.e., occupying the resources for a long time, essentially hamper the cloud from achieving a higher throughput. Meanwhile, due to limited on-device resources, the time to first token (TTFT), i.e., the latency of prefill phase, increases dramatically with the growth on prompt length. In order to concur with such a bottleneck on resources, i.e., long occupation in cloud and limited on-device computing capacity, we propose to separate large language model between cloud and devices. That is, the cloud helps a portion of the content for each device, only in its prefill phase. Specifically, after receiving the first token from the cloud, decoupling with its own prefill, the device responds to the user immediately for a lower TTFT. Then, the following tokens from cloud are presented via a speed controller for smoothed TPOT (the time per output token), until the device catches up with the progress. On-device prefill is then amortized using received tokens while the resource usage in cloud is controlled. Moreover, during cloud prefill, the prompt can be refined, using those intermediate data already generated, to further speed up on-device inference. We implement such a scheme P/D-Device, and confirm its superiority over other alternatives. We further propose an algorithm to decide the best settings. Real-trace experiments show that TTFT decreases at least 60%, maximum TPOT is about tens of milliseconds, and cloud throughput increases by up to 15x.