S Mukherjee

Hanqing Zhu, Wenyan Cong, Zhizhou Sha et al.

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.

M. Doris, S. Guo, S. M. Koh et al.

Here we describe the quantum gas analysis and inference (Q-GAIN) Python package, which enables rapid deployment of machine learning (ML) and physics-informed analysis techniques for cold-atom experiments. Out of the box, Q-GAIN implements classification, object detection, and physics-informed metrics for feature detection in images of atomic Bose-Einstein condensates (BECs). Q-GAIN encourages a natural, module-based workflow: starting with data loading and preprocessing, followed by ML-based feature identification, and ending with conventional analysis techniques. We demonstrate this modularity by configuring Q-GAIN for three ML tasks. First, we demonstrate the basic workflow of the Q-GAIN framework by implementing the standard task of classifying handwritten digits from the MNIST dataset. Then, we re-implement our earlier soliton detection (SolDet) package in the Q-GAIN framework, enabling the detection and analysis of solitonic excitations in time-of-flight data. Finally, we develop an object-detection tool that identifies quantized vortices in images of ring-shaped BECs.