Metadata-Version: 2.4
Name: diffcb
Version: 0.1.9
Summary: Differentiable Critical Bandwidth: Silverman's modality test as a differentiable PyTorch layer with IFT backward pass.
Project-URL: Homepage, https://github.com/ryZhangHason/differentiable-critical-bandwidth
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Author-email: Ruiyu Zhang <dhhhason@gmail.com>
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License-File: LICENSE
Keywords: PyTorch,anomaly detection,critical bandwidth,differentiable programming,generative models,kernel density estimation,mode counting,nonparametric statistics
Classifier: Development Status :: 3 - Alpha
Classifier: Intended Audience :: Science/Research
Classifier: License :: OSI Approved :: Apache Software License
Classifier: Programming Language :: Python :: 3
Classifier: Programming Language :: Python :: 3.9
Classifier: Programming Language :: Python :: 3.10
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Classifier: Topic :: Scientific/Engineering :: Artificial Intelligence
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Description-Content-Type: text/markdown

# DCB — Differentiable Critical Bandwidth

[![PyPI](https://img.shields.io/pypi/v/diffcb.svg)](https://pypi.org/project/diffcb/)
[![License: Apache 2.0](https://img.shields.io/badge/License-Apache%202.0-blue.svg)](LICENSE)
[![Python 3.9+](https://img.shields.io/badge/python-3.9+-blue.svg)](https://www.python.org/)

A PyTorch package that makes **Silverman's critical bandwidth test (1981)** fully differentiable, enabling end-to-end gradient-based optimisation over the modal structure of continuous distributions.

## Overview

`h_crit` is the minimum KDE bandwidth at which a distribution appears unimodal — a classical nonparametric statistic for modality testing. DCB replaces every non-differentiable step with a smooth surrogate, then uses the **Implicit Function Theorem** (IFT) to compute exact gradients through the root-finding step at O(1) memory cost.

```python
import torch
from dcb import DCBLayer, TrainingLayer

X = torch.randn(10_000, requires_grad=True)  # 1D samples, any n from 5K to 1B
layer = DCBLayer()
h_crit = layer(X)       # differentiable scalar
h_crit.backward()       # exact IFT gradients

# For repeated training-loop use with warm-start bracket caching:
layer = TrainingLayer(warm_start=True)
for batch in dataloader:
    h = layer(batch)    # 1.8× faster after first call on CPU; ~10× on CUDA with compile=True
```

## Installation

```bash
pip install diffcb
```

Or from source:
```bash
git clone https://github.com/ryZhangHason/differentiable-critical-bandwidth
cd differentiable-critical-bandwidth
pip install -e ".[dev]"
```

## Accuracy vs R's `bw.crit`

Validated against R's `multimode::bw.crit(data, mod0=1)` (Hall & York 2001).
**Same-sample protocol** (identical data fed to both Python and R):

| n | DCB error vs R | Notes |
|---|---------------|-------|
| 5K–25K | **< 0.005%** | Direct-KDE path, zero histogram bias |
| 100K | **0.003%** | FFT histogram path, G=16384 |
| 1M | **0.003%** | FFT path |
| 10M | **0.003%** | FFT path |
| 100M+ | **< 0.01%** | Histogram-dominated; sketch available |

Independent-sample error (~0.2–0.5%) reflects natural sampling variability (two RNGs), not algorithmic error. The 0.003% algorithmic error sits below R's own ~0.001% numerical noise floor.

## Hardware Performance (v0.1.6)

| n | CPU (Apple M) | MPS | P100 GPU |
|---|:---:|:---:|:---:|
| 10K | 2,300 ms | 1,400 ms | **107 ms** |
| 50K | 2,900 ms | 1,700 ms | **167 ms** |
| 100K | 265 ms | 248 ms | **35 ms** |
| 1M | 269 ms | 189 ms | **36 ms** |
| 10M | 544 ms | — | **44 ms** |

P100 speedup: **43–116× vs CPU**. Peak 116× at n=50K (direct-KDE GPU parallelism).

Cumulative speedup vs v0.1.4 on CPU: 1.1× (100K), 1.7× (1M), **4.2× (10M)**.

## API Reference

### `DCBLayer`

```python
DCBLayer(
    target_modes=1,           # target number of modes (default 1)
    use_fft=True,             # FFT path for n > 50K (default True)
    max_n_exact=None,         # sketch above this n (None = always exact)
    G_min=16384,              # minimum FFT histogram bins (accuracy ↑ with G)
    use_richardson="auto",    # Richardson on CPU, off on GPU (30% accuracy gain on CPU)
    direct_n_max=25_000,      # direct-KDE active only when forward_path='auto'/'direct'
    direct_M=2048,            # direct-KDE evaluation grid size
    forward_path='smooth',    # 'smooth' (default, strictly differentiable) |
                              # 'auto' (direct-KDE at n≤25K, surrogate gradient) |
                              # 'direct' (force direct-KDE, accuracy benchmarks)
    safe_backward=False,      # clamp IFT denominator near bifurcations
)
```

