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What LLM Forecasters Know but Don't Say: Probing Internal Representations for Calibration and Faithfulness
Raphaël Sarfati, Pratyush Ranjan Tiwari, Siddharth Boppana, Christopher J. Earls, Srikar Varadaraj, Eric Ho
TL;DR
LLM forecasters can be accurate yet poorly calibrated, and their chain-of-thought may not faithfully expose the evidence behind forecasts. This paper probes frozen intermediate activations to measure confidence and reasoning fidelity, finding that internal signals outperform verbalized confidence, detect concealed evidence effects, and reveal forecasts are largely committed before reasoning begins.
Problem
LLM forecasters’ verbalized confidence can be miscalibrated, while chain-of-thought reasoning may not faithfully reflect the evidence driving their forecasts.
Method
The paper trains lightweight pooling probes on frozen intermediate activations and evaluates them alongside evidence ablation, diversionary injection, and forced-answering tests.
Results
Internal probes substantially outperform verbalized confidence for calibration, track concealed behavioral shifts, and show that forecasts are largely fixed before reasoning begins.
Takeaways & Limitations
Internal activations provide a practical basis for calibrating, auditing, and routing language-model forecasters.
Takeaways & Limitations
The paper does not test whether the pre-reasoning signal can guide retrieval, and training models to verbalize internal confidence remains future work.
Abstract
from arXiv · showhide
Large language models fine-tuned for forecasting can be accurate yet poorly calibrated, and their chain-of-thought (CoT) reasoning may not faithfully reflect the evidence behind a forecast. We ask whether internal representations offer a more direct window into both. Working with Eternis-Forecaster 8B on OpenForesight, we train representation-pooling probes on intermediate activations and find they achieve substantially better calibration; a result that also holds for GLM-4.7-Flash and GLM-4.5-Air. We then assess CoT faithfulness through evidence ablation and diversionary injection: removing an influential source in the prompt often changes the model's forecast while leaving the reasoning trace untouched. The same probes function as lie detectors: their activations track behavioral shifts far better than the reasoning trace does, and they also predict the direction of change in 84% of cases, including when the CoT conceals the perturbation's influence. Finally, forced answering reveals that forecasts are largely fixed before reasoning begins: a single pre-reasoning pass recovers the committed answer and confidence, and routing questions by the spread of this pre-set answer distribution saves 30-47% of generated tokens, with no loss of accuracy. Together, these results establish probing internal representations as a practical tool for calibrating, auditing, and triaging language model forecasters and reasoning models more broadly.
1 Introduction
LLM forecasters can be accurate yet poorly calibrated, while their chain-of-thought may fail to faithfully represent the evidence driving forecasts. This work tests whether probes of internal activations provide a better window into confidence and reasoning fidelity.
- The study trains lightweight pooling probes on intermediate CoT activations to estimate forecast correctness and confidence.The probes use mean-, attention-, and covariance-pooling representations.
- Internal probes substantially outperform model-verbalized confidence on expected calibration error.The improvement holds across both GLM models without updating model weights.
- Diversionary injection produced a 2.9% stealth rate, indicating the model was largely transparent when shown misleading evidence.
- Probe activations tracked behavioral shifts at ρ = 0.57, including changes concealed by the chain of thought.The probes therefore serve as lie detectors alongside their calibration role.
2 Related Work
Prior work studies how language-model priors transfer to time series, how retrieval and ensembles support forecasting, and how calibration can be incorporated into reasoning-model training. This paper’s math experiment complements calibration-aware reinforcement-learning approaches by probing frozen activations.
- Frozen general-purpose LLMs can extrapolate tokenized time series zero-shot, while other work finds accuracy may remain unchanged after backbone ablation.
- Forecasting benchmarks and systems have progressed from performance far below human experts toward retrieval-based and ensemble approaches nearing crowd-level accuracy.
- RLCR augments correctness rewards with a Brier-score calibration reward and trains models to emit answers with verbalized confidence.
- DCPO separates reasoning-token and confidence-token optimization to improve calibration while preserving reinforcement-learning gains.
