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Rete neurale su mesh geodetica sferica (PyTorch).
- TriangleBlock: pesi locali + router ternario (3 lati)
- CausalAttnBlock: self-attention causale + FF (contesto temporale)
- SphericalMeshModel: emb → CausalAttn × N → walk mesh batched → LM head
- Pesi faccia impacchettati a coppie (pair packing) per buffer contigui GEMM-friendly
"""
from __future__ import annotations
from dataclasses import dataclass
from typing import List, Optional, Tuple
import math
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
from mesh_topology import GeodesicMesh, build_geodesic_mesh, nearest_face
@dataclass
class WalkConfig:
max_hops: int = 8
# Se la probabilità del “exit” (soft) supera la soglia, si ferma prima
exit_threshold: float = 0.55
# Temperatura del router ternario
router_temperature: float = 1.0
# Se True, usa argmax (discreto); altrimenti Gumbel-Softmax straight-through
hard_routing: bool = True
class TriangleBlock(nn.Module):
"""Micro-blocco su una faccia: MLP locale + logits verso 3 lati + exit."""
def __init__(self, d_model: int, d_hidden: Optional[int] = None):
super().__init__()
h = d_hidden or d_model
self.norm = nn.LayerNorm(d_model)
self.ff = nn.Sequential(
nn.Linear(d_model, h),
nn.GELU(),
nn.Linear(h, d_model),
)
# 3 lati + 1 “esci / emetti”
self.router = nn.Linear(d_model, 4)
def forward(self, x: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]:
"""
x: (..., d)
returns: (x_out, router_logits) con logits shape (..., 4)
"""
h = self.ff(self.norm(x))
x_out = x + h
logits = self.router(x_out)
return x_out, logits
class PairedFaceBank(nn.Module):
"""
Banca pesi: per ogni coppia di facce adiacenti memorizza 2 TriangleBlock
in un modulo ModuleList, con indici face→block per lookup O(1).
I parametri di ogni coppia restano contigui nel ModuleList (ordine packing).
"""
def __init__(self, mesh: GeodesicMesh, d_model: int, d_hidden: Optional[int] = None):
super().__init__()
self.num_faces = mesh.num_faces
self.register_buffer("adjacency", torch.from_numpy(mesh.adjacency.astype(np.int64)))
self.register_buffer("pairs", torch.from_numpy(mesh.pairs.astype(np.int64)))
# face_id → index nel ModuleList `blocks`
face_to_slot = np.full(mesh.num_faces, -1, dtype=np.int64)
blocks: List[TriangleBlock] = []
for fa, fb in mesh.pairs:
face_to_slot[int(fa)] = len(blocks)
blocks.append(TriangleBlock(d_model, d_hidden))
face_to_slot[int(fb)] = len(blocks)
blocks.append(TriangleBlock(d_model, d_hidden))
for u in mesh.unpaired:
face_to_slot[int(u)] = len(blocks)
blocks.append(TriangleBlock(d_model, d_hidden))
self.blocks = nn.ModuleList(blocks)
self.register_buffer("face_to_slot", torch.from_numpy(face_to_slot))
def forward_face(self, face_id: int, x: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]:
slot = int(self.face_to_slot[face_id].item())
return self.blocks[slot](x)
class CausalSelfAttention(nn.Module):
"""Multi-head self-attention con maschera causale (lookahead vietato)."""
def __init__(self, d_model: int, n_heads: int, dropout: float = 0.0):
super().__init__()
if d_model % n_heads != 0:
raise ValueError(f"d_model={d_model} non divisibile per n_heads={n_heads}")
self.d_model = d_model
self.n_heads = n_heads
self.head_dim = d_model // n_heads
self.qkv = nn.Linear(d_model, 3 * d_model, bias=False)
self.proj = nn.Linear(d_model, d_model, bias=False)
self.attn_drop = nn.Dropout(dropout)
self.resid_drop = nn.Dropout(dropout)
def forward(self, x: torch.Tensor) -> torch.Tensor:
# x: (B, T, d)
b, t, _ = x.shape
qkv = self.qkv(x).view(b, t, 3, self.n_heads, self.head_dim)
qkv = qkv.permute(2, 0, 3, 1, 4) # (3, B, H, T, hd)
q, k, v = qkv[0], qkv[1], qkv[2]
scale = 1.0 / math.sqrt(self.head_dim)
# PyTorch SDPA con is_causal=True (Flash/mem-efficient quando disponibili)
y = F.scaled_dot_product_attention(
q, k, v,
attn_mask=None,
dropout_p=self.attn_drop.p if self.training else 0.0,
is_causal=True,
scale=scale,
) # (B, H, T, hd)
y = y.transpose(1, 2).contiguous().view(b, t, self.d_model)
return self.resid_drop(self.proj(y))
class CausalAttnBlock(nn.Module):
"""Pre-norm: LayerNorm → causal attn → residual → LayerNorm → FF → residual."""
