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# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.
#
# ---------------------------------------------------------------
import torch
import torch.nn as nn
import torch.nn.functional as F
class PMPSLatentSupervisor(nn.Module):
"""PMPS-style supervisor for latent reasoning hidden states.
Setting
-------
Each example yields two token sequences from the **same** language
model:
* latent hidden states ``H_lat ∈ R^{B × N_l × D}`` (few tokens)
* CoT hidden states ``H_cot ∈ R^{B × N_c × D}`` (many tokens)
Goal: supervise the latent tokens so that
(a) one latent embedding may carry information from *multiple* CoT
tokens (compression / coverage), and
(b) different latent embeddings cover *different* CoT tokens
(diversity / no collapse).
"""
def __init__(
self,
hidden_dim,
feat_dim=128,
hidden_mlp=512,
nmb_prototypes=24, # ~4 × N_l (N_l=6 in CODI default)
temperature=0.1,
match_temperature=0.3, # softer cluster-space matching
epsilon=0.05,
sinkhorn_iterations=3,
use_projector=True,
position_bias_strength=0.0, # NEW: Gaussian positional bias strength; 0 = disabled
):
super().__init__()
self.nmb_prototypes = nmb_prototypes
self.temperature = temperature
self.match_temperature = match_temperature
self.epsilon = epsilon
self.sinkhorn_iterations = sinkhorn_iterations
self.use_projector = use_projector
self.position_bias_strength = position_bias_strength
if use_projector:
self.projector = self._build_projector(hidden_dim, hidden_mlp, feat_dim)
proto_dim = feat_dim
else:
self.projector = nn.Identity()
proto_dim = hidden_dim
self.feat_dim = proto_dim
self.prototypes = nn.Linear(proto_dim, nmb_prototypes, bias=False)
# ------------------------------------------------------------------
# building blocks
# ------------------------------------------------------------------
@staticmethod
def _build_projector(input_dim, hidden_dim, output_dim):
return nn.Sequential(
nn.Linear(input_dim, hidden_dim),
nn.BatchNorm1d(hidden_dim),
nn.ReLU(inplace=True),
nn.Linear(hidden_dim, output_dim),
)
@torch.no_grad()
def normalize_prototypes(self):
"""L2-normalise prototype rows. Call once per step before forward,
mirroring ``main_pmps.py``."""
w = self.prototypes.weight.data.clone()
w = F.normalize(w, dim=1, p=2)
self.prototypes.weight.copy_(w)
def _project_and_score(self, hidden_states):
"""Project (B, N, D) -> normalised (B*N, feat_dim) and score
against prototypes -> (B*N, K)."""
b, n, d = hidden_states.shape
flat = hidden_states.reshape(b * n, d)
emb = self.projector(flat)
emb = F.normalize(emb, dim=1, p=2)
scores = self.prototypes(emb) # (B*N, K)
return scores
@torch.no_grad()
def sinkhorn(self, scores):
"""Sinkhorn-Knopp on un-normalised prototype scores.
scores : (M, K) cosine-similarity scores.
returns Q : (M, K) rows sum to 1 (per-sample distribution over
prototypes), columns sum to M / K (equipartition across
prototypes).
"""
Q = torch.exp(scores / self.epsilon).t() # (K, M)
Q = Q / (Q.sum() + 1e-8)
K, M = Q.shape
for _ in range(self.sinkhorn_iterations):
Q = Q / (Q.sum(dim=1, keepdim=True) + 1e-8)
Q = Q / K
Q = Q / (Q.sum(dim=0, keepdim=True) + 1e-8)
Q = Q / M
Q = Q * M # rows now sum to 1
return Q.t() # (M, K)
@torch.no_grad()
def sinkhorn_per_sample(self, scores, batch_size, seq_len):
"""Per-sample Sinkhorn-Knopp.
Instead of applying Sinkhorn on the flattened (B*N, K) matrix,
apply it independently on each sample's (N, K) sub-matrix.
This enforces that within EACH sample, the N tokens are
distributed uniformly across K prototypes — directly preventing
intra-sample collapse.
