ssubhnil/Reasoning-Failures

Effectiveness of Hidden-State Probes for Localizing Reasoning Failures

NeurIPS 2026 Workshop: Interpretability as a Science

This dataset accompanies the paper Effectiveness of Hidden-State Probes for Localizing Reasoning Failures (Interpretability as a Science: NeurIPS 2026 Workshop). It contains reasoning traces from Qwen3-4B and Qwen3-8B on DeepMath-103K and Hendrycks MATH problems, Monte Carlo continuations from each step of the incorrect traces, the failure labels assigned from those continuations, probe scores and checkpoints, per-step hidden-state features, and the inputs of every table command in the code repository. The traces are generated on DeepMath-103K examples at difficulty ≥ 7 and on levels 4 and 5 of the Hendrycks MATH training split. It also contains evaluation runs of Qwen3-1.7B, 4B, 8B and 14B on nine math benchmarks at token budgets from 2,048 to 32,768, with one sampled generation per problem.

The files keep the layout that the code reads. Download the table inputs with

hf download ssubhnil/Reasoning-Failures --repo-type dataset --local-dir hf_data \
  --include "runs/*" --include "data/*" \
  --exclude "runs/hf_pull/mc_rollouts_locus_k16/*/campaign/branches.jsonl.zst" \
  --exclude "runs/hf_pull/mc_rollouts_locus_k16/*/corpus/*" \
  --exclude "*/conf_probe.pt" --exclude "*/value_probe.pt" \
  --exclude "runs/hf_pull/probe_corpus_16k/*" --exclude "runs/value_probe/ask_a_818/_packed/*"

and omit the --include and --exclude options to download everything.

Failure types

Failure types on three Qwen3-4B traces from the gold collection. Each panel shows the rollout rate $\hat p_t$ at the evaluated steps and the envelope $V^*_t$. For a pit, the envelope crosses $\theta = 0.1$ partway through the trace, at the pit step. For a near miss, the envelope never crosses the threshold. For a capability gap, the envelope is below the threshold from step 0.

Failure types in the broad collection (28,699 incorrect Qwen3-4B traces and 24,871 Qwen3-8B traces): their shares, the relative depth of the pit step, and the best reachable value before the pit step.

Confidence-probe predictions at the final step of each trace on the broad collection (read positions are described under Hidden-state features), with training and validation split by problem. (A) Miss rate by failure type. (B) Pit and near miss, binned by the best reachable value at step 0. (C) Pit-versus-near-miss AUROC of the confidence probe and the combined probe.

Models

Model	Repository	Licence
Qwen3-4B	Qwen/Qwen3-4B	Apache-2.0
Qwen3-8B	Qwen/Qwen3-8B	Apache-2.0
Qwen3-4B transcoders	mwhanna/qwen3-4b-transcoders	MIT
Qwen3-8B transcoders	mwhanna/qwen3-8b-transcoders	MIT

The evaluation runs also use Qwen/Qwen3-1.7B and Qwen/Qwen3-14B (Apache-2.0). Model weights and transcoder weights are not included here.

