Continual learning is a key feature of biological neural systems, but artificial neural networks often suffer from catastrophic forgetting. Instead of backpropagation, biologically plausible learning algorithms may enable stable continual learning. This study proposes columnar-organized spiking neural networks (SNNs) with local learning rules for continual learning and catastrophic forgetting. Using CoLaNET (Columnar Layered Network), we show that its microcolumns adapt most efficiently to new tasks when they lack shared structure with prior learning. We demonstrate how CoLaNET hyperparameters govern the trade-off between retaining old knowledge (stability) and acquiring new information (plasticity). We evaluate CoLaNET on two benchmarks: Permuted MNIST (ten sequential pixel-permuted tasks) and a two-task MNIST/EMNIST setup. Our model learns ten sequential tasks effectively, maintaining 92% accuracy on each. It shows low forgetting, with only 4% performance degradation on the first task after training on nine subsequent tasks.

Accurate assessment of neuromuscular reflexes, such as the H-reflex, plays a critical role in sports science, rehabilitation, and clinical neurology. Traditional analysis of H-reflex EMG waveforms is subject to variability and interpretation bias among clinicians and researchers, limiting reliability and standardization. To address these challenges, we propose a Fine-Tuned Vision-Language Model (VLM) Consortium and a reasoning Large-Language Model (LLM)-enabled Decision Support System for automated H-reflex waveform interpretation and diagnosis. Our approach leverages multiple VLMs, each fine-tuned on curated datasets of H-reflex EMG waveform images annotated with clinical observations, recovery timelines, and athlete metadata. These models are capable of extracting key electrophysiological features and predicting neuromuscular states, including fatigue, injury, and recovery, directly from EMG images and contextual metadata. Diagnostic outputs from the VLM consortium are aggregated using a consensus-based method and refined by a specialized reasoning LLM, which ensures robust, transparent, and explainable decision support for clinicians and sports scientists. The end-to-end platform orchestrates seamless communication between the VLM ensemble and the reasoning LLM, integrating prompt engineering strategies and automated reasoning workflows using LLM Agents. Experimental results demonstrate that this hybrid system delivers highly accurate, consistent, and interpretable H-reflex assessments, significantly advancing the automation and standardization of neuromuscular diagnostics. To our knowledge, this work represents the first integration of a fine-tuned VLM consortium with a reasoning LLM for image-based H-reflex analysis, laying the foundation for next-generation AI-assisted neuromuscular assessment and athlete monitoring platforms.

Reinforcement Learning with Verifiable Rewards (RLVR) has markedly enhanced the reasoning abilities of large language models (LLMs). Its success, however, largely depends on strong base models with rich world knowledge, yielding only modest improvements for small-size language models (SLMs). To address this limitation, we investigate Guided GRPO, which injects ground-truth reasoning steps into roll-out trajectories to compensate for SLMs' inherent weaknesses. Through a comprehensive study of various guidance configurations, we find that naively adding guidance delivers limited gains. These insights motivate G$^2$RPO-A, an adaptive algorithm that automatically adjusts guidance strength in response to the model's evolving training dynamics. Experiments on mathematical reasoning and code-generation benchmarks confirm that G$^2$RPO-A substantially outperforms vanilla GRPO. Our code and models are available at https://github.com/T-Lab-CUHKSZ/G2RPO-A.

In this paper, we present Deep-MacroFin, a comprehensive framework designed to solve partial differential equations, with a particular focus on models in continuous time economics. This framework leverages deep learning methodologies, including conventional Multi-Layer Perceptrons and the newly developed Kolmogorov-Arnold Networks. It is optimized using economic information encapsulated by Hamilton-Jacobi-Bellman equations and coupled algebraic equations. The application of neural networks holds the promise of accurately resolving high-dimensional problems with fewer computational demands and limitations compared to standard numerical methods. This versatile framework can be readily adapted for elementary differential equations, and systems of differential equations, even in cases where the solutions may exhibit discontinuities. Importantly, it offers a more straightforward and user-friendly implementation than existing libraries.

Min-max optimization has attracted much attention in the machine learning community due to the popularization of deep generative models and adversarial training. The optimization is quite different from traditional minimization analysis. For example, gradient descent does not converge in one of the simplest settings -- bilinear games. In this paper, we try to understand several gradient-based algorithms for bilinear min-max games: gradient descent, extra-gradient, optimistic gradient descent and the momentum method, for both simultaneous and alternating updates. We provide necessary and sufficient conditions for their convergence, with the Schur theorem. Furthermore, by extending these algorithms to more general parameter settings, we are able to optimize over larger parameter spaces to find the optimal convergence rates. Our results imply that alternating updates converge more easily in min-max games than simultaneous updates.