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GeoLIP Core β Geometric Building Blocks
==========================================
All reusable geometric components. No losses, no training loops.
Components:
Activations: SquaredReLU, StarReLU, make_activation
Anchor Init: xavier, orthogonal, repulsion
Constellation: Triangulation on S^(d-1)
Patchwork: Round-robin compartmentalized interpretation
RelayLayer: Single constellation relay (vectorized, gated, no attention)
ConstellationRelay: Per-token geometric layer (O(S), 99.4% at depth 16)
MagnitudeFlow: Relay-stack per-compartment magnitude prediction
AnchorPush: Push strategies (raw, gru, momentum)
FlowAttention: ODE flow in tangent space (historical)
Usage:
from geolip_core import Constellation, Patchwork, MagnitudeFlow, AnchorPush
Author: AbstractPhil + Claude Opus 4.6
License: Apache 2.0
"""
import torch
import torch.nn as nn
import torch.nn.functional as F
import math
# ββ ACTIVATIONS ββ
class SquaredReLU(nn.Module):
def forward(self, x): return F.relu(x) ** 2
class StarReLU(nn.Module):
def __init__(self):
super().__init__()
self.scale = nn.Parameter(torch.ones(1) * 0.8944)
self.bias = nn.Parameter(torch.zeros(1) - 0.4472)
def forward(self, x): return F.relu(x) ** 2 * self.scale + self.bias
ACTIVATIONS = {
'squared_relu': SquaredReLU, 'star_relu': StarReLU,
'gelu': lambda: nn.GELU(), 'relu': lambda: nn.ReLU(), 'sigmoid': lambda: nn.Sigmoid(),
}
def make_activation(name='squared_relu'):
if name not in ACTIVATIONS:
raise ValueError(f"Unknown activation '{name}'. Choose from: {list(ACTIVATIONS.keys())}")
return ACTIVATIONS[name]()
# ββ ANCHOR INITIALIZATION ββ
def init_anchors_xavier(n, d):
w = torch.empty(n, d); nn.init.xavier_normal_(w); return F.normalize(w, dim=-1)
def init_anchors_orthogonal(n, d):
if n <= d:
Q, _ = torch.linalg.qr(torch.randn(d, n)); return Q.T.contiguous()
else:
Q, _ = torch.linalg.qr(torch.randn(d, d))
return torch.cat([Q.T, F.normalize(torch.randn(n - d, d), dim=-1)], dim=0)
def init_anchors_repulsion(n, d, iters=200, lr=0.05):
vecs = F.normalize(init_anchors_orthogonal(n, d), dim=-1)
for _ in range(iters):
sim = vecs @ vecs.T; sim.fill_diagonal_(-2.0)
vecs = F.normalize(vecs - lr * vecs[sim.argmax(dim=1)], dim=-1)
return vecs
INIT_METHODS = {'xavier': init_anchors_xavier, 'orthogonal': init_anchors_orthogonal, 'repulsion': init_anchors_repulsion}
# ββ CONSTELLATION ββ
class Constellation(nn.Module):
"""Anchors on S^(d-1). Triangulates input embeddings."""
def __init__(self, n_anchors, dim, anchor_drop=0.0, anchor_init='repulsion'):
super().__init__()
self.anchors = nn.Parameter(INIT_METHODS[anchor_init](n_anchors, dim))
self.anchor_drop = anchor_drop
self.n_anchors = n_anchors
self.dim = dim
def triangulate(self, emb, training=False):
anchors = F.normalize(self.anchors, dim=-1)
if training and self.anchor_drop > 0:
mask = torch.rand(anchors.shape[0], device=anchors.device) > self.anchor_drop
if mask.sum() < 2: mask[:2] = True
anchors = anchors[mask]
cos = emb @ anchors.T; tri = 1.0 - cos
_, nl = cos.max(dim=-1)
return tri, mask.nonzero(as_tuple=True)[0][nl]
cos = emb @ anchors.T; tri = 1.0 - cos; _, nearest = cos.max(dim=-1)
return tri, nearest
def forward(self, emb, training=False): return self.triangulate(emb, training)
# ββ PATCHWORK ββ
class Patchwork(nn.Module):
"""Round-robin compartments reading diverse anchor subsets."""
