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"""
Trainable interface layers for frozen threshold circuits.
BitEncoder, OpRouter, BitDecoder wrap the frozen circuits.
HiddenStateExtractor and AugmentedArithmeticModel for LLM integration.
"""
import torch
import torch.nn as nn
import torch.nn.functional as F
from circuits import FrozenThresholdCircuits, heaviside_ste
MODEL_ID = 'HuggingFaceTB/SmolLM2-360M-Instruct'
OPERATIONS = ['add', 'sub', 'mul', 'gt', 'lt', 'eq']
OP_SYMBOLS = {'add': '+', 'sub': '-', 'mul': '*', 'gt': '>', 'lt': '<', 'eq': '=='}
class BitEncoder(nn.Module):
"""
Encodes two 8-bit operands from input representation.
Uses residual connection to preserve ground truth bits while allowing learned refinement.
"""
def __init__(self, input_dim: int = 16 + 6, hidden_dim: int = 32):
super().__init__()
self.refine = nn.Sequential(
nn.Linear(input_dim, hidden_dim),
nn.Tanh(),
nn.Linear(hidden_dim, 16),
)
self.scale = nn.Parameter(torch.tensor(0.0))
def forward(self, x: torch.Tensor) -> tuple[torch.Tensor, torch.Tensor]:
"""
Args:
x: [batch, input_dim] input with first 16 dims being a_bits, b_bits
Returns:
a_bits: [batch, 8] first operand bits
b_bits: [batch, 8] second operand bits
"""
base_bits = x[:, :16]
refinement = self.refine(x) * torch.sigmoid(self.scale)
bits = base_bits + refinement
bits = torch.clamp(bits, 0, 1)
hard_bits = heaviside_ste(bits - 0.5)
out = hard_bits - bits.detach() + bits
return out[:, :8], out[:, 8:]
class OpRouter(nn.Module):
"""
Routes computation to the appropriate circuit based on input.
Outputs soft weights over operations for gradient flow.
"""
def __init__(self, input_dim: int = 16 + 6, hidden_dim: int = 32, n_ops: int = 6):
super().__init__()
self.net = nn.Sequential(
nn.Linear(input_dim, hidden_dim),
nn.ReLU(),
nn.Linear(hidden_dim, n_ops),
)
def forward(self, x: torch.Tensor) -> torch.Tensor:
"""
Args:
x: [batch, input_dim] input features
Returns:
op_weights: [batch, n_ops] soft operation weights (softmax)
"""
logits = self.net(x)
return F.softmax(logits, dim=-1)
class BitDecoder(nn.Module):
"""
Decodes circuit output bits to target representation.
For standalone training: outputs soft bits for loss computation.
For LLM integration: would project to hidden state delta.
"""
def __init__(self, output_dim: int = 8):
super().__init__()
self.output_dim = output_dim
def forward(self, result_bits: torch.Tensor) -> torch.Tensor:
return result_bits
class ThresholdALU(nn.Module):
"""
Complete trainable interface + frozen circuits.
Learns to encode inputs, route to circuits, decode outputs.
"""
def __init__(self, device: str = 'cuda'):
super().__init__()
self.device = device
self.circuits = FrozenThresholdCircuits(device=device)
for key in self.circuits.weights:
self.circuits.weights[key].requires_grad = False
self.encoder = BitEncoder(input_dim=16 + 6, hidden_dim=64).to(device)
self.router = OpRouter(input_dim=16 + 6, hidden_dim=32, n_ops=6).to(device)
self.decoder = BitDecoder(output_dim=8).to(device)
def forward(self, a_bits_in: torch.Tensor, b_bits_in: torch.Tensor,
op_onehot: torch.Tensor) -> torch.Tensor:
"""
Forward pass through trainable interface + frozen circuits.
