"""
LVQ Multi-Layer Network (LVQMLN).
An MLP backbone transforms input data into a latent space where
prototypes reside. The GLVQ loss backpropagates through both the
backbone and prototype parameters jointly.
Unlike SiameseGLVQ (which transforms both inputs AND prototypes),
LVQMLN only transforms inputs — prototypes live directly in the
latent space.
References
----------
.. [1] Schneider, P., Biehl, M., & Hammer, B. (2009). Adaptive
Relevance Matrices in Learning Vector Quantization. Neural
Computation, 21(12), 3532-3561.
.. [2] Villmann, T., et al. (2017). Prototype-based Neural Network
Layers: Incorporating Vector Quantization. arXiv:1812.01214.
"""
from functools import partial
import jax
import jax.numpy as jnp
from jax import jit
from prosemble.models.prototype_base import SupervisedPrototypeModel
from prosemble.core.losses import glvq_loss_with_transfer
from prosemble.core.distance import squared_euclidean_distance_matrix
def _mlp_init(key, layer_sizes, activation='sigmoid'):
"""Initialize MLP parameters (Xavier/Glorot uniform).
Parameters
----------
key : JAX PRNGKey
layer_sizes : list of int
e.g. [4, 10, 2] means input=4, hidden=10, latent=2.
Returns
-------
params : list of (weight, bias) tuples
"""
params = []
for i in range(len(layer_sizes) - 1):
key, subkey = jax.random.split(key)
fan_in, fan_out = layer_sizes[i], layer_sizes[i + 1]
limit = jnp.sqrt(6.0 / (fan_in + fan_out))
w = jax.random.uniform(subkey, (fan_in, fan_out), minval=-limit, maxval=limit)
b = jnp.zeros(fan_out)
params.append((w, b))
return params
def _mlp_forward(params, x, activation='sigmoid'):
"""Forward pass through MLP.
Parameters
----------
params : list of (weight, bias)
x : array of shape (n, d_in)
activation : str
Activation function for all layers.
Returns
-------
array of shape (n, d_out)
"""
act_fn = _get_activation(activation)
for w, b in params:
x = act_fn(x @ w + b)
return x
def _get_activation(name):
"""Return JAX activation function by name."""
if name == 'sigmoid':
return jax.nn.sigmoid
elif name == 'relu':
return jax.nn.relu
elif name == 'tanh':
return jnp.tanh
elif name == 'leaky_relu':
return jax.nn.leaky_relu
elif name == 'selu':
return jax.nn.selu
else:
raise ValueError(f"Unknown activation: {name}")
# ---------------------------------------------------------------------------
# CNN backbone for image data
# ---------------------------------------------------------------------------
def _cnn_init(key, input_shape, channels, kernel_sizes, latent_dim, activation='relu'):
"""Initialize CNN backbone parameters.
Architecture: Conv layers -> global average pool -> linear -> latent_dim.
Parameters
----------
key : JAX PRNGKey
input_shape : tuple
(height, width, channels) of input images.
channels : list of int
Output channels per conv layer. e.g. [16, 32].
kernel_sizes : list of int
Kernel size per conv layer. e.g. [3, 3].
latent_dim : int
Output dimension after pooling + linear.
activation : str
Returns
-------
params : dict with 'conv_layers' and 'linear'
"""
h, w, c_in = input_shape
conv_params = []
for i, (c_out, k) in enumerate(zip(channels, kernel_sizes)):
key, subkey = jax.random.split(key)
fan_in = k * k * c_in
fan_out = k * k * c_out
limit = jnp.sqrt(6.0 / (fan_in + fan_out))
kernel = jax.random.uniform(subkey, (k, k, c_in, c_out),
minval=-limit, maxval=limit)
bias = jnp.zeros(c_out)
conv_params.append((kernel, bias))
c_in = c_out
# Linear head: last_channels -> latent_dim
key, subkey = jax.random.split(key)
last_c = channels[-1] if channels else c_in
limit = jnp.sqrt(6.0 / (last_c + latent_dim))
w_linear = jax.random.uniform(subkey, (last_c, latent_dim),
minval=-limit, maxval=limit)
b_linear = jnp.zeros(latent_dim)
return {
'conv_layers': conv_params,
'linear': (w_linear, b_linear),
}
def _cnn_forward(params, x, activation='relu'):
"""Forward pass through CNN backbone.
