Hongseok Kim

Hyungmin Kim, Minsoo Kim, Hongseok Kim et al.

Multi-turn Large Language Model (LLM) serving is critical for consistent user experiences, yet the linear growth of the Key-Value (KV) cache imposes significant pressure on GPU memory and bandwidth. Non-uniform KV compression effectively preserves more information by considering the individual importance of each KV cache. However, such KV cache heterogeneity introduces various systemic challenges - including memory fragmentation, scheduling complexities, and diminished kernel utilization - which collectively lead to significant inefficiencies in existing LLM serving systems. To overcome these challenges, we present Tangram, a novel serving system designed to make Non-uniform KV caches practical. Tangram addresses systemic inefficiencies through three core techniques: (1) Deterministic Budget Allocation assigns a static memory footprint to each head based on its intrinsic pattern, entirely eliminating dynamic scheduling overhead and prefill stalls; (2) Head Group Page clusters attention heads with similar retention demands and manages them with independent, vectorized page tables, thereby maximizing physical memory reclamation; and (3) Ahead-of-Time (AOT) Load Balancing leverages static budget profiles to ensure uniform GPU utilization without runtime overhead. Experimental results show that Tangram improves throughput by up to 2.6x compared to existing baselines, while fully preserving model accuracy. Our implementation is publicly available at https://github.com/aiha-lab/TANGRAM.

Kyurae Kim, Jisu Oh, Jacob R. Gardner et al.

Minimizing the inclusive Kullback-Leibler (KL) divergence with stochastic gradient descent (SGD) is challenging since its gradient is defined as an integral over the posterior. Recently, multiple methods have been proposed to run SGD with biased gradient estimates obtained from a Markov chain. This paper provides the first non-asymptotic convergence analysis of these methods by establishing their mixing rate and gradient variance. To do this, we demonstrate that these methods-which we collectively refer to as Markov chain score ascent (MCSA) methods-can be cast as special cases of the Markov chain gradient descent framework. Furthermore, by leveraging this new understanding, we develop a novel MCSA scheme, parallel MCSA (pMCSA), that achieves a tighter bound on the gradient variance. We demonstrate that this improved theoretical result translates to superior empirical performance.

Minsoo Kim, Hongseok Kim

Conventional solvers are often computationally expensive for constrained optimization, particularly in large-scale and time-critical problems. While this leads to a growing interest in using neural networks (NNs) as fast optimal solution approximators, incorporating the constraints with NNs is challenging. In this regard, we propose deep Lagrange dual with equality embedding (DeepLDE), a framework that learns to find an optimal solution without using labels. To ensure feasible solutions, we embed equality constraints into the NNs and train the NNs using the primal-dual method to impose inequality constraints. Furthermore, we prove the convergence of DeepLDE and show that the primal-dual learning method alone cannot ensure equality constraints without the help of equality embedding. Simulation results on convex, non-convex, and AC optimal power flow (AC-OPF) problems show that the proposed DeepLDE achieves the smallest optimality gap among all the NN-based approaches while always ensuring feasible solutions. Furthermore, the computation time of the proposed method is about 5 to 250 times faster than DC3 and the conventional solvers in solving constrained convex, non-convex optimization, and/or AC-OPF.