Args:
a_bits_in: [batch, 8] input A bits (ground truth for training)
b_bits_in: [batch, 8] input B bits (ground truth for training)
op_onehot: [batch, 6] one-hot operation selector
Returns:
result_bits: [batch, 8] output bits
"""
x = torch.cat([a_bits_in, b_bits_in, op_onehot], dim=-1)
a_bits, b_bits = self.encoder(x)
op_weights = self.router(x)
result = self.circuits(a_bits, b_bits, op_weights)
output = self.decoder(result)
return output
def forward_direct(self, a_bits: torch.Tensor, b_bits: torch.Tensor,
op_onehot: torch.Tensor) -> torch.Tensor:
"""
Direct forward through circuits (bypass encoder/router for testing).
"""
return self.circuits(a_bits, b_bits, op_onehot)
class DirectCircuitModel(nn.Module):
"""
Minimal model that directly uses circuits without learned encoding.
For validating that circuits themselves achieve 100% fitness.
"""
def __init__(self, device: str = 'cuda'):
super().__init__()
self.device = device
self.circuits = FrozenThresholdCircuits(device=device)
def forward(self, a_bits: torch.Tensor, b_bits: torch.Tensor,
op_onehot: torch.Tensor) -> torch.Tensor:
return self.circuits(a_bits, b_bits, op_onehot)
class HiddenStateExtractor(nn.Module):
"""
Extracts operands and operation from LLM hidden states.
This is the hard part - must learn to parse numbers from embeddings.
"""
def __init__(self, hidden_dim: int = 960, intermediate_dim: int = 256):
super().__init__()
self.a_extractor = nn.Sequential(
nn.Linear(hidden_dim, intermediate_dim),
nn.GELU(),
nn.Linear(intermediate_dim, 8),
)
self.b_extractor = nn.Sequential(
nn.Linear(hidden_dim, intermediate_dim),
nn.GELU(),
nn.Linear(intermediate_dim, 8),
)
self.op_router = nn.Sequential(
nn.Linear(hidden_dim, intermediate_dim),
nn.GELU(),
nn.Linear(intermediate_dim, len(OPERATIONS)),
)
def forward(self, hidden_states: torch.Tensor):
"""
Args:
hidden_states: [batch, hidden_dim] from LLM
Returns:
a_bits: [batch, 8]
b_bits: [batch, 8]
op_logits: [batch, 6]
"""
a_logits = self.a_extractor(hidden_states)
b_logits = self.b_extractor(hidden_states)
op_logits = self.op_router(hidden_states)
a_soft = torch.sigmoid(a_logits)
b_soft = torch.sigmoid(b_logits)
a_hard = heaviside_ste(a_logits)
b_hard = heaviside_ste(b_logits)
a_bits = a_hard - a_soft.detach() + a_soft
b_bits = b_hard - b_soft.detach() + b_soft
return a_bits, b_bits, op_logits
class AttentionPooling(nn.Module):
"""
Learnable attention pooling over sequence positions.
Replaces mean pooling - learns which tokens matter for extraction.
"""
def __init__(self, hidden_dim: int = 960, num_heads: int = 4):
super().__init__()
self.num_heads = num_heads
self.head_dim = hidden_dim // num_heads
self.query = nn.Linear(hidden_dim, hidden_dim)
self.key = nn.Linear(hidden_dim, hidden_dim)
self.value = nn.Linear(hidden_dim, hidden_dim)
self.out_proj = nn.Linear(hidden_dim, hidden_dim)
self.cls_token = nn.Parameter(torch.randn(1, 1, hidden_dim) * 0.02)
def forward(self, embeddings: torch.Tensor, mask: torch.Tensor) -> torch.Tensor:
"""
Args:
embeddings: [batch, seq_len, hidden_dim]
mask: [batch, seq_len] attention mask (1 = attend, 0 = ignore)
Returns:
pooled: [batch, hidden_dim]
"""
batch_size, seq_len, hidden_dim = embeddings.shape
cls_expanded = self.cls_token.expand(batch_size, -1, -1)
embeddings = torch.cat([cls_expanded, embeddings], dim=1)
cls_mask = torch.ones(batch_size, 1, device=mask.device)
mask = torch.cat([cls_mask, mask], dim=1)
Q = self.query(embeddings[:, :1, :])
K = self.key(embeddings)
V = self.value(embeddings)
Q = Q.view(batch_size, 1, self.num_heads, self.head_dim).transpose(1, 2)
K = K.view(batch_size, seq_len + 1, self.num_heads, self.head_dim).transpose(1, 2)
V = V.view(batch_size, seq_len + 1, self.num_heads, self.head_dim).transpose(1, 2)
scores = torch.matmul(Q, K.transpose(-2, -1)) / (self.head_dim ** 0.5)
mask_expanded = mask.unsqueeze(1).unsqueeze(2)
scores = scores.masked_fill(mask_expanded == 0, -1e9)
attn_weights = torch.softmax(scores, dim=-1)
attn_weights = torch.nan_to_num(attn_weights, nan=0.0)
context = torch.matmul(attn_weights, V)
context = context.transpose(1, 2).contiguous().view(batch_size, 1, hidden_dim)
pooled = self.out_proj(context).squeeze(1)
pooled = torch.nan_to_num(pooled, nan=0.0)
return pooled
class MultiHeadBitExtractor(nn.Module):
"""
8 separate extractors for 8 bits - each bit gets its own specialized network.
