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Kang Liu

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2 published item(s)

preprint2026arXiv

Budget-aware Auto Optimizer Configurator

Optimizer states occupy massive GPU memory in large-scale model training. However, gradients in different network blocks exhibit distinct behaviors, such as varying directional stability and scale anisotropy, implying that expensive optimizer states are not universally necessary and using a global optimizer is often memory-inefficient. We propose the Budget-Aware Optimizer Configurator (BAOC) to reduce memory cost by assigning suitable optimizer configurations to individual blocks under given budgets. Specifically, BAOC samples gradient streams to derive statistical metrics that quantify the potential performance risk of applying cheaper configurations (e.g., low precision or removing momentum). It then solves a constrained allocation problem to minimize total risk under memory and time budgets, selecting a budget-feasible configuration for each block. Experiments across vision, language, and diffusion workloads demonstrate that BAOC maintains training quality while significantly reducing the memory usage of optimizer states. The code is available at https://anonymous.4open.science/r/BAOC-45C6.

preprint2026arXiv

Exact Dual Geometry of SOC-ICNN Value Functions

Input Convex Neural Networks (ICNNs) are commonly used in a two-stage manner: one first trains a convex network and then minimizes it over its input in a downstream inference problem. Recent second-order-cone ICNNs (SOC-ICNNs) enrich ReLU-based ICNNs with quadratic and conic modules and admit an exact representation as value functions of second-order cone programs (SOCPs). This value-function structure enables an explicit convex-analytic treatment of SOC-ICNN inference. In this paper, we study the exact first-order and local second-order geometry of SOC-ICNNs from the dual viewpoint. We show that supporting slopes, subdifferentials, directional derivatives, and local Hessians can be recovered directly from optimal dual variables. These results provide the geometric primitives for white-box SOC-ICNN inference, going beyond black-box automatic differentiation. Numerical experiments validate the exact multiplier readout, the local Hessian formula, and the set-valued behavior at structurally degenerate inputs. We also provide a step-by-step tutorial showing how the readout mechanism instantiates a complete white-box inference loop. The code is available at https://anonymous.4open.science/r/SOC-ICNN-Theory-BEFC/.