The Geometric Reasoner: Manifold-Informed Latent Foresight Search for Long-Context Reasoning

Scaling test-time compute enhances long chain-of-thought (CoT) reasoning, yet existing approaches face a fundamental trade-off between computational cost and coverage quality: either incurring high training expense or yielding redundant trajectories. We introduce The Geometric Reasoner (TGR), a training-free framework that performs manifold-informed latent foresight search under strict memory bounds. At each chunk boundary, TGR scores candidate latent anchors via a lightweight look-ahead estimate combined with soft geometric regularizers that encourage smooth trajectories and diverse exploration. Chunk-wise KV cache resets keep memory linear in chunk length. On challenging math and code benchmarks, TGR improves robust trajectory coverage, measured by the area under the Pass@$k$ curve (AUC), by up to 13 points on Qwen3-8B, with negligible overhead of about 1.1--1.3 times.

Accelerating Chain-of-Thought Reasoning: When Goal-Gradient Importance Meets Dynamic Skipping

Large Language Models leverage Chain-of-Thought (CoT) prompting for complex tasks, but their reasoning traces are often excessively verbose and inefficient, leading to significant computational costs and latency. Current CoT compression techniques typically rely on generic importance metrics and static compression rates, which may inadvertently remove functionally critical tokens or fail to adapt to varying reasoning complexity. To overcome these limitations, we propose Adaptive GoGI-Skip, a novel framework learning dynamic CoT compression via supervised fine-tuning. This approach introduces two synergistic innovations: (1) Goal-Gradient Importance (GoGI), a novel metric accurately identifying functionally relevant tokens by measuring the gradient influence of their intermediate representations on the final answer loss, and (2) Adaptive Dynamic Skipping (ADS), a mechanism dynamically regulating the compression rate based on runtime model uncertainty while ensuring local coherence through an adaptive N-token constraint. To our knowledge, this is the first work unifying a goal-oriented, gradient-based importance metric with dynamic, uncertainty-aware skipping for CoT compression. Trained on compressed MATH data, Adaptive GoGI-Skip demonstrates strong cross-domain generalization across diverse reasoning benchmarks including AIME, GPQA, and GSM8K. It achieves substantial efficiency gains - reducing CoT token counts by over 45% on average and delivering 1.6-2.0 times inference speedups - while maintaining high reasoning accuracy. Notably, it significantly outperforms existing baselines by preserving accuracy even at high effective compression rates, advancing the state of the art in the CoT reasoning efficiency-accuracy trade-off.