"""
Supervised Riemannian Matrix Neural Gas (RiemannianSMNG).
Extends RiemannianSRNG with a global learned metric in the tangent space.
For each prototype, the tangent vector from prototype to data point is
computed via the manifold's logarithmic map, then projected through a
shared matrix :math:`\\Omega` before computing distances.
"""
import jax
import jax.numpy as jnp
import numpy as np
from prosemble.models.riemannian_srng import RiemannianSRNG
from prosemble.models.prototype_base import SupervisedState
from prosemble.core.activations import sigmoid_beta
from prosemble.core.initializers import identity_omega_init
[docs]
class RiemannianSMNG(RiemannianSRNG):
"""Supervised Riemannian Matrix Neural Gas.
Extends RiemannianSRNG with a global metric adaptation matrix
:math:`\\Omega` applied in the tangent space. The distance is:
.. math::
d(x, w_k) = \\|\\Omega \\cdot \\text{Log}_{w_k}(x)_{\\text{flat}}\\|^2
where :math:`\\text{Log}_{w_k}(x)` is the logarithmic map at prototype
:math:`w_k`, flattened to a vector.
The learned relevance matrix :math:`\\Lambda = \\Omega^T \\Omega`
captures feature correlations in the tangent space.
Parameters
----------
manifold : SO, SPD, or Grassmannian
Riemannian manifold instance.
latent_dim : int, optional
Projection dimensionality for omega. Default: n_features (square).
beta : float
Transfer function steepness.
gamma_init : float, optional
Initial neighborhood range. Default: max prototypes per class / 2.
gamma_final : float
Final neighborhood range. Default: 0.01.
gamma_decay : float, optional
Per-step decay factor for gamma.
tau : float
Injectivity radius safety factor. Default: 0.95.
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.
optimizer : str or optax optimizer, optional
Default: 'adam'.
transfer_fn : callable, optional
Transfer function for loss shaping.
margin : float
Margin for loss computation.
callbacks : list, optional
List of Callback objects.
use_scan : bool
If True, use jax.lax.scan. Default: False.
batch_size : int, optional
Mini-batch size.
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
Epochs with no improvement before stopping.
restore_best : bool
Restore best parameters. Default: False.
class_weight : dict or 'balanced', optional
Class weights.
gradient_accumulation_steps : int, optional
Gradient accumulation steps.
ema_decay : float, optional
EMA decay for parameters.
freeze_params : list of str, optional
Parameter groups to freeze.
lookahead : dict, optional
Lookahead optimizer config.
mixed_precision : str or None, optional
Mixed precision dtype.
"""
def __init__(self, manifold, latent_dim=None, beta=10.0,
gamma_init=None, gamma_final=0.01, gamma_decay=None,
lr_ratio=0.5, tau=0.95, n_prototypes_per_class=1, max_iter=100,
lr=0.01, epsilon=1e-6, random_seed=42,
optimizer='adam', transfer_fn=None, margin=0.0,
callbacks=None, use_scan=False, 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__(
manifold=manifold, beta=beta,
gamma_init=gamma_init, gamma_final=gamma_final,
gamma_decay=gamma_decay, lr_ratio=lr_ratio, tau=tau,
n_prototypes_per_class=n_prototypes_per_class,
max_iter=max_iter, lr=lr, epsilon=epsilon,
random_seed=random_seed, 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.omega_ = None
def _diff_log_map(self, w, x):
"""Differentiable log map for a single (base, target) pair.
Dispatches to the appropriate differentiable log map based on
manifold type.
"""
from prosemble.core.manifolds import SO, SPD, Grassmannian, HyperbolicPoincare
from prosemble.models.riemannian_srng import (
_so_log_map_diff, _spd_log_map_diff, _grassmannian_log_map_diff,
_hyperbolic_log_map_diff,
)
if isinstance(self.manifold, SO):
return _so_log_map_diff(w, x)
elif isinstance(self.manifold, SPD):
return _spd_log_map_diff(w, x)
elif isinstance(self.manifold, Grassmannian):
return _grassmannian_log_map_diff(w, x)
elif isinstance(self.manifold, HyperbolicPoincare):
return _hyperbolic_log_map_diff(w, x, eps=self.manifold.eps)
else:
return self.manifold.log_map(w, x)
def _compute_tangent_vectors(self, X_manifold, W_manifold):
"""Compute tangent vectors from prototypes to data via log map.
Uses differentiable log map implementations that support autodiff.