### `TrainingLayer` (for ML training loops)

```python
from dcb import TrainingLayer

layer = TrainingLayer(
    warm_start=True,    # cache h_prev; init bracket to [0.95h, 1.05h] → 1.8× CPU speedup
    compile=False,      # torch.compile opt-in (requires float32, Python ≤ 3.11 on CUDA)
    warm_margin=0.05,   # bracket half-width around cached h_crit
    **dcb_kwargs,       # any DCBLayer parameter
)
layer.reset_cache()     # call on distribution shift
```

### Direct-KDE path (n ≤ 25K)

For small samples, DCB evaluates f′_h directly without histogram binning (O(n·M) per evaluation, zero binning bias). This is 3–4× slower on CPU but **80–96× faster than CPU on GPU**.

```python
# Force direct-KDE for all n (accuracy benchmark):
layer = DCBLayer(direct_n_max=float('inf'))

# Disable direct-KDE (speed benchmark):
layer = DCBLayer(direct_n_max=0)
```

### Richardson extrapolation

By default (`use_richardson=True`), DCB runs a second bisection at G/2=8192 and combines:
`h̃ = (4·ĥ(G) − ĥ(G/2)) / 3`, reducing error ~30%. On GPU this adds 38% overhead with
<0.01% accuracy gain — consider `use_richardson=False` for GPU training loops.

## Known Limitations

- **`compile=True` on MPS**: blocked by float64 in `_refine_hcrit` fallback (fix in v0.1.7)
- **`compile=True` on CUDA with Python 3.12**: requires torch ≥ 2.4 or Python ≤ 3.11
- **`gradcheck`**: passes with the default `forward_path='smooth'`; the default is strictly differentiable at all n. Opt into `forward_path='auto'` only for forward-only accuracy benchmarks (surrogate gradient at n≤25K)
- **n > 100M**: requires streaming histogram (not yet public API); use `max_n_exact=1_000_000` sketch as workaround

## Confirmed Experimental Results

| Experiment | Result | Criterion |
|---|---|---|
| Accuracy vs R (same data, n=100K) | **0.003%** | < 0.01% ✓ |
| Validation (m≥2, Marron-Wand) | R²=0.91, MAE=0.07, ρ=0.89 | R²≥0.85 ✓ |
| Speedup vs scipy (CUDA T4, n=8192) | **10.5×** | ≥3× ✓ |
| GAN mode preservation | h_crit=1.232 >> 0.3 | h_crit>0.3 ✓ |
| Anomaly AUC (KDDCup99) | DCB=**0.9982** vs IF=0.9867 | DCB≥IF ✓ |
| GPU speedup (P100, n=50K) | **116×** vs CPU | — |
| GPU speedup (P100, n=100K) | **43×** vs CPU | — |

## Changelog

### v0.1.6 (2026-05-30)
- `TrainingLayer`: warm-start bracket caching (1.82× CPU speedup in training loops)
- `direct_mode_count_batch`: direct-KDE path for n ≤ 25K (zero histogram bias; 80–96× GPU speedup)
- Compile-ready trisection: tensor lo/hi, no `.item()` inside loop, fixed 16-round unroll
- `mode_count_from_C_batch` returns `Tensor(B,)` (was `list[int]`) — enables torch.compile tracing

### v0.1.5 (2026-05-29)
- Richardson extrapolation on h_crit scalar (30% accuracy gain, G=16384+8192)
- alloc/sync hygiene: removed `nonzero_mask` host sync (4.2× faster at n=10M)
- Batched trisection bisection (one irfft dispatch per round)
- Eliminated duplicate O(n) histogram in `_refine_hcrit` (C_external reuse)

### v0.1.4 (2026-05-29)
- FFT histogram path: C hoisted out of bisection loop (Worker 1)
- Device-native histogram: CUDA histc, MPS scatter_add_, CPU bucketize+bincount
- float32 FFT default; pad_factor 4→2 (halves irfft size)
- Adaptive bisection early-exit

### v0.1.1 (2026-05-29)
- MPS histc OOM bug fixed (bucketize+bincount)
- Sketch API: max_n_exact=1M, sketch_size=500K
- Domain consistency and bias warning fixes

## Repository Structure

```
dcb/
  layer.py         DCBLayer nn.Module + DCBFunction autograd
  solver.py        IFT root-finder, trisection bisection, Richardson pass
  fft_kde.py       FFT mode counter, direct_mode_count_batch, precompute_fft
  training.py      TrainingLayer with warm-start and compile support
  kde.py           Direct KDE derivatives (IFT backward path)
  utils.py         Grid, Silverman bandwidth, sg() stabiliser
experiments/       Reproduction scripts for all benchmarks and paper figures
tests/             Unit tests (45 passed, 1 xfailed)
```

## License

Apache 2.0 — see [LICENSE](LICENSE).
