"""
Localized Matrix Cross-Entropy LVQ with Neural Gas cooperation (LCELVQ-NG).
Combines CELVQ-NG's cross-entropy loss over NG-weighted softmax logits
with per-prototype :math:`\\Omega_k` matrices that learn local metrics adapted to
each prototype's region:
.. math::
d(x, w_k) = \\|\\Omega_k(x - w_k)\\|^2
Each prototype learns its own discriminative subspace while Neural Gas
rank-based cooperation ensures robust prototype placement. The cross-
entropy loss over all classes simultaneously provides gradient flow to
all local matrices.
When :math:`\\gamma \\to 0`, only the nearest prototype per class dominates and
LCELVQ-NG recovers a localized matrix variant of standard CELVQ.
References
----------
.. [1] Villmann, T., et al. (2019). Analysis of variants of
classification learning vector quantization by a stochastic
setting.
.. [2] Hammer, B., Strickert, M., & Villmann, T. (2003). Supervised
Neural Gas with General Similarity Measure. Neural Processing
Letters.
.. [3] Schneider, P., Biehl, M., & Hammer, B. (2009). Adaptive
Relevance Matrices in Learning Vector Quantization.
"""
import jax
import jax.numpy as jnp
import numpy as np
from jax import jit
from prosemble.models.celvq_ng_mixin import CELVQNGMixin
from prosemble.models.crossentropy_lvq import CELVQ
from prosemble.core.competitions import wtac
from prosemble.core.initializers import identity_omega_init
@jit
def _predict_lcelvq_ng_jit(X, prototypes, omegas, proto_labels):
"""JIT-compiled LCELVQ-NG prediction with per-prototype Omega metrics."""
diff = X[:, None, :] - prototypes[None, :, :]
projected = jnp.einsum('npd,pdl->npl', diff, omegas)
distances = jnp.sum(projected ** 2, axis=2)
return wtac(distances, proto_labels)
[docs]
class LCELVQ_NG(CELVQNGMixin, CELVQ):
"""Localized Matrix Cross-Entropy LVQ with Neural Gas cooperation.
Combines three key ideas:
- Cross-entropy loss: softmax over all-class NG-weighted distances
- Neural Gas cooperation: all same-class prototypes participate,
weighted by rank via :math:`\\exp(-\\text{rank} / \\gamma)`
- Per-prototype :math:`\\Omega_k`:
.. math::
d(x, w_k) = \\|\\Omega_k(x - w_k)\\|^2
learns local metrics adapted to each prototype's region
The neighborhood range :math:`\\gamma` decays during training from
:math:`\\gamma_{\\text{init}}` to :math:`\\gamma_{\\text{final}}`.
When :math:`\\gamma \\to 0`, LCELVQ-NG recovers a localized
matrix CELVQ.
Parameters
----------
latent_dim : int, optional
Latent space dimensionality per prototype. If None, uses input dim.
gamma_init : float, optional
Initial neighborhood range for NG cooperation.
Default: max prototypes per class / 2.
gamma_final : float
Final neighborhood range. Default: 0.01.
gamma_decay : float, optional
Per-step multiplicative decay factor for gamma.
Default: computed from max_iter so gamma reaches gamma_final.
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, latent_dim=None, gamma_init=None,
gamma_final=0.01, gamma_decay=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__(
gamma_init=gamma_init, gamma_final=gamma_final,
gamma_decay=gamma_decay,
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.latent_dim = latent_dim
self.omegas_ = None
def _get_resume_params(self, params):
params = super()._get_resume_params(params)
params['omegas'] = self.omegas_
return params
def _init_metric_params(self, params, X, prototypes, key):
n_features = X.shape[1]
latent_dim = self.latent_dim or n_features
n_protos = prototypes.shape[0]
omega_single = identity_omega_init(n_features, latent_dim)
omegas = jnp.tile(omega_single[None, :, :], (n_protos, 1, 1))
params['omegas'] = omegas
return params
def _compute_distances(self, params, X):
diff = X[:, None, :] - params['prototypes'][None, :, :] # (n, p, d)
projected = jnp.einsum('npd,pdl->npl', diff, params['omegas']) # (n, p, l)
return jnp.sum(projected ** 2, axis=2) # (n, p)
def _extract_results(self, params, proto_labels, loss_history, n_iter, **kwargs):
super()._extract_results(params, proto_labels, loss_history, n_iter, **kwargs)
self.omegas_ = params['omegas']
[docs]
def predict(self, X):
"""Predict using per-prototype :math:`\\Omega_k` distances."""
self._check_fitted()
X = jnp.asarray(X, dtype=jnp.float32)
return _predict_lcelvq_ng_jit(
X, self.prototypes_, self.omegas_, self.prototype_labels_
)
[docs]
def predict_proba(self, X):
"""Predict calibrated probabilities using per-prototype :math:`\\Omega_k` distances.
Uses per-class min pooling with the learned local :math:`\\Omega_k` metrics,
consistent with the training objective.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Returns
-------
proba : array of shape (n_samples, n_classes)
"""
self._check_fitted()
X = jnp.asarray(X, dtype=jnp.float32)
# Compute per-prototype Omega-transformed distances
diff = X[:, None, :] - self.prototypes_[None, :, :]
projected = jnp.einsum('npd,pdl->npl', diff, self.omegas_)
distances = jnp.sum(projected ** 2, axis=2)
# Softmax over per-class min distances
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 _get_quantizable_attrs(self):
attrs = super()._get_quantizable_attrs()
if self.omegas_ is not None:
attrs.append('omegas_')
return attrs
def _get_fitted_arrays(self):
arrays = super()._get_fitted_arrays()
if self.omegas_ is not None:
arrays['omegas_'] = np.asarray(self.omegas_)
return arrays
def _set_fitted_arrays(self, arrays):
super()._set_fitted_arrays(arrays)
if 'omegas_' in arrays:
self.omegas_ = jnp.asarray(arrays['omegas_'])
def _get_hyperparams(self):
hp = super()._get_hyperparams()
if self.latent_dim is not None:
hp['latent_dim'] = self.latent_dim
return hp