"""
Supervised Neural Gas (SNG).
Combines GLVQ's classification loss with Neural Gas neighborhood
cooperation using plain squared Euclidean distance. Unlike SRNG,
SNG does not adapt per-feature relevance weights — it operates
purely in the input space with isotropic distance.
References
----------
.. [1] Hammer, B., Strickert, M., & Villmann, T. (2005). Supervised
Neural Gas and Extensions. In Proceedings of the Workshop on
New Challenges in Neural Computation (NC2).
"""
import jax
import jax.numpy as jnp
import numpy as np
from prosemble.models.prototype_base import SupervisedPrototypeModel
[docs]
class SNG(SupervisedPrototypeModel):
"""Supervised Neural Gas.
Combines two key ideas:
- GLVQ loss: :math:`(d^+ - d^-) / (d^+ + d^-)` for margin-based classification
- Neural Gas cooperation: all same-class prototypes participate in
the loss, weighted by rank via :math:`\\exp(-\\text{rank} / \\gamma)`
Uses plain squared Euclidean distance without any metric adaptation.
The neighborhood range :math:`\\gamma` decays during training from
:math:`\\gamma_{\\text{init}}` to :math:`\\gamma_{\\text{final}}`.
When :math:`\\gamma \\to 0`, SNG recovers standard GLVQ.
Parameters
----------
beta : float
Transfer function steepness parameter for sigmoid shaping.
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.
lr_ratio : float
Ratio of wrong-class to correct-class learning rate (ε⁻/ε⁺).
Default: 0.5.
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.
batch_size : int, optional
Mini-batch size. If None (default), use full-batch training.
lr_scheduler : str or optax.Schedule, optional
Learning rate schedule.
lr_scheduler_kwargs : dict, optional
Keyword arguments for the learning rate scheduler.
prototypes_initializer : str or callable, optional
How to initialize prototypes.
patience : int, optional
Number of consecutive epochs with no improvement before stopping.
restore_best : bool
If True, restore parameters that achieved lowest loss. Default: False.
class_weight : dict or 'balanced', optional
Weights for each class. Default: None (uniform).
gradient_accumulation_steps : int, optional
Accumulate gradients over this many steps before applying.
ema_decay : float, optional
Exponential moving average decay for parameters.
freeze_params : list of str, optional
Parameter group names to freeze.
lookahead : dict, optional
Enable lookahead optimizer wrapper.
mixed_precision : str or None, optional
Compute dtype for mixed precision training.
"""
def __init__(self, beta=10.0, gamma_init=None, gamma_final=0.01,
gamma_decay=None, lr_ratio=0.5,
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.beta = beta
self.gamma_init = gamma_init
self.gamma_final = gamma_final
self.gamma_decay = gamma_decay
self.lr_ratio = lr_ratio
self.gamma_ = None
if self.freeze_params is None:
self.freeze_params = ['gamma']
elif 'gamma' not in self.freeze_params:
self.freeze_params = list(self.freeze_params) + ['gamma']
def _get_resume_params(self, params):
gamma = self.gamma_ if self.gamma_ is not None else (
self._gamma_init_actual if hasattr(self, '_gamma_init_actual') else 1.0
)
params['gamma'] = jnp.array(gamma, dtype=jnp.float32)
return params
def _init_state(self, X, y, key):
key1, key2 = jax.random.split(key)
prototypes, proto_labels = self._init_prototypes(
X, y, self.n_prototypes_per_class, key1
)
if isinstance(self.n_prototypes_per_class, int):
max_per_class = self.n_prototypes_per_class
elif isinstance(self.n_prototypes_per_class, dict):
max_per_class = max(self.n_prototypes_per_class.values())
else:
max_per_class = max(self.n_prototypes_per_class)
gamma_init = self.gamma_init if self.gamma_init is not None else max_per_class / 2.0
gamma_init = max(gamma_init, self.gamma_final + 1e-6)
self._gamma_init_actual = gamma_init
if self.gamma_decay is not None:
self._gamma_decay = self.gamma_decay
else:
if self.batch_size is not None:
steps_per_epoch = (X.shape[0] + self.batch_size - 1) // self.batch_size
else:
steps_per_epoch = 1
total_steps = self.max_iter * steps_per_epoch
self._gamma_decay = (self.gamma_final / gamma_init) ** (1.0 / total_steps)
params = {
'prototypes': prototypes,
'gamma': jnp.array(gamma_init, dtype=jnp.float32),
}
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):
prototypes = params['prototypes']
gamma = params['gamma']
# Squared Euclidean distance
diff = X[:, None, :] - prototypes[None, :, :] # (n, p, d)
distances = jnp.sum(diff ** 2, axis=2) # (n, p)
# Compute ranks within same-class prototypes
same_class = (y[:, None] == proto_labels[None, :]) # (n, p)
INF = jnp.finfo(distances.dtype).max
d_same = jnp.where(same_class, distances, INF) # (n, p)
order = jnp.argsort(d_same, axis=1)
ranks = jnp.argsort(order, axis=1).astype(jnp.float32) # (n, p)
# Neighborhood function h = exp(-rank / gamma)
h = jnp.exp(-ranks / (gamma + 1e-10)) # (n, p)
h = jnp.where(same_class, h, 0.0)
# Normalize
C = jnp.sum(h, axis=1, keepdims=True) # (n, 1)
h_normalized = h / (C + 1e-10) # (n, p)
# Closest different-class prototype distance
d_diff = jnp.where(~same_class, distances, INF)
dm = jnp.min(d_diff, axis=1) # (n,)
# Separate learning rates
dm = jax.lax.stop_gradient(dm) + self.lr_ratio * (
dm - jax.lax.stop_gradient(dm))
# GLVQ mu
mu = (distances - dm[:, None]) / (distances + dm[:, None] + 1e-10) # (n, p)
# Transfer function
from prosemble.core.activations import sigmoid_beta
transfer = self.transfer_fn or sigmoid_beta
cost = transfer(mu + self.margin, self.beta) # (n, p)
# Rank-weighted sum
weighted_cost = jnp.sum(h_normalized * cost, axis=1) # (n,)
return jnp.mean(weighted_cost)
def _post_update(self, params):
new_gamma = params['gamma'] * self._gamma_decay
new_gamma = jnp.maximum(new_gamma, self.gamma_final)
return {**params, 'gamma': new_gamma}
def _extract_results(self, params, proto_labels, loss_history, n_iter, **kwargs):
super()._extract_results(params, proto_labels, loss_history, n_iter, **kwargs)
self.gamma_ = float(params['gamma'])
def _get_fitted_arrays(self):
arrays = super()._get_fitted_arrays()
if self.gamma_ is not None:
arrays['gamma_'] = np.asarray(self.gamma_)
return arrays
def _set_fitted_arrays(self, arrays):
super()._set_fitted_arrays(arrays)
if 'gamma_' in arrays:
self.gamma_ = float(arrays['gamma_'])
def _get_hyperparams(self):
hp = super()._get_hyperparams()
hp['beta'] = self.beta
hp['gamma_init'] = self.gamma_init
hp['gamma_final'] = self.gamma_final
hp['gamma_decay'] = self.gamma_decay
hp['lr_ratio'] = self.lr_ratio
return hp