Contents

Path	Contents	Size
probe_corpus_16k/qwen3-{4b,8b}/	All generated traces: 144,000 per model (35,854 problems, about four traces each), with the rendered prompt, the trace, step segmentation and the stored correctness label	7.5 GB (4B), 7.8 GB (8B)
runs/hf_pull/probe_corpus_16k/qwen3-{4b,8b}/_p1_packed/	The same 144,000 traces per model with their hidden-state features (see Hidden-state features); the trace text duplicates probe_corpus_16k/	34.0 GB (4B), 52.7 GB (8B)
runs/value_probe/ask_a_818/_packed/	Hidden-state and next-token features of the 818 gold-collection pit traces	0.2 GB
runs/hf_pull/mc_rollouts_locus_k16/qwen3-{4b,8b}/corpus/	The incorrect traces that the continuations start from (28,699 at 4B, 24,871 at 8B), with the gold answer	2.0 GB (4B), 1.8 GB (8B)
runs/hf_pull/mc_rollouts_locus_k16/qwen3-{4b,8b}/campaign/branches.jsonl.zst	Continuations: 3,600,080 at 4B and 3,270,056 at 8B, one per line, with the step they start from and whether they reach the correct answer	4.1 GB per model
runs/hf_pull/mc_rollouts_locus_k16/qwen3-{4b,8b}/campaign/mc_ground_truth.pt	Rollout rates: for each trace and evaluated step, the fraction of continuations that reach the correct answer and their number (382,449 steps at 4B, 350,346 at 8B)	11 MB (4B), 10 MB (8B)
runs/hf_pull/mc_rollouts_locus_k16/qwen3-{4b,8b}/campaign/gold_pits.json	Failure types of every incorrect trace in the broad collection, with the pit step and the rollout rates along the trace	8 MB (4B), 7 MB (8B)
runs/hf_pull/mc_rollouts_locus_k16/qwen3-{4b,8b}/campaign/gold_pits_by_md5.pt	Pit steps keyed by the MD5 of the trace text	0.5 MB (4B), 0.4 MB (8B)
runs/mc_gold/	The gold collection (campaign_final/, Qwen3-4B): 5,380 traces, 818 of them with a pit step, failure types and rollout rates only; and copies of the broad-collection labels (locus_{4b,8b}_k16/)	19 MB
runs/resp/	Pointer-probe labels, predictions and scores; gold-collection pit steps keyed by MD5 (campaign_final/)	28 MB
runs/conf_probe/, runs/conf_probe_psplit/, runs/mc_conf_probe/ (excluding checkpoints)	Confidence-probe scores per trace, split and seed, their controls, the per-seed calibration scores and the reasoning-dynamics text features (conf_probe/dynamics/)	0.4 GB
runs/conf_probe{,_psplit}/qwen3-{4b,8b}/, runs/mc_conf_probe/qwen3-{4b,8b}/, runs/value_probe/qwen3-*/	Probe checkpoints (PyTorch state dicts) and their metrics	4.6 GB
runs/value_probe/ (excluding checkpoints)	Value-probe readouts and the label-swap per-trace scores	0.1 MB
runs/layer_selection/qwen3-{4b,8b}/	Read-site selection curves: correctness AUROC by layer and by number of layers	37 KB
runs/failure_type_classifier/	Transcoder failure-type classifier: stored per-partition scores and the inputs of the classifier fit	72 MB
runs/paper/labels/, runs/paper/correction_flags/	Label correction flags, keyed by trace	13 MB
data/paper_tables/, data/problem_lookup.parquet	Stored tables read by the figure commands and the supporting table; problem topic and difficulty	1 MB
evaluation/<benchmark>/	Evaluation runs, one sampled generation per model, benchmark, token budget and problem	10.1 GB

Path components such as hf_pull, mc_rollouts_locus_k16, locus_{4b,8b}_k16 and bipp_locus_4b are directory names from the original runs. So are _p1_packed (trace shards with hidden-state features), ask_a_818 (the gold collection's 818 pit traces), campaign_final and campaign (the label directories of the gold and the broad collection) and psplit (problem split); -hidlogit marks the probe variant whose inputs add the five next-token statistics. The code reads these paths, so they are kept.

Loading

The .pt files are pickles; load them only from this repository.

import json, torch
labels = json.load(open("runs/hf_pull/mc_rollouts_locus_k16/qwen3-4b/campaign/gold_pits.json"))
trace_id, row = next(iter(labels.items()))
row["regime"], row["gold_pit"], row["curve"]

steps = torch.load("runs/hf_pull/mc_rollouts_locus_k16/qwen3-4b/campaign/mc_ground_truth.pt", weights_only=False)
steps[trace_id][0]   # {'p_correct_mc': ..., 'n_rollouts': ...}

import pandas as pd, pyarrow as pa
with pa.input_stream("runs/hf_pull/mc_rollouts_locus_k16/qwen3-4b/campaign/branches.jsonl.zst", compression="zstd") as f:
    continuations = pd.read_json(f, lines=True, nrows=1000)   # trace_id, step, idx, correct, text

from datasets import load_dataset
math500 = load_dataset("ssubhnil/Reasoning-Failures", "eval_math500", split="train")

Steps

Each trace is split at blank lines and adjacent blocks are merged until every step has at least 400 tokens (merged_step_char_spans in sst/shared/extractors.py of the code repository, Qwen3 tokenizer); every step index in this dataset uses this segmentation.

Hidden-state features

The feature shards hold one vector per step for every trace: the model's hidden state at layers 23 and 24, read at the stored end position of each step, concatenated, in bfloat16 (5,120 numbers per step at Qwen3-4B, 8,192 at Qwen3-8B). The gold-collection shards add five statistics of the next-token distribution at the same position (entropy, varentropy, top probability, the margin to the second token and the top-5 mass). The shards contain the same traces as probe_corpus_16k/, so download one or the other unless you need both. To use them, either download them, for example

hf download ssubhnil/Reasoning-Failures --repo-type dataset --local-dir hf_data \
  --include "runs/hf_pull/probe_corpus_16k/qwen3-4b/_p1_packed/*"

(34.0 GB for Qwen3-4B, 52.7 GB for Qwen3-8B), or regenerate them with scripts/precompute_p1_features.py in the code repository.