def __init__(
self,
d_model: int,
n_heads: int,
d_ff: Optional[int] = None,
dropout: float = 0.0,
):
super().__init__()
h = d_ff or (4 * d_model)
self.ln1 = nn.LayerNorm(d_model)
self.attn = CausalSelfAttention(d_model, n_heads, dropout=dropout)
self.ln2 = nn.LayerNorm(d_model)
self.ff = nn.Sequential(
nn.Linear(d_model, h),
nn.GELU(),
nn.Linear(h, d_model),
nn.Dropout(dropout),
)
def forward(self, x: torch.Tensor) -> torch.Tensor:
x = x + self.attn(self.ln1(x))
x = x + self.ff(self.ln2(x))
return x
def _default_n_heads(d_model: int) -> int:
for h in (8, 4, 2, 1):
if d_model % h == 0:
return h
return 1
class SphericalMeshModel(nn.Module):
"""
LM: token → emb (+pos) → CausalAttn × N → walk mesh parallelo (B*T) → vocab.
Contesto temporale via attenzione causale (no carry sequenziale).
"""
def __init__(
self,
vocab_size: int,
d_model: int = 64,
frequency: int = 2,
walk: Optional[WalkConfig] = None,
d_hidden: Optional[int] = None,
n_attn_layers: int = 2,
n_heads: Optional[int] = None,
max_seq_len: int = 512,
use_mesh_walk: bool = True,
attn_dropout: float = 0.0,
compass_spiral: bool = False,
):
super().__init__()
self.compass_spiral = bool(compass_spiral)
self.mesh: GeodesicMesh = build_geodesic_mesh(
frequency, compass_spiral=self.compass_spiral
)
self.walk = walk or WalkConfig()
self.d_model = d_model
self.vocab_size = vocab_size
self.n_attn_layers = int(n_attn_layers)
self.use_mesh_walk = bool(use_mesh_walk)
self.max_seq_len = int(max_seq_len)
heads = int(n_heads) if n_heads is not None else _default_n_heads(d_model)
self.tok_emb = nn.Embedding(vocab_size, d_model)
nn.init.normal_(self.tok_emb.weight, mean=0.0, std=0.02)
self.pos_emb = nn.Embedding(self.max_seq_len, d_model)
nn.init.normal_(self.pos_emb.weight, mean=0.0, std=0.02)
self.attn_blocks = nn.ModuleList(
[
CausalAttnBlock(d_model, heads, d_ff=d_hidden or (4 * d_model), dropout=attn_dropout)
for _ in range(self.n_attn_layers)
]
)
# Proietta embedding → direzione 3D sulla sfera (faccia di ingresso)
self.to_sphere = nn.Linear(d_model, 3)
self.bank = PairedFaceBank(self.mesh, d_model, d_hidden)
self.final_norm = nn.LayerNorm(d_model)
self.lm_head = nn.Linear(d_model, vocab_size, bias=False)
# embedding tied (come goTommy2)
self.lm_head.weight = self.tok_emb.weight
self.emb_scale = d_model**-0.5
# Buffer geometria per nearest face su GPU/CPU
self.register_buffer(
"centroids",
torch.from_numpy(self.mesh.face_centroids.astype(np.float32)),
)
self.register_buffer(
"adjacency",
torch.from_numpy(self.mesh.adjacency.astype(np.int64)),
)
def project_to_face(self, h: torch.Tensor) -> torch.Tensor:
"""h (..., d) → face ids (...)"""