- The paper asks whether frozen activation readouts recover out-of-distribution correctness information missed by token statistics or verbalized confidence.
3 Methods
The methods combine frozen forecasting models, OpenForesight and math datasets, lightweight activation probes, and standard calibration, discrimination, and correlation metrics. Probes pool sequence representations before a simple readout, while evaluation uses clustered bootstrap intervals and answer matching.
- Models and data: Experiments focus on Eternis-Forecaster 8B, with Eternis-Forecaster 32B and frozen GLM-4.7-Flash and GLM-4.5-Air used in selected studies.Only probe weights are trained for the GLM comparison models.
- Models and data: The forecasting data use OpenForesight prompts containing instructions, questions, background, resolution criteria, and retrieved news passages.Improved-context and public dataset splits provide in-distribution and broader OOD testing settings.
- Models and data: Probe studies train on forecasting rollouts and evaluate on held-out rollouts, while math probes use MATH training data and pooled AIME/AMC OOD benchmarks.
- Probe design: A probe reads frozen activations from one model layer, applies a pooling function over the context, and uses a typically linear readout to predict correctness.The study sweeps layers, pooling architectures, and positions along the reasoning trace.
- Probe design: Mean pooling averages token activations, attention pooling aggregates them with trained attention, and covariance pooling captures second-order co-fluctuation statistics.Covariance pooling uses trained low-rank projections before a readout.
- Metrics and evaluation: Calibration is evaluated with ECE and Brier score, discrimination with AUROC, and association with Pearson’s r and Spearman’s ρ.ECE compares confidence with empirical accuracy across confidence bins.
- Metrics and evaluation: Unless otherwise noted, 95% confidence intervals use question-level nonparametric percentile bootstrap resampling.All rollouts or perturbation pairs associated with sampled questions are pooled.
- Metrics and evaluation: Answer matching permits multiple valid surface forms for the same ground-truth answer.
4 Experiments
Experiments show that internal probes recover better-calibrated confidence, reveal forecast changes hidden by chain-of-thought, and expose that many forecasts are committed before reasoning unfolds.
- Experimental setup and model behavior: EF-8B’s accuracy is 86%–94% on answer-bearing questions versus 0.26–0.33 when the answer is absent.The per-slice accuracy difference is +57% to +65%, with every 95% bootstrap confidence interval excluding zero.
- Probe calibration: A layer-21 covariance probe matches verbalized confidence in ranking but improves calibration, reducing ECE from 0.093 to 0.044.The probe’s AUROC is 0.756 versus 0.758 for verbalized confidence, while its calibration advantage persists on both OOD sources.
- Probe calibration: Across GLM models, probe probabilities sharply reduce raw ECE without updating model weights, while ranking improvements depend on the model and probe.GLM-4.7-Flash has ECE 0.054 versus 0.287 for verbalized confidence; GLM-4.5-Air improves both AUROC and ECE.
- OOD math stress test: On pooled OOD math, probes improve correctness ranking for both models, although calibration superiority depends on the model and calibration method.For the untrained base, AUROC rises from 0.752 to 0.894 and ECE falls from 0.270 to 0.083; for the DCPO-recipe model, the probe has AUROC 0.929 versus 0.865, while isotonic-recalibrated verbalized confidence has lower ECE, 0.125 versus 0.143.
- Chain-of-thought faithfulness: Evidence ablation shows weak coupling between behavioral and reasoning changes: Spearman ρ = 0.215, with 23% of high-impact pairs showing no CoT change.In diversionary injection, 81.2% of questions openly adopt and cite misleading evidence, while 2.5% adopt it stealthily.
- Probe-based faithfulness auditing: The probes track perturbation-induced behavioral changes better than reasoning text and predict their direction in 83.6% of cases, including 78.5% of stealth ablations.In stealth cases, the mean absolute probe shift is 0.065 despite unchanged reasoning traces.
- Pre-reasoning commitment: Forced answering indicates that forecasts are often pre-committed: the forced answer matches the free modal answer on 67% of test questions.A single empty-think forward pass directly exposes the forced-answer distribution, while forced and free confidence remain highly correlated.