Args:
scores: (B*N, K) prototype scores (flattened).
batch_size: B
seq_len: N (number of tokens per sample, e.g. N_l or N_c)
Returns:
Q: (B*N, K) per-sample normalised codes.
"""
# Reshape to per-sample: (B, N, K)
scores_3d = scores.reshape(batch_size, seq_len, K := scores.size(-1))
Q_list = []
for b in range(batch_size):
Q_b = torch.exp(scores_3d[b] / self.epsilon).t() # (K, N)
Q_b = Q_b / (Q_b.sum() + 1e-8)
N = Q_b.size(1)
for _ in range(self.sinkhorn_iterations):
# Row normalisation: each prototype gets equal total mass
Q_b = Q_b / (Q_b.sum(dim=1, keepdim=True) + 1e-8)
Q_b = Q_b / K
# Column normalisation: each token gets equal total mass
Q_b = Q_b / (Q_b.sum(dim=0, keepdim=True) + 1e-8)
Q_b = Q_b / N
Q_b = Q_b * N # rows sum to 1
Q_list.append(Q_b.t()) # (N, K)
return torch.cat(Q_list, dim=0) # (B*N, K)
@torch.no_grad()
def sinkhorn_per_sample_masked(self, scores_3d, mask):
"""Per-sample Sinkhorn with mask support.
Args:
scores_3d: (B, N, K) prototype scores.
mask: (B, N) binary mask, 1 = valid token.
Returns:
Q: (B, N, K) per-sample normalised codes (masked positions = 0).
"""
B, N, K = scores_3d.shape
Q_out = scores_3d.new_zeros(B, N, K)
for b in range(B):
valid = mask[b].bool() # (N,)
n_valid = valid.sum().item()
if n_valid == 0:
continue
s = scores_3d[b, valid, :] # (n_valid, K)
Q_b = torch.exp(s / self.epsilon).t() # (K, n_valid)
Q_b = Q_b / (Q_b.sum() + 1e-8)
for _ in range(self.sinkhorn_iterations):
Q_b = Q_b / (Q_b.sum(dim=1, keepdim=True) + 1e-8)
Q_b = Q_b / K
Q_b = Q_b / (Q_b.sum(dim=0, keepdim=True) + 1e-8)
Q_b = Q_b / n_valid
Q_b = Q_b * n_valid # each token's row sums to 1
Q_out[b, valid, :] = Q_b.t().to(dtype=Q_out.dtype)
return Q_out # (B, N, K)
# ------------------------------------------------------------------
# positional bias for progressive sequential matching
# ------------------------------------------------------------------
@staticmethod
def _compute_position_bias(N_c, N_l, strength, cot_mask=None, device=None):
"""Compute a Gaussian positional bias matrix.
The bias encourages CoT token j to match latent token i when their
normalised sequential positions are close, implementing the
"progressive sequential PMPS" prior.
Args:
N_c: number of CoT tokens (padded length).
N_l: number of latent tokens.
strength: bias strength (larger = stronger sequential prior).
0 means no bias (original free matching).
cot_mask: optional (B, N_c) binary mask. When provided the
effective CoT length is computed per sample so that
padding positions do not distort normalisation.
device: target device.
Returns:
bias: (B, N_c, N_l) if cot_mask is given, else (1, N_c, N_l).
"""
if strength <= 0:
return 0.0
lat_pos = torch.arange(N_l, device=device, dtype=torch.float32)
lat_pos_norm = lat_pos / max(N_l - 1, 1) # [0, 1]
if cot_mask is not None and cot_mask.dim() == 2:
B = cot_mask.size(0)
bias = torch.zeros(B, N_c, N_l, device=device)
for b in range(B):
n_valid = cot_mask[b].sum().long().item()
if n_valid <= 1:
continue
cot_pos = torch.arange(n_valid, device=device, dtype=torch.float32)
cot_pos_norm = cot_pos / max(n_valid - 1, 1) # [0, 1]
# (n_valid, 1) - (1, N_l) -> (n_valid, N_l)
delta = cot_pos_norm.unsqueeze(1) - lat_pos_norm.unsqueeze(0)
bias[b, :n_valid, :] = -strength * delta.pow(2)
return bias # (B, N_c, N_l)
else:
cot_pos = torch.arange(N_c, device=device, dtype=torch.float32)
cot_pos_norm = cot_pos / max(N_c - 1, 1)
delta = cot_pos_norm.unsqueeze(1) - lat_pos_norm.unsqueeze(0) # (N_c, N_l)
bias = -strength * delta.pow(2)
return bias.unsqueeze(0) # (1, N_c, N_l)
# ------------------------------------------------------------------
# forward
# ------------------------------------------------------------------
def forward(self, latent_hidden, cot_hidden, latent_mask=None, cot_mask=None,
position_bias_strength_override=None):
"""Compute the PMPS-style swapped loss between latent and CoT
token sequences.
