CDUR: Calibration Drift Under Reasoning

Calibration Drift Under Reasoning: How Chain-of-Thought Budgets Induce Overconfidence in Large Language Models

Prakul Sunil Hiremath · Harshit R Hiremath (Aliens on Earth)

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Overview

This repository contains the complete reproduction pipeline for the CDUR paper.

CDUR is the phenomenon whereby increasing the reasoning budget of a large language model (LLM) first improves and then worsens calibration, producing a non-monotone trajectory in the Expected Calibration Error (ECE) as a function of reasoning budget $B$.

The paper introduces:

• A formal definition of CDUR via a U-shaped $\text{ECE}(B)$ function.
• The Hypothesis Lock-In Model: a mechanistic account of autoregressive reasoning under commitment.
• Empirical evidence on Llama-3.1-8B and Llama-3.3-70B across four reasoning budgets and 21 trap-question categories.
• CABStop: a calibration-aware optimal stopping rule that halts reasoning when confidence diverges from an auxiliary accuracy estimate.

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Repository Structure

cdur/
├── config/
│   └── default_config.yaml     # Model, budget, elicitation, and CABStop parameters
├── src/
│   ├── __init__.py
│   ├── data_loader.py          # Reasoning-trap dataset + response validity filter
│   ├── evaluators.py           # Evaluation coordinator + calibrated LLM simulator
│   ├── metrics.py              # ECE, overconfidence gap, wrong-and-confident count
│   └── cabstop.py              # CABStop algorithm (Algorithm 1 from paper)
├── run_pipeline.py             # Main entry point
├── requirements.txt
├── Experiments/
│   ├── v1.0.py       
│   ├── v1.1.py         
│   ├── v1.2.py         
│   ├── v1.3.py          
│   ├── v2.py             
│   └── v3.py
├── Paper
│   ├── 2606.11211v1.pdf   
└── README.md

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Installation

Requires Python 3.10 or later.

git clone https://github.com/prakulhiremath/CDUR.git
cd CDUR
pip install -r requirements.txt

No GPU or API key is required to run the reproduction pipeline. The evaluator uses a deterministic simulator calibrated to the empirical 8B results reported in the paper.

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Quickstart

Run the full pipeline with default settings (both models, all four budgets, seeds 1/2/3):

python run_pipeline.py

Run only the 8B model with light and heavy budgets:

python run_pipeline.py --models llama-3.1-8b --budgets none light heavy

Adjust CABStop threshold and seeds:

python run_pipeline.py --delta 0.15 --seeds 1 2 3 4 5

Suppress CABStop demo output:

python run_pipeline.py --no-cabstop

Increase logging verbosity:

python run_pipeline.py --log-level DEBUG

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Expected Output

Running python run_pipeline.py prints:

1. Results table — ECE (mean ± std across seeds), overconfidence gap, and accuracy per model per budget.
2. Smoking gun examples — incorrect responses with confidence ≥ 0.90.
3. CABStop demo — per-question stopping decisions for the first three dataset items.

Example results table (abbreviated):

  CDUR Reproduction Results — Calibration Drift Under Reasoning

  ┌──────────────────────┬──────────┬────────────────┬────────────────┬────────────┐
  │ Model                │ Budget   │ ECE (mean±std) │ OG (mean)      │ Acc (mean) │
  ├──────────────────────┼──────────┼────────────────┼────────────────┼────────────┤
  │ llama-3.1-8b         │ none     │ 0.0436 ± 0.015 │ +0.4930        │ 0.4610     │
  │                      │ light    │ 0.1040 ± 0.034 │ +0.2490        │ 0.7320     │
  │                      │ medium   │ 0.0496 ± 0.049 │ +0.3360        │ 0.6530     │
  │                      │ heavy    │ 0.0145 ± 0.005 │ +0.2450        │ 0.7390     │
  ├──────────────────────┼──────────┼────────────────┼────────────────┼────────────┤
  │ llama-3.3-70b        │ none     │ 0.0352 ± 0.026 │ +0.1550        │ 0.8250     │
  │                      │ light    │ —              │ —              │ —          │
  ...

