mlsanityData to 14 Oct 2026

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

arXiv 2601.18832 ↗First posted 25 Jan 2026cs.LG cs.AIcited by 3

On the map: LLM reasoning → Test-time compute and efficient thinking

Abstract (arXiv)

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.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 43 of its 53 references that are in the map. First posted on arXiv 25 Jan 2026.

Builds on

43 of 53 references.

Closest ancestors · 7

Same direction, newest first

  1. 2025CarBoN: Calibrated Best-of-N Sampling Improves Test-time Reasoning17 Oct
  2. 2025LaDiR: Latent Diffusion Enhances LLMs for Text Reasoning6 Oct
  3. 2025A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?31 Mar
  4. 2025s1: Simple test-time scaling31 Jan
  5. 2024Reasoning Aware Self-Consistency: Leveraging Reasoning Paths for Efficient LLM Sampling30 Aug
  6. 2024Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models1 Aug
  7. 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Models17 May

Other references · 36

  1. 2017Attention Is All You Needcited by 60,361
  2. 2020Language Models are Few-Shot Learnerscited by 32,419
  3. 2017Proximal Policy Optimization Algorithmscited by 15,215
  4. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  5. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 9,379
  6. 2025Qwen3 Technical Reportcited by 8,820
  7. 2021Evaluating Large Language Models Trained on Codecited by 8,320
  8. 2023Direct Preference Optimization: Your Language Model is Secretly a Reward Modelcited by 8,065
  9. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,708
  10. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
  11. 2022Large Language Models are Zero-Shot Reasonerscited by 4,374
  12. 2017Deep reinforcement learning from human preferencescited by 3,912
24 more
  1. 2022FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awarenesscited by 3,673
  2. 2020Longformer: The Long-Document Transformercited by 3,413
  3. 2023FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioningcited by 2,598
  4. 2024LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Codecited by 2,004
  5. 2023Instruction-Following Evaluation for Large Language Modelscited by 1,228
  6. 2024OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problemscited by 1,136
  7. 2016Geometric deep learning: going beyond Euclidean datacited by 1,048
  8. 2025Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?cited by 982
  9. 2023Graph of Thoughts: Solving Elaborate Problems with Large Language Modelscited by 886
  10. 2025Group Sequence Policy Optimizationcited by 835
  11. 2024BigCodeBench: Benchmarking Code Generation with Diverse Function Calls and Complex Instructionscited by 546
  12. 2024Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Modelscited by 284
  13. 2024Reinforcement learningcited by 247
  14. 2017A Conceptual Introduction to Hamiltonian Monte Carlocited by 209
  15. 2025A Survey of Reinforcement Learning for Large Reasoning Modelscited by 180
  16. 2025Phi-4-reasoning Technical Reportcited by 151
  17. 2025WritingBench: A Comprehensive Benchmark for Generative Writingcited by 106
  18. 2025Reasoning with Sampling: Your Base Model is Smarter Than You Thinkcited by 89
  19. 2025The Path Not Taken: RLVR Provably Learns Off the Principalscited by 56
  20. 2025A Technical Survey of Reinforcement Learning Techniques for Large Language Modelscited by 21
  21. 2024QUEST: Quality-Aware Metropolis-Hastings Sampling for Machine Translationcited by 16
  22. 2025The Bayesian Geometry of Transformer Attentioncited by 13
  23. 2025The Curved Spacetime of Transformer Architecturescited by 5
  24. 2019Sampling and Optimization on Convex Sets in Riemannian Manifolds of Non-Negative Curvaturecited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026The Latent Space: Foundation, Evolution, Mechanism, Ability, and Outlookcited by 43
  2. 2026Semantic Step Prediction: Multi-Step Latent Forecasting in LLM Reasoning Trajectories via Step Samplingcited by 1
  3. 2026Lifted State Policy Optimization: Internalizing Self-Correction through Transition Geometrycited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Port-Hamiltonian Latent Deliberation: Mitigating the Deliberation Drift Cliff in Test-Time Compute Scaling
  2. 2026Geometric Latent Reasoning Induces Shorter Generations in LLMs
  3. 2026Beyond Alignment: Expanding Reasoning Capacity via Manifold-Reshaping Policy Optimization
  4. 2025Learning to Ponder: Adaptive Reasoning in Latent Space
  5. 2026Thought-Level Beam Search for Reasoning
  6. 2026Efficient Reasoning via Constrained Optimization in Latent Space
  7. 2026GTS: Inference-Time Scaling of Latent Reasoning with a Learnable Gaussian Thought Sampler
  8. 2026When Does Longer Reasoning Help? Predicting Mathematical Reasoning Through Discovery and Execution