Latent Reasoning with Normalizing Flows

Large language models often improve reasoning by generating explicit chain-of-thought (CoT), demonstrating the importance of intermediate computation. However, textual CoT forces this computation through a discrete, serial, and communication-oriented token stream: each reasoning step must be verbalized before the model can proceed, even when the underlying update is semantic, uncertain, or only partially formed. Latent reasoning offers a higher-bandwidth alternative by performing intermediate computation in compact continuous states before committing to text. Yet existing latent-reasoning methods often sacrifice key advantages that make CoT effective in autoregressive language models, including native left-to-right generation, probabilistic sampling, compatibility with KV-cache decoding, and tractable likelihood estimation. We propose NF-CoT, a latent reasoning framework that preserves these advantages by modeling continuous thoughts with normalizing flows. NF-CoT instantiates a TARFlow-style normalizing flow inside the LLM backbone, defining a tractable probability model over compact continuous thoughts distilled from explicit CoT. Continuous-thought positions are generated by an NF head, while text positions are generated by the standard LM head within the same causal stream. This design provides exact likelihoods for latent thoughts, enables probabilistic left-to-right decoding with the original KV cache, and supports direct policy-gradient optimization in the latent reasoning space. On code-generation benchmarks, NF-CoT improves pass rates over explicit-CoT and prior latent-reasoning baselines while substantially reducing intermediate-reasoning cost.

Larger Hausdorff Dimension in Scanning Pattern Facilitates Mamba-Based Methods in Low-Light Image Enhancement

We propose an innovative enhancement to the Mamba framework by increasing the Hausdorff dimension of its scanning pattern through a novel Hilbert Selective Scan mechanism. This mechanism explores the feature space more effectively, capturing intricate fine-scale details and improving overall coverage. As a result, it mitigates information inconsistencies while refining spatial locality to better capture subtle local interactions without sacrificing the model's ability to handle long-range dependencies. Extensive experiments on publicly available benchmarks demonstrate that our approach significantly improves both the quantitative metrics and qualitative visual fidelity of existing Mamba-based low-light image enhancement methods, all while reducing computational resource consumption and shortening inference time. We believe that this refined strategy not only advances the state-of-the-art in low-light image enhancement but also holds promise for broader applications in fields that leverage Mamba-based techniques.