Read positions. The features were not read exactly at the last token of each step. The stored step positions (step_spans) were computed from each step tokenized on its own, and the features were extracted in left-padded batches without shifting those positions. Each read therefore sits earlier in the trace than the step's last token, by the same number of tokens for every step of a trace: a median of 157 tokens at Qwen3-4B and 148 at Qwen3-8B, at most 512, and zero for about 22% of traces (pad widths reconstructed from the batching rule). For the final step, the read falls inside the intended step in 51.0% (4B) and 51.6% (8B) of traces and in an earlier step in 48.9% and 48.3% (the remaining 0.1% fall between steps). Tokenizing steps separately adds a smaller drift (a median of 3 tokens on a 40-trace Qwen3-4B sample). The probes in the paper were trained and evaluated on these features, and scripts/precompute_p1_features.py reads at the same positions. No result was re-scored with corrected positions. To read exact last-token states, locate steps with merged_step_char_spans and map their character spans to the token offsets of the joint prompt-and-trace tokenization.

Labels

Each incorrect trace is labelled from the rollout rate $\hat p_t$, the fraction of continuations sampled from step $t$ that reach the correct answer. The best reachable value $V^*_t$ (the envelope) is the largest value at step $t$ or any later step of the trace.

Name in the paper	Value in the files	Definition
capability gap	regime = "capability"	the envelope is at or below $\theta = 0.1$ already at step 0
pit	regime = "pit"	the envelope first falls to $\theta$ or below at an interior step, the pit step
near miss	regime = "reaches"	the envelope never falls to $\theta$ or below
pit step	gold_pit	the first step at which the envelope is at or below $\theta$; empty for capability gaps and near misses
rollout rate	p_correct_mc	$\hat p_t$; n_rollouts is the number of continuations $K$
correctness label	is_correct	the stored verdict of the answer checker on the final answer

Evaluation runs

The evaluation/ files hold one generation per model, benchmark, token budget and problem. The generations were sampled: the sampling temperature was not recorded (the generation code's default was 0.7), and no seed was fixed, so a rerun does not reproduce the traces. The decoding column marks the two math_test files, for Qwen3-1.7B and Qwen3-4B, whose traces agree across token budgets as greedy decoding would (greedy_inferred); every other file reads sampled. Revisions up to 9c2e9ea8 carried temperature and seed columns filled with the constants 0.0 and 42, which did not record the decoding settings. Strict accuracy is the mean of correct_strict: the answer is correct and was produced without forced extraction. Answer-forced accuracy is the mean of correct_answer_forced, which also counts answers extracted after a final answer was forced (answer_forced). The evaluation runs are released with the dataset; the paper does not report them. These runs were previously released as the dataset ssubhnil/Qwen3-Math-Eval, which this repository replaces.

Benchmark	Config	Distinct problems	Models	Token budgets
MATH-500	eval_math500	500	1.7B, 4B, 8B, 14B	2k to 16k
MATH test	eval_math_test	5,000	1.7B, 4B, 8B, 14B	2k to 16k (1.7B and 4B: 2k to 8k)
MATH competition subset	eval_competition_math	251	1.7B, 4B	2k to 16k
MATH train L1-3	eval_math_train_l1_3_indist	2,283	1.7B, 4B, 8B, 14B	2k to 16k
MATH-Perturb	eval_math_perturb	836	1.7B, 4B, 8B, 14B	2k to 16k
GSM-Plus	eval_gsm_plus	2,400	1.7B, 4B, 8B, 14B	2k to 16k
AIME 2024-25	eval_aime	60	1.7B, 4B, 8B, 14B	2k to 32k
Putnam-AXIOM	eval_putnam_axiom	597	1.7B, 4B, 8B, 14B	2k to 32k
DeepMath-103K	eval_deepmath	101,882	4B, 8B, 14B	4k to 32k

Distinct problems are counted by question text. MATH-Perturb has 837 rows per run (one question appears twice), Putnam-AXIOM 600, and DeepMath-103K covers all difficulty levels. GSM-Plus is its 2,400-problem testmini split.

Strict accuracy against token budget for every benchmark and model. Bars are 95% intervals from a bootstrap over problems; n is the number of distinct problems.