More expressive than single MLP predicting all 8 bits at once.
"""
def __init__(self, hidden_dim: int = 960, intermediate_dim: int = 128):
super().__init__()
self.bit_extractors = nn.ModuleList([
nn.Sequential(
nn.Linear(hidden_dim, intermediate_dim),
nn.GELU(),
nn.Linear(intermediate_dim, 1),
)
for _ in range(8)
])
def forward(self, hidden_states: torch.Tensor) -> torch.Tensor:
"""
Args:
hidden_states: [batch, hidden_dim]
Returns:
bits: [batch, 8] - one bit from each extractor
"""
hidden_states = torch.nan_to_num(hidden_states, nan=0.0)
bit_logits = [extractor(hidden_states) for extractor in self.bit_extractors]
logits = torch.cat(bit_logits, dim=-1)
logits = torch.clamp(logits, -20, 20)
soft = torch.sigmoid(logits)
hard = heaviside_ste(logits)
bits = hard - soft.detach() + soft
return bits, logits
class Extractor(nn.Module):
"""
Extracts operands and operation from LLM hidden states.
Uses attention pooling and per-bit extraction networks.
"""
def __init__(self, hidden_dim: int = 960, intermediate_dim: int = 256, num_heads: int = 4):
super().__init__()
self.attention_pool = AttentionPooling(hidden_dim, num_heads)
self.a_extractor = MultiHeadBitExtractor(hidden_dim, intermediate_dim // 2)
self.b_extractor = MultiHeadBitExtractor(hidden_dim, intermediate_dim // 2)
self.op_router = nn.Sequential(
nn.Linear(hidden_dim, intermediate_dim),
nn.GELU(),
nn.Linear(intermediate_dim, len(OPERATIONS)),
)
def forward(self, embeddings: torch.Tensor, mask: torch.Tensor):
"""
Args:
embeddings: [batch, seq_len, hidden_dim]
mask: [batch, seq_len]
Returns:
a_bits: [batch, 8]
b_bits: [batch, 8]
op_logits: [batch, 6]
"""
pooled = self.attention_pool(embeddings, mask)
a_bits, _ = self.a_extractor(pooled)
b_bits, _ = self.b_extractor(pooled)
op_logits = self.op_router(pooled)
return a_bits, b_bits, op_logits
class PositionExtractor(nn.Module):
"""
Position-specific extraction with dynamic operator detection.
Tokenization pattern for "A op B":
[A_digits...] [operator] [space] [B_digits...]