Parameters
----------
latent_hidden : (B, N_l, D)
cot_hidden : (B, N_c, D)
latent_mask : optional (B, N_l) 0/1
cot_mask : optional (B, N_c) 0/1
Returns
-------
loss : scalar
log_dict : diagnostic stats
"""
assert latent_hidden.dim() == 3 and cot_hidden.dim() == 3
assert latent_hidden.size(0) == cot_hidden.size(0)
assert latent_hidden.size(-1) == cot_hidden.size(-1), (
"latent and cot must share the hidden dim (same model)"
)
B, N_l, _ = latent_hidden.shape
_, N_c, _ = cot_hidden.shape
K = self.nmb_prototypes
device = latent_hidden.device
# 1. score each token against the shared prototypes.
latent_scores = self._project_and_score(latent_hidden) # (B*N_l, K)
cot_scores = self._project_and_score(cot_hidden) # (B*N_c, K)
# masks (flat)
if latent_mask is None:
latent_mask = torch.ones(B, N_l, device=device, dtype=latent_hidden.dtype)
if cot_mask is None:
cot_mask = torch.ones(B, N_c, device=device, dtype=cot_hidden.dtype)
latent_keep = latent_mask.reshape(-1).bool()
cot_keep = cot_mask.reshape(-1).bool()
# 2. compute per-token codes via Sinkhorn (no grad).
with torch.no_grad():
q_latent_valid = self.sinkhorn(latent_scores[latent_keep]) # (M_l, K)
q_cot_valid = self.sinkhorn(cot_scores[cot_keep]) # (M_c, K)
Q_lat = latent_scores.new_zeros(B * N_l, K)
Q_lat[latent_keep] = q_latent_valid.to(dtype=Q_lat.dtype)
Q_lat = Q_lat.reshape(B, N_l, K)
Q_cot = cot_scores.new_zeros(B * N_c, K)
Q_cot[cot_keep] = q_cot_valid.to(dtype=Q_lat.dtype)
Q_cot = Q_cot.reshape(B, N_c, K)
# q_latent_valid = self.sinkhorn_per_sample(latent_scores[latent_keep], batch_size=B, seq_len=N_l)
# cot_scores_3d = cot_scores.reshape(B, N_c, K)
# Q_cot = self.sinkhorn_per_sample_masked(cot_scores_3d, mask=cot_mask) # (B, N_c, K)
# Q_lat = latent_scores.new_zeros(B * N_l, K)
# Q_lat[latent_keep] = q_latent_valid.to(dtype=Q_lat.dtype)
# Q_lat = Q_lat.reshape(B, N_l, K)
# Q_cot is already (B, N_c, K) with masked positions = 0, no need to reshape
# 3. per-token softmax predictions over prototypes.
log_p_lat = F.log_softmax(latent_scores.reshape(B, N_l, K) / self.temperature, dim=-1)
log_p_cot = F.log_softmax(cot_scores.reshape(B, N_c, K) / self.temperature, dim=-1)
p_lat = log_p_lat.exp() # (B, N_l, K)
p_cot = log_p_cot.exp() # (B, N_c, K)
