CorrDim: Correlation Dimension for Language Models

CorrDim is a Python library for computing the correlation dimension of autoregressive language models from next-token log-probability vectors, based on the paper "Correlation Dimension of Auto-Regressive Large Language Models" (NeurIPS 2025).

Documentation

Full documentation is available at corrdim.readthedocs.io.

Use the docs site for:

• installation details and backend notes
• the full Python API reference
• CLI documentation
• examples and usage patterns

What CorrDim measures

Given a text and an autoregressive language model, CorrDim measures the text's global structural complexity as perceived by that model.

In practice:

• repetitive or degenerate text tends to have a lower correlation dimension
• ordinary fluent text tends to have a higher dimension
• richer long-range structure can produce an even higher dimension

CorrDim is complementary to local metrics such as perplexity: it focuses on sequence-level geometry, not just token-level prediction quality.

How it works

At a high level, CorrDim:

1. converts text into a sequence of next-token log-probability vectors
2. optionally reduces the vocabulary dimension
3. computes a correlation-integral curve over epsilon thresholds
4. estimates the correlation dimension by fitting a line in log-log space

For the mathematical details, see the paper.

Installation

CorrDim requires Python 3.10 or newer. You may use pip or uv to install corrdim.

pip

Linux GPU users: By default, PyPI distributes CPU-only PyTorch on Linux. If you have an NVIDIA GPU, install CUDA PyTorch first. Choose based on your driver version:

CUDA version	Min driver	Install command
cu126 (default)	≥ 525	pip install torch --index-url https://download.pytorch.org/whl/cu126
cu130	≥ 580	pip install torch --index-url https://download.pytorch.org/whl/cu130

(For NVIDIA DGX Spark with GB10, use cu130)

Then, run

pip install corrdim

uv

If using uv, please install PyTorch first before installing corrdim

Linux GPU users: By default, PyPI distributes CPU-only PyTorch on Linux. If you have an NVIDIA GPU, install CUDA PyTorch first. Choose based on your driver version:

CUDA version	Min driver	Install command
cu126 (default)	≥ 525	uv add torch --index https://download.pytorch.org/whl/cu126
cu130	≥ 580	uv add torch --index https://download.pytorch.org/whl/cu130

(For NVIDIA DGX Spark with GB10, use cu130)

Then, run

uv add corrdim

Quick start

import torch
import corrdim

result = corrdim.measure_text(
    "Your text here...",
    model="Qwen/Qwen3-0.6B",
    precision=torch.float16,
)

print("corrdim:", result.corrdim)
print("fit_r2:", result.fit_r2)
print("linear_region_bounds:", result.linear_region_bounds)

For batched input:

import torch
import corrdim

results = corrdim.measure_texts(
    [
        "Short sample A...",
        "Short sample B...",
    ],
    model="Qwen/Qwen3-0.6B",
    precision=torch.float16,
)

for result in results:
    print(result.corrdim, result.fit_r2)

Progressive dimension along the sequence

To fit correlation dimension at multiple prefix lengths without re-running the model for each prefix, use measure_text_progressive. It calls progressive_curve_from_text once, then subsamples prefix indices:

• skip_prefix_tokens: first prefix index to include (shorter prefixes are skipped)
• measure_every_tokens: stride between measured indices, or None (default) to choose from length: fewer than 100 tokens → 1, fewer than 1000 → 10, otherwise 100

The return value is a ProgressiveDimensionResult: by_prefix maps prefix index to a full DimensionResult; corrdims maps index to the fitted scalar only.

import torch
import corrdim

prog_dims = corrdim.measure_text_progressive(
    long_text,
    model="Qwen/Qwen3-0.6B",
    precision=torch.float16,
    skip_prefix_tokens=100,
)

for prefix_len, d in sorted(prog_dims.corrdims.items()):
    print(prefix_len, d)

API overview

The most important entry points are:

• measure_text / measure_texts for end-to-end text measurement
• measure_text_progressive for multiple fitted dimensions along sequence prefixes (one model pass)
• curve_from_text / curve_from_vectors when you want the curve first
• estimate_dimension_from_curve when you already have saved curve data
• progressive_curve_from_text for prefix-wise analysis
• correlation_integral and related functions for lower-level tensor workflows

For full API details, signatures, return types, and backend behavior, see the documentation site.

CLI

CorrDim includes a corrdim command-line interface:

corrdim measure-text \
  --file data/sep60/chaos.txt \
  --model Qwen/Qwen3-0.6B

Additional CLI commands and options are documented at corrdim.readthedocs.io.

Backends

CorrDim supports multiple backends for correlation-integral computation:

• triton
• pytorch
• pytorch_fast
• auto

Set the default backend with:

export CORRDIM_CORRINT_BACKEND=pytorch

Or in Python:

import corrdim

print(corrdim.set_corrint_backend("auto"))
print(corrdim.available_corrint_backends())

Tips for systems with limited GPU RAM (e.g., <10GB)

If you run into out-of-memory errors, reduce block_size (default 512) to lower the peak memory usage during correlation-integral computation:

result = corrdim.measure_text(
    text,
    model="Qwen/Qwen3-0.6B
",
    block_size=128,
)

You can also set forward_chunk_size to control how many tokens are processed per forward pass (reduce this value, e.g. 128, on systems with limited GPU RAM):

result = corrdim.measure_text(
    text,
    model="Qwen/Qwen3-0.6B",
    block_size=128,
    forward_chunk_size=128,
)

Citation

@inproceedings{du2025correlation,
  title={Correlation Dimension of Auto-Regressive Large Language Models},
  author={Du, Xin and Tanaka-Ishii, Kumiko},
  booktitle={Advances in Neural Information Processing Systems},
  year={2025},
  arxiv={2510.21258}
}

Links

• Documentation: https://corrdim.readthedocs.io
• Paper: https://arxiv.org/abs/2510.21258
• Repository: https://github.com/kduxin/corrdim

License

MIT License