Hanqing Zhu
Publications
ISO: An RLVR-Native Optimization Stack
Reinforcement learning with verifiable rewards (RLVR) is rapidly advancing the reasoning capabilities of language models, yet the optimization layer that converts reward feedback into weight-space updates remains poorly understood. Building on our prior analysis (Zhu et al., 2025), we study this missing layer through the singular structure of model weights and identify spectral inheritance: RLVR can reuse the base model's weight spectra while acquiring new behavior through changes in the associated input and output singular frames. We operationalize spectral inheritance as Isospectral Optimization (ISO), an RLVR-native, fixed-spectrum optimization framework with complementary offline and online instantiations. Offline, ISO-Merger combines the frame changes of shared-base specialists into a single fixed-spectrum model, requiring no post-merge data, rollouts, gradient updates, or on-policy distillation (OPD). It recovers complementary specialist capabilities and achieves the strongest aggregate performance among the compared data-free merging methods. Online, ISO-Optimizer applies a chosen base optimizer, including AdamW and Muon, to the frame variables while keeping the base spectra fixed. Across reasoning and coding tasks ranging from 1.5B to 8B parameters, ISO-Optimizer improves accuracy in the reported runs and reaches matched scores with substantially fewer training steps. On Qwen3-8B-Base, AdamW reaches an aggregate accuracy of 0.495 after 270 training steps. ISO-AdamW reaches the same accuracy after only 100 training steps and improves further to 0.509 after 210 training steps. Together, ISO offers a concrete answer to RLVR's missing optimization layer: rather than inheriting pre-training optimization wholesale, design post-training around the structure of reward-driven adaptation: inherit the spectrum, optimize the frames.
Geometry-Preserving Orthonormal Initialization for Low-Rank Adaptation in RLVR
Low-rank adaptation (LoRA) and its variants enable parameter-efficient fine-tuning of large language models under the supervised fine-tuning (SFT) paradigm. However, their efficacy and behavior under Reinforcement learning with verifiable rewards (RLVR) are less well understood. In particular, two structurally initialized LoRA variants, PiSSA and MiLoRA, which outperform standard LoRA under SFT, can underperform standard LoRA under RLVR and may even exhibit training instability. These observations suggest that how to initialize the low-rank matrices in RLVR remains unclear. In this work, we develop a theoretical analysis of LoRA in RLVR, showing that orthonormal initialization achieves the minimal gap between LoRA outcome and that of full fine-tuning. Guided by this insight, we propose geometry-preserving orthonormal initialization for low-rank adaptation in RLVR, leading to two new variants, RLPO and RLMO. Experiments on mathematical reasoning benchmarks show that the proposed orthonormal initialization stabilizes RLVR training and outperforms standard LoRA, contrasting with PiSSA and MiLoRA. Finally, our unified analysis for LoRA initialization also explains why PiSSA and MiLoRA can underperform in RLVR, which may be of independent interest. Code and checkpoints are publicly available at https://github.com/Richard-ZZZ/geometry-preserving-orthonormal-init-rlvr.
Harnessing Photonics for Machine Intelligence
The exponential growth of machine-intelligence workloads is colliding with the power, memory, and interconnect limits of the post-Moore era, motivating compute substrates that scale beyond transistor density alone. Integrated photonics is emerging as a candidate for artificial intelligence (AI) acceleration by exploiting optical bandwidth and parallelism to reshape data movement and computation. This review reframes photonic computing from a circuits-and-systems perspective, moving beyond building-block progress toward cross-layer system analysis and full-stack design automation. We synthesize recent advances through a bottleneck-driven taxonomy that delineates the operating regimes and scaling trends where photonics can deliver end-to-end sustained benefits. A central theme is cross-layer co-design and workload-adaptive programmability to sustain high efficiency and versatility across evolving application domains at scale. We further argue that Electronic-Photonic Design Automation (EPDA) will be pivotal, enabling closed-loop co-optimization across simulation, inverse design, system modeling, and physical implementation. By charting a roadmap from laboratory prototypes to scalable, reproducible electronic-photonic ecosystems, this review aims to guide the CAS community toward an automated, system-centric era of photonic machine intelligence.