# Learning to Ponder: Adaptive Reasoning in Latent Space

arXiv: https://arxiv.org/abs/2509.24238 · HTML: https://mlsanity.com/paper/2509.24238/

## Key facts

- Cited by 5 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 58 of its 65 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- Mechanistic interpretability / [Steering and interpreting LLM reasoning](https://mlsanity.com/mechinterp/steering-and-interpreting-llm-reasoning/)

## Builds on (most cited first, 30 of 58)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [A Systematic Survey of Prompt Engineering in Large Language Models: Techniques and Applications](https://mlsanity.com/paper/2402.07927/) (2024)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Confident Adaptive Language Modeling](https://mlsanity.com/paper/2207.07061/) (2022)
- [LayerSkip: Enabling Early Exit Inference and Self-Speculative Decoding](https://mlsanity.com/paper/2404.16710/) (2024)
- [Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspective](https://mlsanity.com/paper/2305.15408/) (2023)
- [BERT Loses Patience: Fast and Robust Inference with Early Exit](https://mlsanity.com/paper/2006.04152/) (2020)

## Built on by (most cited first, 5 of 5)

- [The Latent Space: Foundation, Evolution, Mechanism, Ability, and Outlook](https://mlsanity.com/paper/2604.02029/) (2026)
- [RISER: Orchestrating Latent Reasoning Skills for Adaptive Activation Steering](https://mlsanity.com/paper/2601.09269/) (2026)
- [PonderLM-3: Adaptive Token-Wise Pondering with Differentiable Masking](https://mlsanity.com/paper/2603.02023/) (2026)
- [Resource Consumption Threats in Large Language Models](https://mlsanity.com/paper/2603.16068/) (2026)
- [SphMind: Towards Robust, Training-Free VLM-based Spatial Reasoning with a 360 Camera](https://mlsanity.com/paper/2609.33462/) (2026)

## Abstract (arXiv)

Test-time compute has emerged as a key paradigm for enhancing LLM reasoning, yet prevailing approaches like Best-of-N and majority voting apply uniform depth across inputs, wasting computation on simple queries while potentially under-thinking complex ones. We present FR-Ponder, a single-graph, backbone-training-free framework that allocates instance-adaptive reasoning compute via latent steering. A less than 1M-param controller observes hidden states and decides to halt or apply a small ponder step by adding a pre-computed steering vector to frozen representations. Our method extracts the latent steering vector associated with deeper reasoning outputs and direct IO from LLM and re-applies it through a tunable scaling factor, allowing the model to adapt its reasoning depth to the complexity of each input. To balance performance and computational cost, we employ Group Relative Policy Optimization (GRPO) as a reward signal to adaptively regulate reasoning depth, achieving task accuracy while mitigating overreasoning. Through curriculum learning and careful reward engineering, FR-Ponder learns calibrated compute allocation correlated with problem difficulty. On GSM8K and MATH500, FR-Ponder improves the compute-accuracy frontier, delivering lower FLOPs with better matched accuracy and comparing favorably to early-exit baselines, without modifying backbone weights. Analyses visualize interpretable steering directions and show learned compute allocation correlates with problem difficulty.