pages/bayesian-deep-learning/00_function_space_manifold.py

import streamlit as st
import numpy as np
import matplotlib.pyplot as plt

import config  # noqa: F401


@st.cache_data
def generate_scatter_plot(
    activation, sigma, sigma_bias, include_bias, num_samples=5000
):
    """Generate scatter plot of function space samples with theoretical curve."""
    rng = np.random.default_rng(42)
    theta = rng.normal(0, sigma, num_samples)
    if include_bias:
        bias = rng.normal(0, sigma_bias, num_samples)
    else:
        bias = 0.0
    x1, x2 = 1.0, 2.0
    z1 = theta * x1 + bias
    z2 = theta * x2 + bias
    if activation == "sin":
        f1, f2 = np.sin(z1), np.sin(z2)
        label1, label2 = (
            r"$f_1 = \sin(\theta \cdot x_1 + b)$",
            r"$f_2 = \sin(\theta \cdot x_2 + b)$",
        )
    elif activation == "tanh":
        f1, f2 = np.tanh(z1), np.tanh(z2)
        label1, label2 = (
            r"$f_1 = \tanh(\theta \cdot x_1 + b)$",
            r"$f_2 = \tanh(\theta \cdot x_2 + b)$",
        )
    else:  # relu
        f1, f2 = np.maximum(0, z1), np.maximum(0, z2)
        label1, label2 = (
            r"$f_1 = \mathrm{ReLU}(\theta \cdot x_1 + b)$",
            r"$f_2 = \mathrm{ReLU}(\theta \cdot x_2 + b)$",
        )

    fig, ax = plt.subplots(figsize=(6, 2))
    ax.scatter(f1, f2, alpha=0.3, s=5, c="tab:blue")

    if activation == "relu":
        ax.set_xlim(-0.05, 4.05)
        ax.set_ylim(-0.05, 8.05)
    else:
        ax.set_xlim(-1.02, 1.02)
        ax.set_ylim(-1.05, 1.05)
    ax.set_xlabel(label1)
    ax.set_ylabel(label2)

    return fig


# --- Page UI ---
st.title("Function Space Priors: Low-Dimensional Manifolds")

col1, col2 = st.columns([0.5, 2])
with col1:
    activation = st.selectbox(
        "Activation",
        options=["sin", "tanh", "relu"],
        index=0,
    )
    sigma = st.slider(
        "Weight std ($\\sigma$)",
        min_value=0.1,
        max_value=3.0,
        value=1.0,
        step=0.1,
    )
    include_bias = st.toggle("Include bias")
    if include_bias:
        sigma_bias = st.slider(
            "Bias std ($\\sigma_b$)",
            min_value=0.1,
            max_value=3.0,
            value=1.0,
            step=0.1,
        )
    else:
        sigma_bias = 0.0

with col2:
    scatter_fig = generate_scatter_plot(activation, sigma, sigma_bias, include_bias)
    st.pyplot(scatter_fig)