TorchKM: A GPU-Oriented Library for Kernel Learning and Model Selection

TorchKM is a GPU-accelerated PyTorch-based library for kernel machines including kernel SVM with a focus on fast and integrated train + tune workflows.

It delivers GPU-native and calibrated classifier for tabular data that your code, or your AI agent, can call, and verify.

You give it a table of rows and labels. It trains and tunes a kernel model in one call, on your GPU, and hands back a calibrated probability for each prediction. The result is the exact and provably optimal solution for the objective you asked for. That makes it what a program (or an LLM agent) can call as a trusted tool.

It uses a scikit-learn–style API, for easy integration into existing Python workflows. If you've used scikit-learn, the API will feel immediately familiar, just much faster, and built for the GPU.

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Install

pip install torchkm

30 seconds to a calibrated prediction

from torchkm.estimators import TorchKMSVC

# X: your feature table (n rows x p columns), y: labels in {-1, 1}
clf = TorchKMSVC(kernel="rbf", cv=5, device="cuda", probability=True)
clf.fit(X_train, y_train)          # trains AND tunes (5-fold CV over 50 settings) in one call

clf.predict(X_new)                 # hard labels
clf.predict_proba(X_new)           # calibrated P(class) — a real confidence to threshold on

That's the whole loop: fit → predict_proba. No separate grid search, no manual cross-validation, no second library. Set device="cpu" if you don't have a GPU (same code, slower).

Use it from Claude Code, Codex, Cursor, or any AI agent

Paste this one line into your coding agent and let it wire up the rest:

"Install torchkm and use TorchKMSVC to train a calibrated kernel classifier on my tabular data. Call fit to train and tune, then return predict_proba for new rows."

Because the call surface is tiny and the output is a real probability, an agent can use TorchKM as a reliable tool inside a larger workflow: classify a batch, read the confidence, decide what to do next without hallucinating a label.

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Why a program — or an AI agent — can trust it

• Exact, not approximate. TorchKM returns the provably lowest-objective kernel-SVM solution. Same input → same, well-defined answer. A caller can rely on it.
• Calibrated probabilities. predict_proba (Platt scaling) gives a genuine confidence in [0, 1], not a raw score — so you can set thresholds, abstain when unsure, or route low-confidence cases to a human.
• Fast enough to call in a loop. Full train + tune in tens of seconds on one GPU, where standard tools take minutes to hours (see chart above).
• GPU-native and light. Pure PyTorch/CUDA, a handful of dependencies, with a safe CPU fallback. No CUDA build steps, no C++ toolchain.

Why use TorchKM instead of what you have?

You're using…	The pain	What TorchKM does
scikit-learn SVM	Tuning means an outer GridSearchCV loop that refits from scratch for every setting — minutes to hours.	Folds tuning into the algorithm and reuses matrix work across folds and settings. Often 100×+ faster end-to-end.
ThunderSVM	Fast SVM fitting, but you still bolt on your own CV loop, and it's SVM-only.	One call trains and tunes; also does DWD, logistic, and quantile regression.
A neural net for small tabular data	Overkill, finicky to train, poorly calibrated, no guarantees.	A convex model with a single global optimum, calibrated out of the box, strong on small/mid data.
Raw scores / uncalibrated models	Your agent or rule engine can't reason about "how sure."	Calibrated probabilities you can threshold and trust.

On small-to-mid tabular datasets (roughly hundreds to a few hundred thousand rows), well-tuned kernel methods are still some of the most accurate models there are, and they come with a calibrated probability and a convex, reproducible solution. TorchKM makes the tuning, usually the slow part, very efficient.

Where people use it

Click to expand: example application areas across domains

Anywhere you have a table of rows and want an accurate, calibrated yes/no (or a conditional quantile), especially when the dataset is small-to-mid sized and you care that the model is well-tuned and trustworthy:

Healthcare & life sciences

• Disease / readmission / adverse-event risk from clinical and lab features, where a calibrated probability matters more than a raw score.
• Bioinformatics classification (gene expression, omics, sequence-derived features): a classic stronghold of kernel methods on wide, small-sample data.
• Drug-response and compound-activity (active/inactive) screening.

Finance & risk

• Credit default, fraud, and churn scoring where you need a probability to set a decision threshold or expected-loss cutoff.
• Quantile regression for value-at-risk and prediction intervals (TorchKMKQR).

Industry & operations

• Predictive maintenance: pass/fail and time-to-failure from sensor features.
• Manufacturing QC and anomaly flagging on tabular process data.
• Demand or load quantile forecasting for capacity planning.

Security & trust

• Spam, phishing, malware, and intrusion detection on engineered features.
• Bot / abuse classification where calibrated confidence drives auto-block vs. review.

Marketing & product

• Lead scoring, propensity-to-buy, conversion and retention prediction.
• A/B segment classification on behavioral features.

Science & engineering

• Materials and chemistry property classification on small experimental datasets.
• Remote-sensing / geospatial pixel classification on tabular feature vectors.
• Any lab setting where you have a few hundred to a few thousand measurements and want the most accurate model you can defend.