5 Conclusion
The paper concludes that internal activations reveal confidence, evidence influence, and pre-reasoning forecast commitments more reliably than the model’s verbalized reasoning. These signals support calibration, auditing, and routing applications, while motivating future work on introspective training.
- Lightweight probes recover calibrated confidence that the model’s verbalization distorts.The probes operate on intermediate activations without changing the model weights.
- Internal activations track evidence influence that chain-of-thought reasoning fails to disclose.This connects the probes’ confidence readout to auditing reasoning fidelity.
- Forecasts are largely committed before reasoning begins, enabling routing between committing, reasoning, and retrieving.The conclusion presents this pre-reasoning commitment as an exploitable property of the forecaster.
- The calibrated signal is present from the final prompt token onward, but stated probabilities do not report it.The paper frames overconfidence as a self-report problem rather than simply a failure of self-knowledge.
- Future work could distill probe signals into verbalized probabilities or train against calibration-aware rewards, while testing effects on the internal signal.The authors explicitly leave open whether such training would sharpen or degrade the signal probes read.
A Data audit
The data audit examines prompt construction, split overlap, and representative examples in OpenForesight. Exact-qid overlap reflects index reuse rather than question leakage, while semantic near-duplicates remain outside this audit’s detection scope.
- Audit scope: The audit checks OpenForesight for prompt-length issues, question leakage, and related dataset concerns.The supplied audit description identifies these as the principal checks.
- Prompt construction: Prompts in the last two splits omit retrieval articles, limiting that forecasting setting to instructions, questions, and brief background information.Splits that include retrieval generally contain five news articles, apart from a few anomalous prompts.
- Split overlap: Nine of fifteen split pairs share qids, totaling 429 instances, but every shared qid maps to different titles and gold answers.The held-out evaluation splits are qid-disjoint from train, and the same-question rate is 0.
- Audit limitation: The audit detects exact-qid and exact-text matches but not semantic near-duplicates under different qids or wording.Embedder- or judge-based detection is required for those semantic matches.
- Examples: Representative OpenForesight examples include short prompts with no retrieved articles, whereas most prompts embed retrieved news passages.The table caption identifies the examples as public test-split rows and contrasts them with the longer typical prompts.
B Temperature sweep
The temperature sweep separates stable correctness and confidence from declining self-consistency. EF-8B becomes less accurate only at high temperatures, while verbalized confidence remains near 50% across the moderate range.
- Stable regime: 37 ± 1% accuracy and approximately 50% confidence remain flat across T ≲1.6.The reported accuracy spread is 1.3 percentage points, within the stated binomial standard error.
- Self-consistency: Self-consistency falls from 66% at T = 0.2 to 30% at T = 2.0 as answer clusters increase from 1.86 to 3.50.The decline spans the full temperature sweep, unlike correctness and confidence.
C Probe training and sweep
The probe sweep evaluates pooling architectures across layers and reasoning-trace locations using frozen-model activations. Probes are trained on one rollout per training question and tested across 3,020 held-out generations.
- Probe sweep: The study sweeps every pooling architecture at every layer and across several reasoning-trace locations.The evaluated sites include the initial span, four rollout fractions, and the final span.
- Data split: Probes train on OpenForesight-train with one rollout per question and evaluate on 302 questions × 10 rollouts = 3,020 test generations.Answer correctness is labeled by an LLM judge.
- Readout sites: Each probe pools a reasoning-anchored span ending at an initial, fractional, or final trace site.The initial span is shared across a question’s rollouts and therefore carries question-level signal only.
- Training objective: Each probe emits logit z, converts it to p = σ(z) = 1/(1 + e^-z), and trains with binary cross-entropy.The setup uses AdamW, temperature T = 1.0, and a covariance bottleneck of dhidden = 64.
Training.
The probe is trained with binary cross-entropy on correctness labels, so its output is optimized to estimate empirical correctness probabilities directly.
- The loss uses −log p for correct forecasts and −log(1 − p) for incorrect forecasts.
- Minimizing binary cross-entropy drives the probe output toward the empirical probability of correctness rather than a hard classification.
