GPU-accelerated intrinsic dimension estimators in PyTorch. A port of scikit-dimension with batched/vectorized implementations and CUDA support.

Why

scikit-dimension is the reference library for intrinsic dimension (ID) estimation but is CPU-only and relies heavily on per-point Python loops. torchid re-implements every estimator using batched torch ops so the same methods run 100–2700× faster on GPU (measured on an NVIDIA H100, see BENCHMARKS.md) while producing outputs that match the reference library within documented tolerances.

Install

pip install "torchid[cpu]"   # CPU-only (faiss-cpu)
pip install "torchid[cuda]"  # GPU-enabled (faiss-cuda-cu128, manylinux_2_28+)

For a CUDA-capable install, also pick the PyTorch wheel that matches your driver, e.g.:

pip install torch --index-url https://download.pytorch.org/whl/cu128
pip install "torchid[cuda]"

For running parity tests against scikit-dimension from a clone:

uv sync --extra cpu --group validation

Usage

import torch
from torchid.estimators import lPCA

X = torch.randn(10_000, 50, device="cuda")
est = lPCA().fit(X)
print(est.dimension_)

Differentiable ID as a loss

The estimator classes are fit-only; torchid.functional provides differentiable functional forms (mle_id, twonn_id, mom_id, mada_id, pr_id) and torchid.losses wraps them into a minimizable objective — maximizing ID becomes minimizing the ratio 1 - id/D:

from torchid import IntrinsicDimensionLoss

id_loss = IntrinsicDimensionLoss(method="twonn", mode="maximize")

feats = encoder(batch)                    # (B, D), requires_grad
loss = task_loss + 0.1 * id_loss(feats)  # regularize toward higher ID
loss.backward()

Neighbor selection comes from a no-grad kNN; distances are recomputed differentiably from the gathered coordinates, so gradients are exact away from neighbor-order ties. See the API reference for details.

Citation

If you use torchid in your research, please cite:

@software{isaac_corley_2026_22236221,
  author       = {Isaac Corley},
  title        = {isaaccorley/torchid: v0.5.1},
  month        = sep,
  year         = 2026,
  publisher    = {Zenodo},
  version      = {v0.5.1},
  doi          = {10.5281/zenodo.22236221},
  url          = {https://doi.org/10.5281/zenodo.22236221},
}