AI agents & tooling

• A callable classification tool for LLM agents: hand the agent a fast, calibrated classifier so it stops guessing on structured data and starts deciding on a real probability.
• A confidence gate in automated pipelines: act when predict_proba is high, escalate to a human when it isn't.
• A cheap, reproducible second opinion to cross-check an LLM's structured-data judgments.

Scope note: TorchKM does binary classification (SVM, DWD, logistic) and kernel quantile regression today. For multiclass, wrap it one-vs-rest (a good first contribution — see below). It shines on small-to-mid tabular data; for millions of rows, use the built-in Nyström mode (low_rank=True).

The same three lines, on different jobs. Ask in plain language, get a fast calibrated probability back:

Finance — fraud	Healthcare — readmission
Security — phishing	Industry — predictive maintenance
Marketing — churn	Life sciences — tumor vs normal

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What's inside

scikit-learn-style estimators: same fit / predict / predict_proba interface across all of them:

Estimator	Task
TorchKMSVC	kernel SVM classifier
TorchKMDWD	kernel distance-weighted discrimination classifier
TorchKMLogit	kernel logistic regression
TorchKMKQR	kernel quantile regression

Common methods: fit(X, y), predict(X), decision_function(X), predict_proba(X) (when probability=True), platt_plot(X, y).

Kernels: rbf (default) and poly. Utilities: rbf_kernel, kernelMult, sigest, standardize, data_gen.

Key benefits, in one place:

• Integrated train + tune — pathwise solutions over a grid of regularization values (Cs) with cross-validation built in, not bolted on.
• Exact cross-validation for kernel machines (including exact LOOCV for kernel SVM).
• GPU acceleration via PyTorch/CUDA, with safe CPU fallback.
• Nyström low-rank mode (low_rank=True) for large datasets.
• Calibrated probabilities via Platt scaling.

How it's so fast

In a normal workflow the slow part isn't fitting one model. It's refitting the model for every cross-validation fold and every tuning value. TorchKM avoids that: it reuses one kernel computation across all folds and settings (an exact cross-validation formula plus a single eigendecomposition reused along the regularization path). You still get the exact solution, without paying for it 500 times.

The result, from the paper's benchmarks (one GPU, full train + tune, 10-fold CV over 50 settings):

Dataset	scikit-learn	ThunderSVM	TorchKM
n=10,000, p=1,000	14,322.8 s (~4 h)	279.4 s	37.7 s
n=20,000, p=1,000	did not finish in 8 h	580.8 s	129.3 s

In every case TorchKM also reached the best (lowest) objective, i.e. a provably better solution, not just a faster one.

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More examples

Larger datasets — Nyström low-rank mode

clf = TorchKMSVC(
    kernel="rbf",
    low_rank=True, num_landmarks=40, nys_k=20,
    cv=5, device="cuda", probability=True,
)
clf.fit(X_train, y_train)

You can also enable it at fit time: clf.fit(X, y, low_rank=True, num_landmarks=40, nys_k=20).

Kernel quantile regression

from torchkm.estimators import TorchKMKQR

qr = TorchKMKQR(kernel="rbf", cv=3, tau=0.5, device="cuda")  # tau = the quantile
qr.fit(X_train, y_train)
qr.predict(X_new)

Use TorchKMKQR(low_rank=True) for the Nyström approximation on large data. (There is no separate TorchKMNysKQR class.)

Probabilities

Set probability=True to enable Platt scaling and predict_proba. platt_plot(X, y) visualizes the calibration.

Device

import torch
device = "cuda" if torch.cuda.is_available() else "cpu"

TorchKM runs on GPU when CUDA is available and falls back safely to CPU otherwise.

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Documentation

Full docs, API reference, tutorials, and benchmark-reproduction notes: https://yikaizhang95.github.io/torchkm/

Development install

git clone https://github.com/YikaiZhang95/torchkm.git
cd torchkm
pip install -e ".[dev,examples,viz]"
python -m pytest -q

Testing and coverage

python -m pytest -q

CI runs the CPU-safe suite across Python 3.10, 3.11, and 3.12, and enforces a minimum 90% coverage on 3.11. The most recent CUDA validation reports 214 tests passed and 98% coverage on an NVIDIA L40S. CUDA smoke tests (pytest.mark.cuda) skip automatically when CUDA is unavailable; run them with python -m pytest -q -m cuda.

Contributing

Issues, bug reports, benchmarks, docs, and pull requests are welcome — see CONTRIBUTING.md.

Good first contributions:

• additional kernels
• a multiclass (one-vs-rest) wrapper
• more benchmark scripts
• expanded examples and tutorials

Citation

If you use TorchKM in academic work, please cite:

@article{zhang2026torchkm,
  title   = {TorchKM: A GPU-Oriented Library for Kernel Learning and Model Selection},
  author  = {Zhang, Yikai and Jia, Gaoxiang and Ding, Jie and Wang, Boxiang},
  year    = {2026},
  url    = {https://arxiv.org/pdf/2606.06742}
}

License

MIT License. See LICENSE.

Contact

Yikai Zhang — [email protected]