- Each rollout contributes one raw probe probability p = σ(z) paired with a binary correctness label y ∈{0, 1}.
Metric.
The paper evaluates probe discrimination and calibration across layers, reasoning sites, pooling families, temperatures, and model comparisons. Covariance pooling performs best in the EF-8B calibration analysis, while verbalized confidence remains overconfident.
- Probe metrics: Covariance pooling is strongest, with its best EF-8B cell at layer 21/final, motivating the deployed probe.Discrimination improves with reasoning depth and concentrates in mid-to-late layers around 18–24.
- Calibration: Brier score is used as the more reliable single calibration summary than ECE, while AUROC is temperature-invariant.EF-8B verbalized confidence achieves Br = 0.190.
- Temperature effects: 37 ± 1% per-rollout accuracy remains flat through T=1.6, then drops to 32.8% at T=2.0.The temperature sweep uses 10 rollouts per question across all 296 test questions.
- Temperature effects: Self-consistency falls from 65.9% at T=0.2 to 30.1% at T=2.0.Self-consistency is defined as the fraction of rollouts in a question’s modal answer cluster.
- Calibration: EF-8B verbalized confidence is overconfident at every tested temperature, with probability mass concentrated in theReliability diagrams group stated probabilities into ten equal-width confidence bins; bars below the diagonal indicate overconfidence.
Models and data.
The GLM probe experiments use frozen models and an OpenForesight dataset with improved question contexts. Probes are trained, selected, and evaluated on separate rollout splits.
- Models and data: The dataset uses 11,835 train rollouts, 1,930 validation rollouts, and 2,960 held-out test rollouts per model.Training comprises 3,945 questions × 3 completions; validation selects the checkpoint, layer, and architecture.
- Models and data: The experiments evaluate frozen GLM-4.7-Flash and GLM-4.5-Air models of two different sizes.The OpenForesight version uses question contexts described as more relevant than those in the OpenForecaster paper.
- Models and data: The validation split determines the checkpoint, layer, and architecture before held-out test reporting.This separates model-selection decisions from final evaluation.
Probe input and training.
The probe setup reads frozen residual-stream activations from reasoning truncated before the final answer, then evaluates correctness decodability across layers and probe families. GLM-4.5-Air shows both ranking and calibration gains, with effects surviving controls.
- Controls and comparisons: GLM-4.5-Air’s clean AUROC delta is +0.110 after removing rollouts that leak a probability tag mid-reasoning.The clean subset contains 1,747 rollouts.
- Controls and comparisons: GLM-4.7-Flash’s leakage-controlled probe-minus-verbalized-confidence AUROC delta is +0.055 with 95% CI [−0.006, 0.111].The comparison uses 423 rollouts with answer-clean reasoning and usable self-report.
- Controls and comparisons: GLM-4.5-Air supports both ranking and calibration gains.Shuffled-label and chain-of-thought-length controls do not explain its signal, and matched comparisons reproduce the effect across both GLM models.
- Layer and family analysis: GLM-4.5-Air’s best layer lies in a broad mid-stack plateau around layers 18–23.The depth profile compares forecast-correctness decodability across residual-stream layers and probe families.
- Probe input and training: Probes receive the prompt plus chain-of-thought truncated before the first boxed answer, excluding the final answer and trailing confidence line.Each probe is a one-stage binary correctness readout trained with BCE on frozen residual-stream activations.
- Probe input and training: The selected sites are L18 last-token for the untrained base and L21 last-token for the DCPO-recipe model.Sites are chosen on held-out validation data and then frozen for evaluation.
Probe training and evaluation.
Evaluation compares correctness probes against multiple confidence baselines and tests whether probe performance reflects genuine activation structure rather than artifacts.
- The evaluation includes token-logprob, recalibrated logprob, verbalized-confidence, and decode-based confidence baselines.
- Controls using random correctness labels and shuffled activations remain near chance, supporting that real probes detect correctness structure in activations.
- Figure 18 marks chance performance at AUROC = 0.5 for randomly labeled and shuffled-activation probes trained with five seeds each.