Parameters
----------
params : dict with 'conv_layers' and 'linear'
x : array of shape (n, h, w, c)
activation : str
Returns
-------
array of shape (n, latent_dim)
"""
act_fn = _get_activation(activation)
# Conv layers with same padding
for kernel, bias in params['conv_layers']:
x = jax.lax.conv_general_dilated(
x, kernel,
window_strides=(1, 1),
padding='SAME',
dimension_numbers=('NHWC', 'HWIO', 'NHWC'),
)
x = x + bias[None, None, None, :]
x = act_fn(x)
# Global average pooling: (n, h, w, c) -> (n, c)
x = jnp.mean(x, axis=(1, 2))
# Linear head
w, b = params['linear']
x = x @ w + b
x = act_fn(x)
return x
[docs]
class LVQMLN(SupervisedPrototypeModel):
"""LVQ Multi-Layer Network.
An MLP backbone maps inputs into a latent space. Prototypes reside
directly in that latent space. The GLVQ loss trains both the backbone
and the prototypes jointly via gradient descent.
Architecture::
Input (d) -> MLP -> Latent (latent_dim)
|
v
distance(latent_x, prototypes)
|
v
GLVQ loss
Parameters
----------
hidden_sizes : list of int
Sizes of hidden layers. e.g. [10] for one hidden layer of 10 units.
latent_dim : int
Dimension of the latent/embedding space where prototypes live.
activation : str
Activation function: 'sigmoid', 'relu', 'tanh', 'leaky_relu', 'selu'.
beta : float
Transfer function parameter for GLVQ loss.
bb_lr : float, optional
Separate learning rate for the backbone network. If None,
uses the same lr as prototypes. Default: None.
n_prototypes_per_class : int
Number of prototypes per class.
max_iter : int
Maximum training iterations.
lr : float
Learning rate.
epsilon : float
Convergence threshold on loss change.
random_seed : int
Random seed for reproducibility.
distance_fn : callable, optional
Distance function (default: squared Euclidean).
optimizer : str or optax optimizer, optional
Optimizer name ('adam', 'sgd') or optax GradientTransformation.
Default: 'adam'.
transfer_fn : callable, optional
Transfer function for loss shaping (default: identity).
margin : float
Margin for loss computation.
callbacks : list, optional
List of Callback objects.
use_scan : bool
If True (default), use jax.lax.scan for training (faster, JIT-compiled,
but runs all max_iter iterations even after convergence).
If False, use a Python for-loop with true early stopping (no wasted
compute after convergence, but slower per iteration).
batch_size : int, optional
Mini-batch size. If None (default), use full-batch training.
When set, each epoch iterates over shuffled mini-batches of this size.
lr_scheduler : str or optax.Schedule, optional
Learning rate schedule. Supported strings: 'exponential_decay',
'cosine_decay', 'warmup_cosine_decay', 'warmup_exponential_decay',
'warmup_constant', 'polynomial', 'linear', 'piecewise_constant',
'sgdr'. Or pass a custom optax.Schedule. Default: None.
lr_scheduler_kwargs : dict, optional
Keyword arguments passed to the learning rate scheduler
(e.g. ``decay_rate``, ``transition_steps``). Default: None.
prototypes_initializer : str or callable, optional
How to initialize prototypes. Supported strings: 'stratified_random'
(default), 'class_mean', 'class_conditional_mean', 'stratified_noise',
'random_normal', 'uniform', 'zeros', 'ones', 'fill_value'.
