Technical Summary: Real-Time Progress Prediction in Reasoning Language Models

Problem Statement

Recent reasoning language models (Reasoning LMs), particularly those utilizing long latent chains of thought (CoT), have demonstrated strong performance on complex agentic tasks. However, as these models operate over increasingly long time horizons, their internal progress becomes opaque to users. This opacity creates significant challenges for user interaction, specifically regarding expectation management and real-time oversight. Users cannot easily determine how long a task will take or whether the model is making genuine progress toward a solution. While some prior work attempts to enforce fixed reasoning budgets, this strategy fails when the required budget cannot be inferred from the query alone, potentially leading to premature termination or incorrect answers.

The core question addressed is whether Reasoning LMs encode information about their remaining computational distance to a final answer within their hidden states, and if this information can be leveraged for real-time progress prediction.

Methodology

The authors employ a two-pronged approach: diagnostic probing of existing models and supervised fine-tuning (SFT) to generate explicit progress reports.

1. Diagnostic Probing (Hidden State Analysis)

To determine if progress information is inherently encoded in model representations, the authors trained linear probes on intermediate hidden states.

• Dataset: Approximately 25,000 mathematical reasoning traces from OpenR1-Math.
• Labeling: Reasoning progress was discretized into 10 bins (0–10%, 11–20%, ..., 91–100%) based on the normalized token position ($k/m$) within a trace of length $m$.
• Probe Architecture: Two types of linear probes were trained:
  • $f_{token}$: Predicts progress bucket from the current token's hidden state.
  • $f_{q+token}$: Predicts from the concatenation of the current state and the hidden states of the preceding $n=2$ tokens.
• Evaluation: Performance was measured using top-1 accuracy and Mean Absolute Error (MAE) on both in-domain data and out-of-distribution (OOD) long traces (>16K tokens).

2. Supervised Fine-Tuning (Explicit Progress Reporting)

The authors investigated whether explicit supervision could improve progress estimation by training models to output progress percentages directly within the CoT.

• Data Construction: Traces from OpenR1-Math were augmented with <progressbar> X% </progressbar> tokens inserted after paragraph segments. The progress value $a_i$ was calculated as the cumulative token count of the segment relative to the total trace length.
• Training Variants:
  • Standard SFT: Models were fine-tuned using LoRA with cross-entropy loss, upweighting tokens within progress annotations.
  • Masking Schedule: To prevent models from relying on the regular spacing of markers rather than reasoning content, a masking schedule was applied where preceding progress annotations were randomly masked during training (cosine schedule from 0 to 0.5).
• Models Evaluated: DEEPSCALER-1.5B, QWEN3-0.6B, and QWEN3-4B.
• Baselines: Comparisons were made against token-position baselines (Global mean length, Task mean/median length) and a "Previous marker" baseline that extrapolates from prior reports.

3. Intrinsic Ambiguity Analysis

To quantify the inherent uncertainty in progress labels, the authors measured the dispersion of progress values across multiple stochastic continuations from the same partial prefix.

• Metric: Mean Absolute Deviation (MAD) and Mean Absolute Percentage Deviation (MAPD) of realized progress values ($g_{i,\ell}$) across $r=8$ sampled continuations.

Key Results

Hidden State Encoding

Linear probes demonstrated that hidden states contain information correlated with normalized trace position, though this signal is not purely semantic.

• Accuracy: Probes achieved accuracies significantly above random guessing (10%), with the best in-domain results reaching ~35.9% (QWEN3-4B, middle layer).
• Generalization: Performance dropped significantly on OOD long traces, indicating difficulty in length generalization.
• Interpretation: The authors note that these results serve as a "representation diagnostic" rather than conclusive evidence of semantic progress tracking, as labels are derived from token position ($k/m$).

Progress Reporting Performance

Fine-tuned models successfully learned to generate progress estimates, with performance varying by model size and training strategy.

• Best Performance: The masked QWEN3-4B checkpoint achieved the strongest results, with an MAE of 0.161 on mathematical reasoning traces and 0.157 on the BBEH (Big-Bench Extra Hard) out-of-domain set.
• Masking Effect: Masking generally improved progress prediction quality (lower MAE) but sometimes resulted in a trade-off with downstream task accuracy. For instance, the masked QWEN3-4B had slightly lower macro accuracy on math benchmarks compared to its unmasked counterpart but significantly better progress estimation.
• Baseline Comparison: On mathematical benchmarks, the best progress-SFT checkpoints outperformed token-position baselines in aggregate. However, on BBEH, simple length-based baselines were highly competitive, suggesting that out-of-domain progress estimates may rely heavily on structural regularities rather than content-sensitive reasoning.

Intrinsic Ambiguity

The study quantified the "noise" inherent in stochastic reasoning.

• Dispersion: QWEN3-4B exhibited the lowest rollout dispersion (MAD = 0.027), followed by DEEPSCALER-1.5B (0.059) and QWEN3-0.6B (0.065).
• Correlation: The model with the lowest dispersion (QWEN3-4B) also achieved the lowest prediction MAE. This suggests that larger models can make progress labels more stable by reducing variation in the remaining solution length.
• Gap: The observed MAE remains higher than the intrinsic dispersion (MAD), indicating that while stochasticity explains part of the error, there is still room for improvement in estimation algorithms.

Significance and Claims

The paper claims four primary contributions:

1. Real-Time Visibility: It introduces a framework for real-time progress prediction in Reasoning LMs, offering a potential solution to the opacity of long reasoning trajectories.
2. Representation Evidence: It demonstrates that reasoning models encode progress-related information in their internal representations, as evidenced by the success of linear probes.
3. Direct Integration: It shows that progress reporting can be directly incorporated into the generation process via SFT, with the masked QWEN3-4B checkpoint achieving an MAE of 0.161 on math traces.
4. Ambiguity Quantification: It quantifies the intrinsic ambiguity of progress labels by measuring rollout dispersion, finding that larger models (QWEN3-4B) produce more stable progress estimates due to reduced variation in remaining solution lengths.

The authors maintain a modest stance, acknowledging that progress signals are often tied to token position and trace length regularities rather than purely semantic understanding. They note that while progress reports are parseable and numerically aligned out-of-domain, their interpretation must be relative to structural controls. The study is limited to three compact models and primarily mathematical reasoning, with prediction performance degrading on traces longer than the training distribution.