"""
Supervised Tangent Neural Gas (STNG).
Combines GTLVQ's per-prototype tangent subspaces with Neural Gas
neighborhood cooperation. Each prototype has an orthonormal basis
defining a tangent subspace; the tangent distance measures distance
in the orthogonal complement. Neighborhood cooperation ensures
robust prototype placement.
Cost function:
.. math::
E_{\\text{STNG}} = \\frac{1}{N} \\sum_\\mu \\sum_{r: c(w_r)=c(x_\\mu)}
\\frac{h(\\text{rank}_r, \\gamma)}{C(\\gamma)} \\cdot \\Phi(\\mu_r)
where:
.. math::
d(x, w_r) = \\|(I - \\Omega_r \\Omega_r^T)(x - w_r)\\|^2 \\quad \\text{(tangent distance)}
.. math::
\\mu_r = \\frac{d_r - d_r^-}{d_r + d_r^-}
.. math::
h(\\text{rank}, \\gamma) = \\exp(-\\text{rank} / \\gamma)
References
----------
.. [1] Hammer, B., Strickert, M., & Villmann, T. (2003). Supervised
Neural Gas with General Similarity Measure. Neural Processing
Letters.
.. [2] Saralajew, S., & Villmann, T. (2016). Adaptive tangent
distances in generalized learning vector quantization.
"""
import jax
import jax.numpy as jnp
import numpy as np
from jax import jit
from prosemble.models.prototype_base import SupervisedPrototypeModel
from prosemble.core.competitions import wtac
from prosemble.core.initializers import random_omega_init
from prosemble.core.utils import orthogonalize
@jit
def _predict_stng_jit(X, prototypes, omegas, proto_labels):
"""JIT-compiled STNG prediction with tangent distance."""
diff = X[:, None, :] - prototypes[None, :, :]
proj = jnp.einsum('npd,pds->nps', diff, omegas)
recon = jnp.einsum('nps,pds->npd', proj, omegas)
tang_diff = diff - recon
distances = jnp.sum(tang_diff ** 2, axis=2)
return wtac(distances, proto_labels)
[docs]
class STNG(SupervisedPrototypeModel):
"""Supervised Tangent Neural Gas.
Combines three 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)`
- Tangent subspaces:
.. math::
d(x, w_k) = \\|(I - \\Omega_k \\Omega_k^T)(x - w_k)\\|^2
measures distance in the orthogonal complement of each prototype's
learned invariance subspace
The neighborhood range :math:`\\gamma` decays during training from
:math:`\\gamma_{\\text{init}}` to :math:`\\gamma_{\\text{final}}`.
When :math:`\\gamma \\to 0`, STNG recovers standard GTLVQ.
Parameters
----------
subspace_dim : int
Dimension of each prototype's tangent subspace.
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.
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, subspace_dim=2, 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.subspace_dim = subspace_dim
self.beta = beta
self.gamma_init = gamma_init
self.gamma_final = gamma_final
self.gamma_decay = gamma_decay
self.lr_ratio = lr_ratio
self.omegas_ = None
self.gamma_ = None
# Ensure gamma is frozen from optimizer (not trainable)
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):
params['omegas'] = self.omegas_
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):
n_features = X.shape[1]
key1, key2 = jax.random.split(key)
prototypes, proto_labels = self._init_prototypes(
X, y, self.n_prototypes_per_class, key1
)
n_protos = prototypes.shape[0]
# Initialize each Omega as random orthogonal
keys = jax.random.split(key2, n_protos)
omegas = jnp.stack([
random_omega_init(n_features, self.subspace_dim, k) for k in keys
]) # (p, d, subspace_dim)
# Compute gamma_init from prototype count if not set
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
# Compute decay factor
if self.gamma_decay is not None:
self._gamma_decay = self.gamma_decay
else:
self._gamma_decay = (self.gamma_final / gamma_init) ** (1.0 / self.max_iter)
params = {
'prototypes': prototypes,
'omegas': omegas,
'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']
omegas = params['omegas'] # (p, d, s)
gamma = params['gamma']
# 1. Tangent distance: d(x, w_k) = ||(I - Omega_k Omega_k^T)(x - w_k)||^2
diff = X[:, None, :] - prototypes[None, :, :] # (n, p, d)
proj_onto_subspace = jnp.einsum('npd,pds->nps', diff, omegas) # (n, p, s)
reconstruction = jnp.einsum('nps,pds->npd', proj_onto_subspace, omegas) # (n, p, d)
tangent_diff = diff - reconstruction # (n, p, d)
distances = jnp.sum(tangent_diff ** 2, axis=2) # (n, p)
# 2. 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)
# Double argsort for ranks
order = jnp.argsort(d_same, axis=1)
ranks = jnp.argsort(order, axis=1).astype(jnp.float32) # (n, p)
# 3. Neighborhood function h = exp(-rank / gamma)
h = jnp.exp(-ranks / (gamma + 1e-10)) # (n, p)
h = jnp.where(same_class, h, 0.0) # zero for wrong-class
# 4. Normalize: C = sum of h over same-class prototypes per sample
C = jnp.sum(h, axis=1, keepdims=True) # (n, 1)
h_normalized = h / (C + 1e-10) # (n, p)
# 5. Closest different-class prototype distance
d_diff = jnp.where(~same_class, distances, INF)
dm = jnp.min(d_diff, axis=1) # (n,)
# 5b. Separate learning rates (Hammer et al. 2003: ε⁻ = lr_ratio × ε⁺)
# Scale gradient through dm by lr_ratio; forward pass unchanged.
dm = jax.lax.stop_gradient(dm) + self.lr_ratio * (
dm - jax.lax.stop_gradient(dm))
# 6. GLVQ mu for each (sample, same-class prototype) pair
mu = (distances - dm[:, None]) / (distances + dm[:, None] + 1e-10) # (n, p)
# 7. Apply 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)
# 8. Rank-weighted sum over same-class prototypes, then mean over samples
weighted_cost = jnp.sum(h_normalized * cost, axis=1) # (n,)
return jnp.mean(weighted_cost)
def _post_update(self, params):
# Decay gamma AND re-orthogonalize tangent bases
new_gamma = params['gamma'] * self._gamma_decay
new_gamma = jnp.maximum(new_gamma, self.gamma_final)
omegas = jax.vmap(orthogonalize)(params['omegas'])
return {**params, 'gamma': new_gamma, 'omegas': omegas}
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']
self.gamma_ = float(params['gamma'])
[docs]
def predict(self, X):
"""Predict using tangent distance."""
self._check_fitted()
X = jnp.asarray(X, dtype=jnp.float32)
return _predict_stng_jit(
X, self.prototypes_, self.omegas_, self.prototype_labels_
)
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_)
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 'omegas_' in arrays:
self.omegas_ = jnp.asarray(arrays['omegas_'])
if 'gamma_' in arrays:
self.gamma_ = float(arrays['gamma_'])
def _get_hyperparams(self):
hp = super()._get_hyperparams()
hp['subspace_dim'] = self.subspace_dim
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