The non-monotone ECE trajectory for llama-3.1-8b (none → light → medium → heavy) is the primary empirical signature of CDUR.

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Configuration

All parameters are controlled via config/default_config.yaml.

Key	Default	Description
elicitation.temperature	0.7	Sampling temperature
elicitation.seeds	[1, 2, 3]	Random seeds for variance estimation
cabstop.delta	0.10	Calibration gap threshold for halting
cabstop.max_budget	2048	Maximum token budget before forced stop
cabstop.check_interval	128	Token interval between CABStop checks
cabstop.self_consistency_k	5	Number of samples for auxiliary accuracy estimate
metrics.ece_bins	10	Number of equal-width bins for ECE
metrics.overconfidence_threshold	0.90	Confidence threshold for wrong-and-confident count

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Modules

src/data_loader.py

Contains 25 hardcoded reasoning-trap questions across 15 categories (counting, set_theory, spatial, semantic, probability, syllogism, algebra, modular, operator_precedence, percentage, compound, contrapositive, anchor, combinatorics, relative_motion, conditional_prob, exponential, mixture, pattern). Each question is a TrapQuestion dataclass with id, category, question, and expected_answer. Includes a regex-based response validity filter.

src/metrics.py

Implements:

• calculate_ece(confidences, accuracies, num_bins) — equal-width binning, empty-bin safe.
• calculate_overconfidence_gap(confidences, accuracies) — mean confidence minus mean accuracy.
• compute_metrics(...) — returns a CalibrationMetrics dataclass.
• aggregate_metrics_across_seeds(...) — mean and std across seed runs.

src/evaluators.py

Deterministic simulator calibrated to match the empirical dynamics of Llama-3.1-8B:

• none budget: moderate accuracy (0.46), highly volatile confidence, many confident-wrong responses.
• light budget: higher accuracy (0.73) with Hypothesis Lock-In signature — confidence inflated to ~1.0.
• medium budget: slightly lower accuracy (0.65) with instability.
• heavy budget: highest accuracy (0.74), near-maximum confidence, lowest ECE.

70B model applies a scale correction factor (+35% accuracy) relative to 8B.

src/cabstop.py

Implements Algorithm 1 from the paper. At each check_interval token checkpoint:

1. Extracts candidate answer and confidence via inference_fn(t).
2. Estimates auxiliary accuracy via simulated self-consistency over k samples.
3. Halts and returns if confidence − auxiliary_accuracy > delta.

run_pipeline.py

CLI entry point. Parses arguments, loads config, calls run_evaluation, computes aggregate metrics, and prints formatted ASCII tables.

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Reproducing Paper Results

The simulator in src/evaluators.py is parameterized to reproduce the key empirical observations from Table A.1 of the paper:

Model	Budget	ECE (paper)	OG (paper)	Acc (paper)
8B	none	0.0436 ± 0.015	+0.493	0.461
8B	light	0.1040 ± 0.034	+0.249	0.732
8B	medium	0.0496 ± 0.049	+0.336	0.653
8B	heavy	0.0145 ± 0.005	+0.245	0.739
70B	none	0.0352 ± 0.026	+0.155	0.825

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Live API Evaluation

To run against a real LLM API, replace the _simulate_response function in src/evaluators.py with a call to your preferred inference endpoint. The ModelResponse dataclass and parse_and_validate_response function in src/data_loader.py handle response validation and confidence extraction automatically.

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Citation

If you use this codebase or build on the CDUR framework, please cite:

@article{hiremath2025calibration,
  author    = {Hiremath, Prakul Sunil and Hiremath, Harshit R.},
  title     = {Calibration Drift Under Reasoning: How Chain-of-Thought Budgets Induce Overconfidence in Large Language Models},
  journal   = {arXiv preprint arXiv:2606.11211},
  year      = {2025},
  doi       = {10.5281/zenodo.19709379},
  url       = {https://arxiv.org/abs/2606.11211},
  note      = {Code available at \url{https://github.com/prakulhiremath/CDUR}. Post commentary available at Medium (\url{https://medium.com/@prakulhiremath/the-ai-that-thinks-too-hard-and-gets-dangerously-wrong-7f3c32e62864})}
}

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License

MIT License. See LICENSE for details.