Strict (solid) and answer-forced (dashed) accuracy for Qwen3-4B and Qwen3-8B.

DeepMath-103K strict accuracy by difficulty at the 16k token budget, on rows whose gold answer is not yes/no, true/false, a single letter or empty (these forms are affected by the answer-checker correction; see Limitations). The lower strip gives the number of problems per difficulty; difficulties at most 2.5 and at least 9.5 are pooled. The dashed line marks difficulty 7, the lower bound of the examples used for the traces.

Limitations

• Correctness labels are stored as produced. The correction flags in runs/paper/ mark traces whose label changes under the corrected answer checker (binary answers, letter answers and unparseable answers); the labels themselves are not rewritten.
• The evaluation labels were produced by an answer checker that predates a correction for yes/no, true/false and letter answers. The released correct_strict and correct_answer_forced columns are these stored labels; the corrected checker is the one in the code repository, and nothing here was regraded. The stored gold answers show the affected forms: in DeepMath, 218,916 of 1,235,860 rows have a yes/no or true/false gold parsed as a product of symbols (for example [e*s*y] for yes), 42,406 have a single-letter gold and 18,225 have an empty gold ([]). The other benchmarks have few such rows. The share of affected gold forms rises with DeepMath difficulty, from 14% at difficulty 6.5 or below to above 65% at 8.5 and above.
• The continuations were sampled with settings (temperature, top-p, seed) that were not recorded with the files and cannot be recovered. Each continuation is capped at 4,096 tokens. In the broad collection, refined steps received 16 continuations and scanned steps 8 (both models); in the gold collection, refined steps received 8 and scanned steps 4.
• The step_rewards field of the traces is a constant placeholder (0.5) and carries no information. Problem ids in probe_corpus_16k are indices within the dataset named by their directory.
• data/problem_lookup.parquet gives the DeepMath-103K level-two topic and difficulty for DeepMath problems. For Hendrycks MATH problems the difficulty is the MATH level (4 or 5) where known and is otherwise empty.
• The DeepMath-103K solution fields (r1_solution_*) are not included.
• Transcoder activations are not distributed. The code repository contains the extraction script.
• In the evaluation files, problem_id is not one scheme across models: MATH test uses 0, 1, … for Qwen3-1.7B and 4B and hmath_algebra_0, … for Qwen3-8B and 14B, and DeepMath ids repeat across source_shard. Match problems on question.
• The DeepMath runs of Qwen3-4B miss 202 (4,096 tokens), 105 (8,192) and 97 (16,384) of the 101,882 distinct DeepMath questions that the Qwen3-14B runs cover.

Sources and licences

The material produced for this dataset (traces, continuations, labels, probe scores and checkpoints, tables) is released under CC BY 4.0. Benchmark problems keep the licence of their source.

Source	Used in	Licence declared by the source
DeepMath-103K	problems of the traces; topic and difficulty; evaluation/deepmath	MIT
Hendrycks MATH	problems of the traces; evaluation/math_test, evaluation/competition_math	MIT
MATH-500	evaluation/math500	no licence declared by the source
MATH-Perturb	evaluation/math_perturb	Apache-2.0
GSM-Plus	evaluation/gsm_plus	CC BY-SA 4.0; these files are distributed under CC BY-SA 4.0
Putnam-AXIOM	evaluation/putnam_axiom	Apache-2.0
AIME 2024, AIME 2025	evaluation/aime	no licence declared by the source
NuminaMath-CoT	evaluation/math_train_l1_3_indist	Apache-2.0

Licences were read from each source's card or repository on 2026-10-04.

Citation

@inproceedings{
subhnil2026effectiveness,
title={Effectiveness of Hidden-State Probes for Localizing Reasoning Failures},
author={Shubham Subhnil and Yannis Belkhiter and Erik Miehling and Adam Dahlgren Lindstr{\"o}m and Elizabeth M. Daly},
booktitle={Interpretability as a Science: NeurIPS 2026 Workshop},
year={2026},
url={https://openreview.net/forum?id=X1D0ZeEeZ4}
}

Please also cite the source benchmarks above.

Acknowledgement

This work was funded in part by the EU Horizon project ELIAS (#101120237). Views and opinions expressed are those of the author(s) only and do not necessarily reflect those of the European Union or The European Research Executive Agency. This work was partially supported by the Knut and Alice Wallenberg Foundation. Experiments were run on the Cognitive Compute Cluster (CCC) at IBM Research.