Parameters
----------
X_manifold : array of shape (n_samples, *point_shape)
W_manifold : array of shape (n_prototypes, *point_shape)
Returns
-------
tangents_flat : array of shape (n_samples, n_prototypes, d_flat)
"""
log_to_all_x = jax.vmap(self._diff_log_map, in_axes=(None, 0))
log_matrix = jax.vmap(log_to_all_x, in_axes=(0, None))
# log_matrix(W, X) → (p, n, *point_shape)
tangents = log_matrix(W_manifold, X_manifold)
# Transpose to (n, p, *point_shape)
tangents = jnp.moveaxis(tangents, 0, 1)
# Flatten to (n, p, d_flat)
n = X_manifold.shape[0]
p = W_manifold.shape[0]
return tangents.reshape(n, p, -1)
def _get_resume_params(self, params):
gamma = params.get('gamma', jnp.array(self.gamma_final))
omega = params.get('omega', self.omega_) if self.omega_ is not None else params.get('omega')
return {
'prototypes': params['prototypes'],
'omega': omega,
'gamma': gamma,
}
def _init_state(self, X, y, key):
state, params, proto_labels = super()._init_state(X, y, key)
d_flat = X.shape[1]
latent_dim = self.latent_dim if self.latent_dim is not None else d_flat
omega = identity_omega_init(d_flat, latent_dim)
params = {**params, 'omega': omega}
opt_state = self._optimizer.init(params)
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']
omega = params['omega']
gamma = params['gamma']
n = X.shape[0]
p = prototypes.shape[0]
X_m = self._reshape_to_manifold(X, n)
W_m = self._reshape_to_manifold(prototypes, p)
# 1. Tangent vectors via log map, then global omega projection
tangent_flat = self._compute_tangent_vectors(X_m, W_m) # (n, p, d_flat)
projected = jnp.einsum('npd,dl->npl', tangent_flat, omega) # (n, p, l)
distances = jnp.sum(projected ** 2, axis=2) # (n, p)
# 2. Compute ranks within same-class prototypes
same_class = (y[:, None] == proto_labels[None, :])
INF = jnp.finfo(distances.dtype).max
d_same = jnp.where(same_class, distances, INF)
order = jnp.argsort(d_same, axis=1)
ranks = jnp.argsort(order, axis=1).astype(jnp.float32)
# 3. Neighborhood function
h = jnp.exp(-ranks / (gamma + 1e-10))
h = jnp.where(same_class, h, 0.0)
# 4. Normalize
C = jnp.sum(h, axis=1, keepdims=True)
h_normalized = h / (C + 1e-10)
# 5. Closest different-class distance
d_diff = jnp.where(~same_class, distances, INF)
dm = jnp.min(d_diff, axis=1)
# Separate learning rates (Hammer et al. 2003: epsilon^- = lr_ratio * epsilon^+)
# 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
mu = (distances - dm[:, None]) / (distances + dm[:, None] + 1e-10)
# 7. Transfer function
transfer = self.transfer_fn or sigmoid_beta
cost = transfer(mu + self.margin, self.beta)
# 8. Rank-weighted sum
weighted_cost = jnp.sum(h_normalized * cost, axis=1)
return jnp.mean(weighted_cost)
def _extract_results(self, params, proto_labels, loss_history, n_iter, **kwargs):
super()._extract_results(params, proto_labels, loss_history, n_iter, **kwargs)
self.omega_ = params['omega']
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def predict(self, X):
"""Predict using tangent-space omega metric.
Parameters
----------
X : array-like of shape (n_samples, n_features_flat)
Returns
-------
labels : array of shape (n_samples,)
"""
self._check_fitted()
X = jnp.asarray(X, dtype=jnp.float32)
n = X.shape[0]
p = self.prototypes_.shape[0]
X_m = self._reshape_to_manifold(X, n)
W_m = self._reshape_to_manifold(self.prototypes_, p)
tangent_flat = self._compute_tangent_vectors(X_m, W_m)
projected = jnp.einsum('npd,dl->npl', tangent_flat, self.omega_)
distances = jnp.sum(projected ** 2, axis=2)
from prosemble.core.competitions import wtac
return wtac(distances, self.prototype_labels_)
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def relevance_matrix(self):
"""Return learned relevance matrix Lambda = Omega^T Omega.
Returns
-------
array of shape (d_flat, d_flat)
"""
return self.omega_.T @ self.omega_
def _get_quantizable_attrs(self):
return {'prototypes_': self.prototypes_, 'omega_': self.omega_}
def _get_fitted_arrays(self):
arrays = super()._get_fitted_arrays()
if self.omega_ is not None:
arrays['omega_'] = np.asarray(self.omega_)
return arrays
def _set_fitted_arrays(self, arrays):
super()._set_fitted_arrays(arrays)
if 'omega_' in arrays:
self.omega_ = jnp.asarray(arrays['omega_'])
def _get_hyperparams(self):
hp = super()._get_hyperparams()
hp['latent_dim'] = self.latent_dim
hp['lr_ratio'] = self.lr_ratio
return hp