Stibor

Normalizing flows and neural flows for PyTorch.

• Normalizing flow defines a complicated probability density function as a transformation of the random variable.
• Neural flow defines continuous time dynamics with invertible neural networks.

Install package and dependencies

pip install stribor

Normalizing flows

Base densities

• Normal st.Normal and st.UnitNormal and st.MultivariateNormal
• Uniform st.UnitUniform
• Or, use distributions from torch.distributions

Invertible transformations

• Activation functions
  • ELU st.ELU
  • Leaky ReLU st.LeakyReLU
  • Sigmoid st.Sigmoid
  • Logit (inverse sigmoid) st.Logit
• Affine
  • Element-wise transformation st.Affine
  • Linear layer with LU factorization st.AffineLU
  • Matrix exponential st.MatrixExponential
• Coupling layer that can be combined with any element-wise transformation st.Coupling
• Continuous normalizing flows st.ContinuousTransform
  • Differential equations with stochastic trace estimation:
    • st.net.DiffeqMLP
    • st.net.DiffeqDeepset
    • st.net.DiffeqSelfAttention
  • Differential equations with fixed zero trace:
    • st.net.DiffeqZeroTraceMLP
    • st.net.DiffeqZeroTraceDeepSet
    • st.net.DiffeqZeroTraceAttention
  • Differential equations with exact trace computation:
    • st.net.DiffeqExactTraceMLP
    • st.net.DiffeqExactTraceDeepSet
    • st.net.DiffeqExactTraceAttention
• Cummulative sum st.Cumsum and difference st.Diff
  • Across single column st.CumsumColumn and st.DiffColumn
• Permutations
  • Flipping the indices st.Flip
  • Random permutation of indices st.Permute
• Spline (quadratic or cubic) element-wise transformation st.Spline

Example: Normalizing flow

To define a normalizing flow, define a base distribution and a series of transformations, e.g.:

import stribor as st
import torch

dim = 2

base_dist = st.UnitNormal(dim)

transforms = [
    st.Coupling(
        transform=st.Affine(dim, latent_net=st.net.MLP(dim, [64], 2 * dim)),
        mask='ordered_right_half',
    ),
    st.ContinuousTransform(
        dim,
        net=st.net.DiffeqMLP(dim + 1, [64], dim),
    )
]

flow = st.NormalizingFlow(base_dist, transforms)

x = torch.rand(10, dim)
y = flow(x) # Forward transformation
log_prob = flow.log_prob(y) # Log-probability p(y)

Example: Neural flow

Neural flows are defined similarly but now we don't need the base density and all the invertible transformations must depend on time. In particular, at t=0, the transformation becomes an identity.

import torch
import stribor as st

dim = 2

f = st.NeuralFlow([
    st.ContinuousAffineCoupling(
        latent_net=st.net.MLP(dim, [32], 2 * dim),
        time_net=st.net.TimeLinear(dim),
        mask='ordered_0',
        concatenate_time=False,
    ),
])

x = torch.randn(10, 4, dim)
t = torch.randn_like(x[...,:1])
y = f(x, t=t) # Outputs the same dimension as x

Run tests

pytest --pyargs stribor