torchfbm 0.1.0

Fractional Brownian motion and related processes in PyTorch

torchfbm

Fractional Brownian motion (fBm) and fractional Gaussian noise (fGn) generators, layers, and processes in PyTorch.

Features

• Fast Davies–Harte and exact Cholesky fGn generators: see torchfbm/generators.generate_davies_harte and torchfbm/generators.generate_cholesky.
• fBm paths via cumulative sum: torchfbm/generators.fbm.
• Fractional OU and Geometric fBm processes: torchfbm/processes.fractional_ou_process, torchfbm/processes.geometric_fbm.
• Noisy linear layer and positional embeddings using fBm: torchfbm/layers.FBMNoisyLinear, torchfbm/layers.FractionalPositionalEmbedding.
• Hurst exponent estimator: torchfbm/estimators.estimate_hurst.
• RL action noise stream: torchfbm/rl.FBMActionNoise.

Install

• Editable install:
  • In VS Code terminal:
    • pip install -e .

Quick Usage

• Generate fBm (torch-only):
  • Python:
    • import torch
    • from torchfbm import fbm, get_default_device, set_seed
    • device = get_default_device(); set_seed(42)
    • path = fbm(n=1024, H=0.7, size=(4,), method='davies_harte', device=device, dtype=torch.float32)
• Noisy Linear:
  • Python:
    • from torchfbm import FBMNoisyLinear
    • layer = FBMNoisyLinear(32, 10, H=0.5, method='davies_harte', device=device, dtype=torch.float32, seed=123)
    • x = torch.randn(8, 32, device=device)
    • layer.train(); y1 = layer(x); y2 = layer(x)
    • layer.eval(); y3 = layer(x)
• Processes:
  • Python:
    • from torchfbm import geometric_fbm, fractional_ou_process
    • s = geometric_fbm(n=1000, H=0.7, mu=0.05, sigma=0.2, t_max=1.0, s0=100.0, device=device, dtype=torch.float32)
    • x = fractional_ou_process(n=2048, H=0.6, theta=0.2, mu=0.0, sigma=0.5, dt=1/256, device=device, dtype=torch.float32)

Hurst Estimation

• from torchfbm import estimate_hurst
• H = estimate_hurst(path.unsqueeze(0), min_lag=4, max_lag=64, assume_path=True)

RL Action Noise

• from torchfbm import FBMActionNoise
• noise = FBMActionNoise(mean=0.0, sigma=0.2, H=0.7, size=(1,), buffer_size=10000, method='davies_harte', device=device, return_torch=True, dtype=torch.float32, seed=7)
• a = noise()

Notes

• Choose method='davies_harte' for speed ($O(N \log N)$), cholesky for validation ($O(N^3)$).
• H is clamped to $[0.01, 0.99]$ for stability.
• Set dtype and seed in generators for reproducibility.
• Torch-only: examples avoid .numpy() to work even if NumPy isn't available.