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Fuel Gauge: Estimating Chain-of-Thought Length Ahead of Time in Large Multimodal Models

CVPR 2026 · Vision-language and multimodal › Multimodal LLMs · approach: Chain-of-thought multimodal reasoning · 0 citations (OpenAlex)

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Proposes Fuel Gauge, a tiny (82k-parameter) probe on hidden states that estimates a linearly decaying "fuel level" to extrapolate CoT length ahead of time, and applies it to predictive KV cache allocation and CoT length modulation in reasoning LMMs.

Problem

Reasoning LMMs produce long, unpredictable chains of thought, which cause KV-cache memory fragmentation in serving and mis-calibrated over- or under-thinking, and the CoT length is unknown before generation.

Approach

A lightweight hidden-state probe extracts a fuel-level signal that decreases roughly linearly with generation step; linear extrapolation of this signal to zero gives a running CoT length estimate, and gradient steps on the hidden states at the probe's input modulate CoT length.

Key results

• On GPQA-Diamond with Qwen3-8B, Fuel Gauge achieves rMAE 0.2732 for CoT length versus 0.5003 for the Mean baseline and 0.5795 for Direct, and reduces memory allocations 13.37x versus HF.
• Fuel level estimation rMAE on MathVision-m with Qwen3VL-2B is 0.1186 for Fuel Gauge versus 0.3399 for Mean and 0.4999 for EoC Prob.
• CoT length modulation via a single factor eta shows Pearson correlations near 0.99 between eta and CoT length across text, image and video settings.

Surprising findings

• The EoC token probability baseline yields a near-constant rMAE of 0.4999 regardless of benchmark, indicating the end-of-think token probability is uninformative until it fires.
• The Direct baseline, using the same probe architecture and training data, fails to generalize to LongVideoBench, producing unreasonable CoT lengths, while the two-stage design generalizes.

Limitations

• Relies on the linear-decay assumption of fuel level; extrapolation quality depends on the probe's denoising.
• Evaluated only on Qwen3, Qwen3-VL and Intern-S1 families; LongVideoBench results show larger errors (rMAE ~0.45-0.50) than other benchmarks.
• Results for the KV allocator are reported as allocation counts, not measured fragmentation or end-to-end serving latency.

Experimental setup

Datasets: MMLU MMMU

Benchmarks: GPQA-Diamond AIME24 AIME25 MathVision-m LongVideoBench-15 LongVideoBench-60

Metrics: relative MAE number of memory allocations accuracy vs CoT length

Baselines: Mean Median EoC Prob Direct HF

Builds on: chain-of-thought prompting steering vectors classifier guidance

Closest papers by meaning

• MME-CoT: Benchmarking Chain-of-Thought in Large Multimodal Models for Reasoning Quality, Robustness, and Efficiency (ICML 2025 · similarity 0.89)
• KAM-CoT: Knowledge Augmented Multimodal Chain-of-Thoughts Reasoning (AAAI 2024 · similarity 0.88)
• Visual CoT: Advancing Multi-Modal Language Models with a Comprehensive Dataset and Benchmark for Chain-of-Thought Reasoning (NeurIPS 2024 · similarity 0.87)
• SIM-CoT: Supervised Implicit Chain-of-Thought (ICLR 2026 · similarity 0.87)
• L2V-CoT: Cross-Modal Transfer of Chain-of-Thought Reasoning via Latent Intervention (AAAI 2026 · similarity 0.87)
• Semantic Integrity Matters: Benchmarking and Preserving High-Density Reasoning in KV Cache Compression (ICML 2026 · similarity 0.87)