Or pass a callable ``(X, y, n_per_class, key) -> (protos, labels)``.
patience : int, optional
Number of consecutive epochs with no improvement before stopping.
If None (default), stops after a single non-improving step (epsilon
check). Requires use_scan=False for true early stopping.
restore_best : bool
If True, restore the parameters that achieved the lowest loss
(or validation loss if validation data is provided). Default: False.
class_weight : dict or 'balanced', optional
Weights for each class. Dict maps class label to weight, e.g.
{0: 1.0, 1: 2.0, 2: 1.5}. 'balanced' auto-computes weights
inversely proportional to class frequencies. Default: None (uniform).
gradient_accumulation_steps : int, optional
Accumulate gradients over this many steps before applying an update.
Effective batch size = batch_size * gradient_accumulation_steps.
Default: None (no accumulation).
ema_decay : float, optional
Exponential moving average decay for parameters (0 < ema_decay < 1).
After training, model parameters are replaced with EMA-smoothed values.
Typical values: 0.999, 0.9999. Default: None (no EMA).
freeze_params : list of str, optional
List of parameter group names to freeze (zero gradients).
E.g. ['backbone'] to freeze the backbone and only train prototypes.
Default: None (all parameters trainable).
lookahead : dict, optional
Enable lookahead optimizer wrapper. Dict with keys:
- 'sync_period': int (default 6) — sync every k steps
- 'slow_step_size': float (default 0.5) — interpolation factor
Default: None (no lookahead).
mixed_precision : str or None, optional
Compute dtype for mixed precision training. 'float16' or 'bfloat16'.
Master weights stay in float32; forward/backward pass runs in lower
precision for ~2x speed and ~half memory on GPU. Float16 uses static
loss scaling to prevent gradient underflow. Default: None (disabled).
"""
def __init__(self, hidden_sizes=None, latent_dim=2,
activation='sigmoid', beta=10.0, bb_lr=None,
n_prototypes_per_class=1, max_iter=100, lr=0.01,
epsilon=1e-6, random_seed=42, distance_fn=None,
optimizer='adam', transfer_fn=None, margin=0.0,
callbacks=None, use_scan=True, batch_size=None,
lr_scheduler=None, lr_scheduler_kwargs=None,
prototypes_initializer=None, patience=None,
restore_best=False, class_weight=None,
gradient_accumulation_steps=None, ema_decay=None,
freeze_params=None, lookahead=None,
mixed_precision=None):
super().__init__(
n_prototypes_per_class=n_prototypes_per_class,
max_iter=max_iter, lr=lr, epsilon=epsilon,
random_seed=random_seed, distance_fn=distance_fn,
optimizer=optimizer, transfer_fn=transfer_fn, margin=margin,
callbacks=callbacks, use_scan=use_scan, batch_size=batch_size,
lr_scheduler=lr_scheduler,
lr_scheduler_kwargs=lr_scheduler_kwargs,
prototypes_initializer=prototypes_initializer,
patience=patience, restore_best=restore_best,
class_weight=class_weight,
gradient_accumulation_steps=gradient_accumulation_steps,
ema_decay=ema_decay, freeze_params=freeze_params,
lookahead=lookahead, mixed_precision=mixed_precision,
)
self.hidden_sizes = hidden_sizes or [10]
self.latent_dim = latent_dim
self.activation = activation
self.beta = beta
self.bb_lr = bb_lr
self.backbone_params_ = None
# Rebuild optimizer with per-parameter LRs if bb_lr is specified
if bb_lr is not None:
self._optimizer = self._build_multi_lr_optimizer(
self._optimizer_spec, self.lr, bb_lr
)
def _build_multi_lr_optimizer(self, optimizer, proto_lr, bb_lr):
"""Build optimizer with separate learning rates for prototypes and backbone."""
