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Abstract: Looped Transformers increase computational capacity through the repeated application of shared blocks, but their recurrent depth makes conventional full-depth decoding expensive. While existing speculative pipelines accelerate generation by processing consecutive token positions at varying depths, they are typically limited by sequential decoding overheads. We introduce CopyLoop, a training-free decoding algorithm that combines low-cost context-copy proposals with shallow screening and continuous recurrent scheduling. Rather than step-by-step generation, CopyLoop proposes multi-token suffixes from repeated context. It then evaluates them early at a shallow recurrent depth to efficiently filter out incorrect branches, processing newer blocks concurrently while earlier blocks are still progressing toward full-depth verification. We evaluate CopyLoop across six model checkpoints from the Ouro, Raven, and Huginn families, covering code generation and multi-step mathematical reasoning. CopyLoop achieves decoding speedups of 2.98x--10.70x over full-depth autoregressive decoding on Base models and 2.74x--3.52x on Thinking models, consistently outperforming or closely matching all competing baselines across evaluation tasks. Furthermore, ablation studies confirm a strong synergy between shallow screening and continuous scheduling, while our analyses show that CopyLoop requires only lightweight model calibration and yields greater speedups on longer generations with reusable contexts.

Abstract: We propose HiLo-RD (High-to-Low Budget Representation Distillation) to improve masked diffusion language models (MDLMs) under a limited generation budget. Unlike autoregressive models, MDLMs choose both what to generate and where to commit it. This creates two coupled challenges: predicting useful content before reasoning is complete, and deciding when to fix answer tokens that shape later predictions. We identify budget-induced premature commitment: even when a correct solution fits, the model can fix answer fragments near the window boundary before resolving intermediate steps. These fragments become context for later predictions and redirect subsequent reasoning. Existing post-training methods do not directly transfer the stronger trajectories that the same model follows with a larger window. HiLo-RD addresses this gap by (1) pairing large-window teacher states with cropped small-window views and (2) matching their hidden representations at committed positions. This supervision guides both token prediction and commitment order without an external teacher. Across mathematics benchmarks, HiLo-RD improves low-budget accuracy and shortens responses; these gains extend to code generation without code-domain training. On GSM8K, accuracy rises by 9.4 percentage points as mean readable length falls by about 25%. Attention diagnostics and fixed-budget order interventions support the proposed mechanism. Together, these results show that large-window reasoning can improve small-window decoding.

Abstract: Reasoning language models are trained to produce solutions, not to refuse them, and this bias persists when the problem they are handed is false. Asked to prove a corrupted theorem, a strong model will typically comply and produce a confident derivation of something untrue. We present Euston, an 8B mathematical claim-verification model trained to resist exactly this. Training data were generated with GraphSynth, a probabilistic factor-graph generator that couples attribute-level diversity to decode-time structural masking and span-synchronized verification, yielding 3{,}026 matched true/corrupted statement pairs (6,052 statements) drawn from arXiv papers spanning 2010--2025. We fine-tuned DeepSeek-R1-8B with GRPO under a rule-based, zero-API reward for 189 steps on four H100 GPUs. On a balanced 200-true/200-false held-out split, balanced accuracy rises from 29.50% to 63.75% and the discrimination gap---the difference between the rate of calling false statements false and the rate of calling true statements false moves from -0.5% (z=-0.1) to +27.5% (z=+6.0). Critically, the gain is not purchased with general mathematical ability: AIME 2026 accuracy under official semantics is 65.00% against a 69.17% base, a difference of -4.17% that is not statistically significant, whereas an earlier run of the same recipe on a smaller GraphSynth corpus collapsed to 40.00%. Median response length also falls from 19,217 to 18,296 tokens and the truncation rate from 25.8% to 8.3%, so the improvement does not come from thinking longer. We report the result together with the confounds that bound its interpretation, principally the all-false composition of the official evaluation sets and the low precision implied at realistic error prevalence.

Abstract: Plane geometry remains a significant challenge in AI, requiring the integration of visual perception and mathematical reasoning. While Large Multimodal Models (LMMs) naturally handle visuo-linguistic inputs, they are often computationally intensive and opaque. We demonstrate that a pure Large Language Model (LLM), when equipped with specialized modules, can rival state-of-the-art LMMs on complex geometry problems. Our framework integrates a Geometric Vision Parser, which translates diagrams into symbolic form, with a Symbolic Solver that performs formal deductions, thereby mitigating hallucinations and promoting interpretable reasoning. To enable rigorous evaluation, we curate a benchmark of challenging problems from the 2025 Chinese Zhongkao examinations, ensuring data novelty and testing deeper deductive skills. Experiments demonstrate that our approach achieves performance comparable to Gemini 2.5 Pro while delivering clearer, human-like solutions.