# 4. cluster-based cross-view matching (codes-only) + positional bias.
match_logits_c2l = torch.bmm(Q_cot, Q_lat.transpose(1, 2)) / self.match_temperature # (B, N_c, N_l)
# NEW: apply Gaussian positional bias for progressive sequential matching
effective_strength = (
position_bias_strength_override
if position_bias_strength_override is not None
else self.position_bias_strength
)
if isinstance(effective_strength, (int, float)) and effective_strength > 0:
pos_bias = self._compute_position_bias(
N_c, N_l, effective_strength,
cot_mask=cot_mask, device=device,
)
match_logits_c2l = match_logits_c2l + pos_bias
match_logits_l2c = match_logits_c2l.transpose(1, 2) # (B, N_l, N_c)
very_neg = torch.finfo(match_logits_c2l.dtype).min / 4
match_logits_c2l = match_logits_c2l.masked_fill(
~latent_mask.bool().unsqueeze(1), very_neg
)
match_logits_l2c = match_logits_l2c.masked_fill(
~cot_mask.bool().unsqueeze(1), very_neg
)
A_c2l = F.softmax(match_logits_c2l, dim=-1) # (B, N_c, N_l)
A_l2c = F.softmax(match_logits_l2c, dim=-1) # (B, N_l, N_c)
# 5. mixture predictions.
p_lat_mix_for_cot = torch.bmm(A_c2l, p_lat) # (B, N_c, K)
p_cot_mix_for_lat = torch.bmm(A_l2c, p_cot) # (B, N_l, K)
log_p_lat_mix_for_cot = (p_lat_mix_for_cot.clamp(min=1e-12)).log()
log_p_cot_mix_for_lat = (p_cot_mix_for_lat.clamp(min=1e-12)).log()
# 6. PMPS swapped CE loss (no pooling on the targets).
ce_c2l = -(Q_cot * log_p_lat_mix_for_cot).sum(dim=-1) # (B, N_c)
ce_l2c = -(Q_lat * log_p_cot_mix_for_lat).sum(dim=-1) # (B, N_l)
loss_c2l = (ce_c2l * cot_mask).sum() / cot_mask.sum().clamp(min=1)
loss_l2c = (ce_l2c * latent_mask).sum() / latent_mask.sum().clamp(min=1)
loss = 0.5 * (loss_c2l + loss_l2c)
# 7. diagnostics
with torch.no_grad():
ent_lat = -(q_latent_valid * q_latent_valid.clamp(min=1e-8).log()).sum(-1).mean()
ent_cot = -(q_cot_valid * q_cot_valid.clamp(min=1e-8).log()).sum(-1).mean()
A_c2l_valid = A_c2l[cot_mask.bool()]
match_entropy = -(A_c2l_valid * A_c2l_valid.clamp(min=1e-8).log()).sum(-1).mean()
# NEW: match order correlation — measures whether the matching
# preserves sequential order (Pearson correlation between CoT
# token position and attended latent position).
lat_indices = torch.arange(N_l, device=device, dtype=torch.float32)
# weighted average latent position attended by each CoT token
attended_lat_pos = (A_c2l * lat_indices.view(1, 1, -1)).sum(dim=-1) # (B, N_c)
cot_indices = torch.arange(N_c, device=device, dtype=torch.float32)
corr_list = []
for b in range(B):
valid = cot_mask[b].bool()
x = cot_indices[valid]
y = attended_lat_pos[b, valid]
if len(x) > 2:
vx = x - x.mean()
vy = y - y.mean()
denom = (vx.pow(2).sum().sqrt() * vy.pow(2).sum().sqrt()).clamp(min=1e-8)
corr = (vx * vy).sum() / denom
if not torch.isnan(corr):
corr_list.append(corr)
match_order_corr = (
torch.stack(corr_list).mean()
if corr_list
else torch.tensor(0.0, device=device)
)
log_dict = {
"pmps_loss": loss.detach(),
"pmps_loss_c2l": loss_c2l.detach(),
"pmps_loss_l2c": loss_l2c.detach(),
"code_entropy_latent": ent_lat,
"code_entropy_cot": ent_cot,
"match_entropy_c2l": match_entropy,
"match_order_correlation": match_order_corr,
}
return loss_c2l, log_dict
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