import optax
if not isinstance(optimizer, str):
return optimizer
proto_opt = self._build_optimizer(optimizer, proto_lr)
bb_opt = self._build_optimizer(optimizer, bb_lr)
return optax.multi_transform(
{'prototypes': proto_opt, 'backbone': bb_opt},
param_labels=lambda params: {k: k for k in params},
)
def _get_resume_params(self, params):
params['backbone'] = self.backbone_params_
return params
def _init_state(self, X, y, key):
"""Initialize backbone + prototypes in latent space."""
n_features = X.shape[1]
n_classes = int(jnp.max(y)) + 1
# Build layer sizes: input -> hidden... -> latent
layer_sizes = [n_features] + list(self.hidden_sizes) + [self.latent_dim]
key1, key2, key3 = jax.random.split(key, 3)
# Initialize backbone
backbone_params = _mlp_init(key1, layer_sizes, self.activation)
# Project data into latent space for prototype initialization
latent_X = _mlp_forward(backbone_params, X, self.activation)
# Initialize prototypes in latent space using projected data
latent_y = y
prototypes, proto_labels = self._init_prototypes(
latent_X, latent_y, self.n_prototypes_per_class, key2
)
# Pack all trainable params
params = {
'prototypes': prototypes,
'backbone': backbone_params,
}
opt_state = self._optimizer.init(params)
from prosemble.models.prototype_base import SupervisedState
state = SupervisedState(
prototypes=prototypes,
opt_state=opt_state,
loss=jnp.array(float('inf')),
iteration=0,
converged=False,
)
return state, params, proto_labels
def _compute_loss(self, params, X, y, proto_labels):
"""GLVQ loss in latent space."""
# Transform input through backbone
latent_x = _mlp_forward(params['backbone'], X, self.activation)
# Compute distances in latent space
distances = squared_euclidean_distance_matrix(latent_x, params['prototypes'])
return glvq_loss_with_transfer(
distances, y, proto_labels,
transfer_fn=self.transfer_fn,
margin=self.margin,
beta=self.beta,
)
def _extract_results(self, params, proto_labels, loss_history, n_iter, **kwargs):
"""Store backbone params alongside prototypes."""
super()._extract_results(params, proto_labels, loss_history, n_iter, **kwargs)
self.backbone_params_ = params['backbone']
[docs]
def predict(self, X):
"""Predict class labels.
Transforms X through the backbone, then finds nearest prototype.
"""
self._check_fitted()
X = jnp.asarray(X, dtype=jnp.float32)
latent_x = _mlp_forward(self.backbone_params_, X, self.activation)
distances = squared_euclidean_distance_matrix(latent_x, self.prototypes_)
from prosemble.core.competitions import wtac
return wtac(distances, self.prototype_labels_)
[docs]
def predict_proba(self, X):
"""Predict class probabilities."""
self._check_fitted()
X = jnp.asarray(X, dtype=jnp.float32)
latent_x = _mlp_forward(self.backbone_params_, X, self.activation)
distances = squared_euclidean_distance_matrix(latent_x, self.prototypes_)
from prosemble.core.pooling import stratified_min_pooling
class_dists = stratified_min_pooling(
distances, self.prototype_labels_, self.n_classes_
)
return jax.nn.softmax(-class_dists, axis=1)
def transform(self, X):
"""Transform data into latent space.
Parameters
----------
X : array of shape (n, d)
Returns
-------
latent : array of shape (n, latent_dim)
"""
self._check_fitted()
X = jnp.asarray(X, dtype=jnp.float32)
return _mlp_forward(self.backbone_params_, X, self.activation)
def _check_fitted(self):
"""Check that model has been fitted."""
if self.prototypes_ is None or self.backbone_params_ is None:
from prosemble.models.base import NotFittedError
raise NotFittedError("Model not fitted. Call fit() first.")
def _get_hyperparams(self):
hp = super()._get_hyperparams()
hp.update({
'hidden_sizes': self.hidden_sizes,
'latent_dim': self.latent_dim,
'activation': self.activation,
'beta': self.beta,
})
return hp