def __init__(self, n_anchors, n_comp=8, d_comp=64, activation='squared_relu'):
super().__init__()
self.n_comp, self.d_comp = n_comp, d_comp
self.output_dim = n_comp * d_comp
self.register_buffer('asgn', torch.arange(n_anchors) % n_comp)
apc = n_anchors // n_comp
self.comps = nn.ModuleList([
nn.Sequential(nn.Linear(apc, d_comp*2), make_activation(activation),
nn.Linear(d_comp*2, d_comp), nn.LayerNorm(d_comp))
for _ in range(n_comp)])
def forward(self, tri):
return torch.cat([self.comps[k](tri[:, self.asgn == k]) for k in range(self.n_comp)], dim=-1)
# ββ RELAY LAYER ββ
class RelayLayer(nn.Module):
"""Single constellation relay. Vectorized, gated, no attention.
Patches β S^(patch_dim-1) β triangulate at 3 SLERP phases β patchwork β gated residual."""
def __init__(self, input_dim, patch_dim=16, n_anchors=16, n_phases=3, pw_hidden=32, gate_init=-3.0):
super().__init__()
assert input_dim % patch_dim == 0
self.input_dim, self.patch_dim = input_dim, patch_dim
self.n_patches = input_dim // patch_dim
self.n_anchors, self.n_phases = n_anchors, n_phases
P, A, d = self.n_patches, n_anchors, patch_dim
home = torch.empty(P, A, d); nn.init.xavier_normal_(home.view(P*A, d))
home = F.normalize(home.view(P, A, d), dim=-1)
self.register_buffer('home', home)
self.anchors = nn.Parameter(home.clone())
tri_dim = n_phases * A
self.pw_w1 = nn.Parameter(torch.empty(P, tri_dim, pw_hidden))
self.pw_b1 = nn.Parameter(torch.zeros(1, P, pw_hidden))
self.pw_w2 = nn.Parameter(torch.empty(P, pw_hidden, d))
self.pw_b2 = nn.Parameter(torch.zeros(1, P, d))
for p in range(P):
nn.init.xavier_normal_(self.pw_w1.data[p])
nn.init.xavier_normal_(self.pw_w2.data[p])
self.pw_norm = nn.LayerNorm(d)
self.gates = nn.Parameter(torch.full((P,), gate_init))
self.norm = nn.LayerNorm(input_dim)
def drift(self):
h, c = F.normalize(self.home, dim=-1), F.normalize(self.anchors, dim=-1)
return torch.acos((h * c).sum(dim=-1).clamp(-1+1e-7, 1-1e-7))
def at_phase(self, t):
h, c = F.normalize(self.home, dim=-1), F.normalize(self.anchors, dim=-1)
omega = self.drift().unsqueeze(-1); so = omega.sin().clamp(min=1e-7)
return torch.sin((1-t)*omega)/so * h + torch.sin(t*omega)/so * c
def forward(self, x):
B, D = x.shape; P, A, d = self.n_patches, self.n_anchors, self.patch_dim
patches = self.norm(x).reshape(B, P, d)
patches_n = F.normalize(patches, dim=-1)
tris = []
for t in [0.0, 1/3, 2/3]:
at = F.normalize(self.at_phase(t), dim=-1)
tris.append(1.0 - torch.einsum('bpd,pad->bpa', patches_n, at))
tri = torch.cat(tris, dim=-1)
h = F.gelu(torch.einsum('bpt,pth->bph', tri, self.pw_w1) + self.pw_b1)
pw = self.pw_norm(torch.einsum('bph,phd->bpd', h, self.pw_w2) + self.pw_b2)
gate = self.gates.sigmoid().unsqueeze(0).unsqueeze(-1)
return x + (gate * pw + (1-gate) * patches).reshape(B, D)
# ββ CONSTELLATION RELAY (sequence-aware) ββ
class ConstellationRelay(nn.Module):
"""Per-token geometric processing. O(S). Handles (B,D) and (B,S,D)."""