direction = self.to_sphere(h)
direction = F.normalize(direction, dim=-1)
# (..., F)
scores = direction @ self.centroids.T
return scores.argmax(dim=-1)
def _route_step(
self,
face: torch.Tensor,
logits: torch.Tensor,
) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
"""
face: (B,) long — faccia corrente
logits: (B, 4) — 3 lati + exit
returns: next_face (B,), exit_mask (B,) bool, side_choice (B,) in {0,1,2,-1}
"""
temp = max(self.walk.router_temperature, 1e-6)
probs = F.softmax(logits / temp, dim=-1)
exit_prob = probs[:, 3]
side_probs = probs[:, :3]
if self.walk.hard_routing:
side = side_probs.argmax(dim=-1)
else:
# Gumbel-softmax straight-through sui 3 lati
side = F.gumbel_softmax(logits[:, :3] / temp, hard=True, dim=-1).argmax(dim=-1)
exit_mask = exit_prob >= self.walk.exit_threshold
# lookup vettoriale: adjacency[face, side]
next_face = self.adjacency[face.long(), side.long()]
side_out = torch.where(exit_mask, torch.full_like(side, -1), side)
return next_face, exit_mask, side_out
def walk_token(
self,
h: torch.Tensor,
start_face: Optional[torch.Tensor] = None,
record_path: bool = False,
) -> Tuple[torch.Tensor, Optional[List[List[int]]]]:
"""
h: (B, d) stato iniziale token — tipicamente B*T flattened
returns: h_final (B, d), paths opzionale list per batch
"""
b = h.shape[0]
face = start_face if start_face is not None else self.project_to_face(h)
paths: Optional[List[List[int]]] = [[int(face[i].item())] for i in range(b)] if record_path else None
active = torch.ones(b, dtype=torch.bool, device=h.device)
for _ in range(self.walk.max_hops):
if not active.any():
break
# Esegue i blocchi per-faccia (batch misto: loop su facce uniche)
logits = h.new_zeros(b, 4)
h_new = h.clone()
unique_faces = face[active].unique()
for f_id in unique_faces.tolist():
mask = active & (face == f_id)
if not mask.any():
continue
out, lg = self.bank.forward_face(int(f_id), h[mask])
h_new[mask] = out
logits[mask] = lg
h = h_new
next_face, exit_mask, _ = self._route_step(face, logits)
# Solo i token ancora attivi possono uscire / muoversi
moved = active & ~exit_mask
face = torch.where(moved, next_face, face)
just_exit = active & exit_mask
active = active & ~exit_mask
if record_path and paths is not None:
for i in range(b):
if moved[i]:
paths[i].append(int(face[i].item()))
elif just_exit[i]:
paths[i].append(-1) # sentinel exit
return h, paths
def forward(
self,
input_ids: torch.Tensor,
record_path: bool = False,
) -> Tuple[torch.Tensor, Optional[List[List[List[int]]]]]:
"""
input_ids: (B, T)
returns: logits (B, T, V), paths [B][T][hops] se richiesto
Pipeline:
emb(+pos) → CausalAttnBlock × N → walk_token(B*T) → final_norm → lm_head
"""
b, t = input_ids.shape
if t > self.max_seq_len:
raise ValueError(f"seq_len={t} > max_seq_len={self.max_seq_len}")
pos = torch.arange(t, device=input_ids.device).unsqueeze(0) # (1, T)
h = self.tok_emb(input_ids) * self.emb_scale + self.pos_emb(pos)
for block in self.attn_blocks:
h = block(h) # (B, T, d)
paths: Optional[List[List[List[int]]]] = None
if self.use_mesh_walk:
flat = h.reshape(b * t, self.d_model)
flat_out, paths_flat = self.walk_token(flat, record_path=record_path)
h = flat_out.view(b, t, self.d_model)
if record_path and paths_flat is not None:
# paths_flat[bi*T + ti] → paths[bi][ti]
paths = [
[paths_flat[bi * t + ti] for ti in range(t)]
for bi in range(b)
]
h = self.final_norm(h)
logits = self.lm_head(h)
# soft-cap: evita CE esplosa con residual walk + tied emb
logits = 30.0 * torch.tanh(logits / 30.0)
return logits, paths
def count_parameters(model: nn.Module) -> int:
return sum(p.numel() for p in model.parameters() if p.requires_grad)
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