"""
One-Class GTLVQ (OC-GTLVQ).
Extends OC-GLVQ with per-prototype tangent subspaces (GTLVQ-style).
Each prototype :math:`w_k` learns an orthonormal basis :math:`\\Omega_k` defining a local
invariance subspace. The tangent distance measures the orthogonal
complement:
.. math::
d_T(x, w_k) = \\|(I - \\Omega_k \\Omega_k^T)(x - w_k)\\|^2
References
----------
.. [1] Sato, A., & Yamada, K. (1995). Generalized Learning Vector
Quantization. NIPS.
.. [2] Saralajew, Villmann (2016). Adaptive tangent distances in
generalized learning vector quantization. WSOM 2016.
"""
import jax
import jax.numpy as jnp
import numpy as np
from prosemble.models.oc_glvq import OCGLVQ
from prosemble.core.initializers import random_omega_init
from prosemble.core.utils import orthogonalize
from prosemble.core.activations import sigmoid_beta
[docs]
class OCGTLVQ(OCGLVQ):
"""One-Class GTLVQ with per-prototype tangent subspaces.
Each prototype learns an orthonormal basis :math:`\\Omega_k` that defines
directions of local invariance. Only the distance orthogonal
to this subspace is used for classification.
Parameters
----------
subspace_dim : int
Dimensionality of each tangent subspace. Default: 2.
n_prototypes : int
Number of prototypes for the target class.
target_label : int, optional
Target (normal) class label. Default: auto-detect.
beta : float
Sigmoid steepness. Default: 10.0.
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).
Attributes
----------
omegas_ : array of shape (n_prototypes, n_features, subspace_dim)
Learned per-prototype orthonormal tangent bases.
"""
def __init__(self, subspace_dim=2, n_prototypes=3, target_label=None,
beta=10.0, 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=n_prototypes, target_label=target_label,
beta=beta, 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.omegas_ = None
def _get_resume_params(self, params):
params = super()._get_resume_params(params)
params['omegas'] = self.omegas_
return params
def _init_state(self, X, y, key):
state, params, proto_labels = super()._init_state(X, y, key)
n_features = X.shape[1]
n_protos = self.n_prototypes
key1, key2 = jax.random.split(self.key, 2)
keys = jax.random.split(key2, n_protos)
params['omegas'] = jnp.stack([
random_omega_init(n_features, self.subspace_dim, k) for k in keys
])
opt_state = self._optimizer.init(params)
from prosemble.models.prototype_base import SupervisedState
state = SupervisedState(
prototypes=params['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']
thetas = params['thetas']
omegas = params['omegas']
# Tangent distance: ||(I - Omega_k Omega_k^T)(x - w_k)||^2
diff = X[:, None, :] - prototypes[None, :, :] # (n, K, d)
proj = jnp.einsum('nkd,kds->nks', diff, omegas) # (n, K, s)
recon = jnp.einsum('nks,kds->nkd', proj, omegas) # (n, K, d)
tang_diff = diff - recon # orthogonal complement
distances = jnp.sum(tang_diff ** 2, axis=2) # (n, K)
# OC-GLVQ mu
n = X.shape[0]
nearest_idx = jnp.argmin(distances, axis=1)
d_nearest = distances[jnp.arange(n), nearest_idx]
theta_nearest = thetas[nearest_idx]
s = jnp.where(y == self._target_label, 1.0, -1.0)
mu = s * (d_nearest - theta_nearest) / (d_nearest + theta_nearest + 1e-10)
transfer = self.transfer_fn or sigmoid_beta
return jnp.mean(transfer(mu + self.margin, self.beta))
def _post_update(self, params):
params = super()._post_update(params)
omegas = jax.vmap(orthogonalize)(params['omegas'])
return {**params, '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']
[docs]
def decision_function(self, X):
"""Compute scores using tangent distances."""
self._check_fitted()
X = jnp.asarray(X, dtype=jnp.float32)
diff = X[:, None, :] - self.prototypes_[None, :, :]
proj = jnp.einsum('nkd,kds->nks', diff, self.omegas_)
recon = jnp.einsum('nks,kds->nkd', proj, self.omegas_)
tang_diff = diff - recon
distances = jnp.sum(tang_diff ** 2, axis=2)
n = X.shape[0]
nearest_idx = jnp.argmin(distances, axis=1)
d_nearest = distances[jnp.arange(n), nearest_idx]
theta_nearest = self.thetas_[nearest_idx]
mu = (d_nearest - theta_nearest) / (d_nearest + theta_nearest + 1e-10)
return 1.0 - jax.nn.sigmoid(self.beta * mu)
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()
hp['subspace_dim'] = self.subspace_dim
return hp