def __init__(self, dim, n_anchors=16, n_comp=8, d_comp=64,
gate_init=-3.0, anchor_init='repulsion', activation='squared_relu'):
super().__init__()
self.dim = dim; self.norm = nn.LayerNorm(dim)
self.constellation = Constellation(n_anchors, dim, anchor_init=anchor_init)
self.patchwork = Patchwork(n_anchors, n_comp, d_comp, activation)
self.proj = nn.Linear(self.patchwork.output_dim, dim)
self.gate = nn.Parameter(torch.full((dim,), gate_init))
def forward(self, x):
squeeze = x.dim() == 2
if squeeze: x = x.unsqueeze(1)
B, S, D = x.shape; residual = x
h_flat = F.normalize(self.norm(x).reshape(B*S, D), dim=-1)
tri, _ = self.constellation.triangulate(h_flat)
update = self.proj(self.patchwork(tri)).reshape(B, S, D)
out = residual + torch.sigmoid(self.gate) * update
return out.squeeze(1) if squeeze else out
# ββ MAGNITUDE FLOW ββ
class MagnitudeFlow(nn.Module):
"""Relay-stack per-compartment magnitude. No attention."""
def __init__(self, dim, n_anchors, hidden_dim=64, n_heads=4,
n_layers=2, mag_min=0.1, mag_max=5.0, n_comp=8):
super().__init__()
self.dim, self.n_anchors = dim, n_anchors
self.mag_min, self.mag_max, self.n_comp, self.n_layers = mag_min, mag_max, n_comp, n_layers
patch_dim = 16; relay_dim = n_comp * patch_dim
self.patch_dim, self.relay_dim = patch_dim, relay_dim
self.emb_proj = nn.Linear(dim, relay_dim // 2)
self.tri_proj = nn.Linear(n_anchors, relay_dim // 4)
self.ctx_proj = nn.Linear(relay_dim // 2 + relay_dim // 4 + 1, relay_dim)
self.relays = nn.ModuleList([
RelayLayer(relay_dim, patch_dim, 16, 3, hidden_dim, -3.0) for _ in range(n_layers)])
self.mag_heads = nn.ModuleList([
nn.Sequential(nn.Linear(patch_dim, patch_dim//2), nn.GELU(), nn.Linear(patch_dim//2, 1))
for _ in range(n_comp)])
self.register_buffer('stats_bias_cached', torch.zeros(n_comp), persistent=False)
def update_stats(self, push_diag, anchor_push):
with torch.no_grad():
device = self.stats_bias_cached.device
if anchor_push.strategy == 'momentum' and anchor_push.accumulator is not None:
mn = anchor_push.accumulator.norm(dim=-1)
apc = self.n_anchors // self.n_comp
self.stats_bias_cached = torch.stack([
mn[k*apc : (k+1)*apc if k < self.n_comp-1 else self.n_anchors].mean()
for k in range(self.n_comp)])
else: self.stats_bias_cached.zero_()
def forward(self, emb, triangulation, raw_magnitude):
B, A = emb.shape[0], self.n_anchors
x = self.ctx_proj(torch.cat([self.emb_proj(emb), self.tri_proj(triangulation), raw_magnitude], -1))
for relay in self.relays: x = relay(x)
patches = x.reshape(B, self.n_comp, self.patch_dim)
mc = torch.cat([self.mag_heads[k](patches[:, k]) for k in range(self.n_comp)], -1)
mc = self.mag_min + (self.mag_max - self.mag_min) * torch.sigmoid(mc + self.stats_bias_cached)
apc = A // self.n_comp
mag = torch.cat([mc[:, k:k+1].expand(-1, apc if k < self.n_comp-1 else A - k*apc)
for k in range(self.n_comp)], -1)
return mag, mc
def get_relay_diagnostics(self):
return [{'layer': i, 'drift_mean': r.drift().mean().item(),
'gate_mean': r.gates.sigmoid().mean().item()} for i, r in enumerate(self.relays)]
# ββ ANCHOR PUSH ββ
def _project_tangent(vec, point):
return vec - (vec * point).sum(dim=-1, keepdim=True) * point
def _compute_centroids_and_assign(anchors_n, emb_n, label_buffer, device):
n_a = anchors_n.shape[0]; classes = label_buffer.unique(); n_cls = classes.shape[0]
centroids = torch.cat([F.normalize(emb_n[label_buffer==c].mean(0, keepdim=True), dim=-1)
for c in classes if (label_buffer==c).sum() > 0], dim=0)
if centroids.shape[0] == 0: return None, None, None, None
cos = anchors_n @ centroids.T; apc = n_a // n_cls
assigned = torch.full((n_a,), -1, dtype=torch.long, device=device)
cc = torch.zeros(n_cls, dtype=torch.long, device=device)
for idx in cos.flatten().sort(descending=True).indices:
a, c = (idx // n_cls).item(), (idx % n_cls).item()
if assigned[a] >= 0 or cc[c] >= apc + 1: continue
assigned[a] = c; cc[c] += 1
if (assigned >= 0).all(): break
u = (assigned < 0).nonzero(as_tuple=True)[0]
if len(u) > 0: assigned[u] = (anchors_n[u] @ centroids.T).argmax(1)
nearest = (emb_n @ anchors_n.T).argmax(1)
util = torch.bincount(nearest, minlength=n_a).float()
return centroids, assigned, util / util.sum().clamp(min=1), classes
def _perturb_target(target, apc, rank):
if apc > 1 and rank > 0:
noise = torch.randn_like(target) * 0.05
return F.normalize(target + noise - (noise * target).sum() * target, dim=-1)
return target
class AnchorPush:
"""Configurable anchor push. Strategies: raw, gru, momentum."""
def __init__(self, strategy, n_anchors, dim, **kw):
self.strategy, self.n_anchors, self.dim, self.push_count = strategy, n_anchors, dim, 0
if strategy == 'raw': self.lr = kw.get('lr', 0.1)
elif strategy == 'momentum':
self.decay, self.alpha, self.beta = kw.get('decay', 0.9), kw.get('alpha', 0.1), kw.get('beta', 0.05)
self.util_floor, self.accumulator = kw.get('util_floor', 0.001), None
elif strategy == 'gru':
self.ema_decay = kw.get('ema_decay', 0.9); self.z_scale = kw.get('z_scale', 3.0)
self.r_scale = kw.get('r_scale', 5.0)
self.prev_pos = self.util_ema = self.drift_ema = None
@torch.no_grad()
def push(self, core, emb_buf, lbl_buf):
anchors = core.constellation.anchors.data; n_a = anchors.shape[0]; device = anchors.device
emb_n = F.normalize(emb_buf, dim=-1); anchors_n = F.normalize(anchors, dim=-1)
centroids, assigned, util, classes = _compute_centroids_and_assign(anchors_n, emb_n, lbl_buf, device)
if centroids is None: return {'moved': 0}
if hasattr(core, 'anchor_classes'):
for a in range(n_a): core.anchor_classes[a] = classes[assigned[a]]
if hasattr(core, 'class_centroids'):
for i, c in enumerate(classes): core.class_centroids[c] = centroids[i]
apc = n_a // centroids.shape[0]
targets = torch.stack([_perturb_target(centroids[assigned[a].item()], apc,
(assigned[:a]==assigned[a]).sum().item()) for a in range(n_a)])
if self.strategy == 'raw':
for a in range(n_a): anchors[a] = F.normalize(anchors_n[a] + self.lr*(targets[a]-anchors_n[a]), dim=-1)
d = torch.acos((anchors_n * F.normalize(anchors, dim=-1)).sum(-1).clamp(-1+1e-6, 1-1e-6))
diag = {'drift_mean': d.mean().item(), 'drift_max': d.max().item()}
elif self.strategy == 'momentum':
if self.accumulator is None: self.accumulator = torch.zeros(n_a, self.dim, device=device)
res = _project_tangent(targets - anchors_n, anchors_n)
self.accumulator = self.decay * _project_tangent(self.accumulator, anchors_n) + res
corr = self.alpha * res + self.beta * self.accumulator
dead = util < self.util_floor
if dead.any(): corr[dead] = res[dead] * 0.5
new = F.normalize(anchors_n + corr, dim=-1)
d = torch.acos((anchors_n * new).sum(-1).clamp(-1+1e-6, 1-1e-6))
anchors.copy_(new)
diag = {'drift_mean': d.mean().item(), 'drift_max': d.max().item(),
'momentum_mean': self.accumulator.norm(dim=-1).mean().item(), 'dead_count': dead.sum().item()}
else:
diag = {}
diag.update({'moved': n_a, 'n_active': (util > 0).sum().item(),
'util_min': util.min().item(), 'util_max': util.max().item()})
self.push_count += 1; return diag
# ββ FLOW ATTENTION (historical) ββ
class FlowAttention(nn.Module):
"""3-step Euler flow in tangent space. Superseded by relay."""
def __init__(self, dim, n_anchors, flow_dim=64, n_steps=3, time_dim=32, gate_init=-3.0):
super().__init__()
self.dim, self.flow_dim, self.n_anchors, self.n_steps, self.time_dim = dim, flow_dim, n_anchors, n_steps, time_dim
self.to_flow = nn.Sequential(nn.Linear(n_anchors+dim, flow_dim), nn.LayerNorm(flow_dim))
self.time_mlp = nn.Sequential(nn.Linear(time_dim, flow_dim), nn.GELU())
self.stats_proj = nn.Linear(3, flow_dim, bias=False)
self.velocity = nn.Sequential(nn.Linear(flow_dim, flow_dim*2), nn.GELU(), nn.Linear(flow_dim*2, flow_dim))
self.to_correction = nn.Linear(flow_dim, dim, bias=False)
self.gate = nn.Parameter(torch.full((dim,), gate_init))
self.register_buffer('stats_bias_cached', torch.zeros(flow_dim), persistent=False)
def update_stats(self, push_diag, anchor_push):
with torch.no_grad():
dev = self.stats_proj.weight.device
mn = anchor_push.accumulator.norm(dim=-1) if (anchor_push.strategy=='momentum' and anchor_push.accumulator is not None) else torch.zeros(self.n_anchors, device=dev)
dr = torch.tensor(push_diag.get('drift_mean',0.0), device=dev).expand(self.n_anchors)
ut = torch.tensor(push_diag.get('util_max',0.0), device=dev).expand(self.n_anchors)
self.stats_bias_cached = self.stats_proj(torch.stack([mn, ut, dr], -1)).mean(0)
def forward(self, emb, constellation):
B, D, dev = *emb.shape, emb.device
tri = emb @ F.normalize(constellation.anchors, dim=-1).T
z = self.to_flow(torch.cat([tri, emb], -1)); dt = 1.0/self.n_steps
half = self.time_dim // 2
freqs = torch.exp(-math.log(10000.0) * torch.arange(half, device=dev) / half)
for s in range(self.n_steps):
args = (s*dt)*freqs; t_emb = torch.cat([args.sin(), args.cos()])
z = z + dt * (self.velocity(z + self.time_mlp(t_emb)) + self.stats_bias_cached)
c = self.to_correction(z); c = c - (c*emb).sum(-1,keepdim=True)*emb
return F.normalize(emb + torch.sigmoid(self.gate)*c, dim=-1)
# ββ GEOMETRIC AUTOGRAD ββ
class GeometricAutograd(torch.autograd.Function):
"""Manifold-aware gradient correction on S^(D-1). Forward: identity."""
@staticmethod
def forward(ctx, emb, anchors, tang_strength, sep_strength):
ctx.save_for_backward(emb, anchors); ctx.tang, ctx.sep = tang_strength, sep_strength
return emb
@staticmethod
def backward(ctx, grad):
emb, anchors = ctx.saved_tensors
dot = (grad * emb).sum(-1, keepdim=True)
corrected = grad - ctx.tang * dot * emb
if ctx.sep > 0:
an = F.normalize(anchors.detach(), dim=-1)
nearest = an[(emb @ an.T).argmax(-1)]
toward = (corrected * nearest).sum(-1, keepdim=True)
corrected = corrected - ctx.sep * F.relu(toward) * nearest
return corrected, None, None, None
# ββ UTILITIES ββ
def param_count(module, name=""):
t = sum(p.numel() for p in module.parameters())
tr = sum(p.numel() for p in module.parameters() if p.requires_grad)
if name: print(f" {name}: {t:,} ({tr:,} trainable)")
return t, tr
def model_summary(model):
total = sum(p.numel() for p in model.parameters())
print(f" Total: {total:,}")
for n, m in model.named_children():
c = sum(p.numel() for p in m.parameters())
if c > 0: print(f" {n}: {c:,}")
return total |