Examples:
"5 + 3" -> ['5', ' +', ' ', '3'] (positions: A=0, op=1, B=3)
"47 + 86" -> ['4', '7', ' +', ' ', '8', '6'] (positions: A=0-1, op=2, B=4-5)
"127 + 128" -> ['1','2','7',' +', ' ','1','2','8'] (positions: A=0-2, op=3, B=5-7)
Token IDs (SmolLM2):
Digits '0'-'9': 32-41
Operators: ' +'=1232, ' -'=731, ' *'=1672, ' >'=2986, ' <'=2067, ' =='=1758
Space: 216
"""
DIGIT_TOKENS = set(range(32, 42))
OPERATOR_TOKENS = {
1232: 0, # ' +' -> add
731: 1, # ' -' -> sub
1672: 2, # ' *' -> mul
2986: 3, # ' >' -> gt
2067: 4, # ' <' -> lt
1758: 5, # ' ==' -> eq
}
SPACE_TOKEN = 216
MAX_DIGITS = 3
def __init__(self, hidden_dim: int = 960, intermediate_dim: int = 256):
super().__init__()
self.hidden_dim = hidden_dim
self.a_extractor = nn.Sequential(
nn.Linear(hidden_dim * self.MAX_DIGITS, intermediate_dim),
nn.GELU(),
nn.Linear(intermediate_dim, intermediate_dim // 2),
nn.GELU(),
nn.Linear(intermediate_dim // 2, 8),
)
self.b_extractor = nn.Sequential(
nn.Linear(hidden_dim * self.MAX_DIGITS, intermediate_dim),
nn.GELU(),
nn.Linear(intermediate_dim, intermediate_dim // 2),
nn.GELU(),
nn.Linear(intermediate_dim // 2, 8),
)
self.op_extractor = nn.Sequential(
nn.Linear(hidden_dim, intermediate_dim // 2),
nn.GELU(),
nn.Linear(intermediate_dim // 2, len(OPERATIONS)),
)
def _find_operator_position(self, token_ids: torch.Tensor) -> tuple[int, int]:
"""
Find operator token position and its operation index.
Args:
token_ids: [seq_len] tensor of token IDs
Returns:
(position, op_index) or (-1, -1) if not found
"""
for pos, tid in enumerate(token_ids.tolist()):
if tid in self.OPERATOR_TOKENS:
return pos, self.OPERATOR_TOKENS[tid]
return -1, -1
def _extract_digit_features(self, hidden: torch.Tensor, start: int, end: int) -> torch.Tensor:
"""
Extract and pad digit hidden states to fixed size.
Args:
hidden: [seq_len, hidden_dim]
start: start position (inclusive)
end: end position (exclusive)
Returns:
[hidden_dim * MAX_DIGITS] flattened features, zero-padded on the LEFT
(so units digit is always at the same position regardless of number length)
"""
n_digits = end - start
features = torch.zeros(self.MAX_DIGITS * self.hidden_dim, device=hidden.device)
if n_digits > 0 and n_digits <= self.MAX_DIGITS:
digit_hidden = hidden[start:end, :].reshape(-1)
pad_size = (self.MAX_DIGITS - n_digits) * self.hidden_dim
features[pad_size:] = digit_hidden
return features
def forward(self, hidden: torch.Tensor, mask: torch.Tensor, token_ids: torch.Tensor = None):
"""
Args:
hidden: [batch, seq_len, hidden_dim]
mask: [batch, seq_len] attention mask
token_ids: [batch, seq_len] token IDs (required for operator detection)
Returns:
a_bits: [batch, 8]
b_bits: [batch, 8]
op_logits: [batch, 6]
"""
if token_ids is None:
raise ValueError("PositionExtractor requires token_ids for operator detection")
batch_size, seq_len, hidden_dim = hidden.shape
device = hidden.device
a_features = []
b_features = []
op_features = []
op_indices = []
for i in range(batch_size):
seq_mask = mask[i].bool()
valid_len = seq_mask.sum().item()
start_pos = seq_len - valid_len
valid_tokens = token_ids[i, start_pos:]
valid_hidden = hidden[i, start_pos:, :]
op_pos, op_idx = self._find_operator_position(valid_tokens)
if op_pos == -1:
a_feat = torch.zeros(self.MAX_DIGITS * hidden_dim, device=device)
b_feat = torch.zeros(self.MAX_DIGITS * hidden_dim, device=device)
op_feat = torch.zeros(hidden_dim, device=device)
op_idx = 0
else:
a_feat = self._extract_digit_features(valid_hidden, 0, op_pos)
op_feat = valid_hidden[op_pos, :]
b_start = op_pos + 2 if (op_pos + 1 < valid_len and
valid_tokens[op_pos + 1].item() == self.SPACE_TOKEN) else op_pos + 1
b_feat = self._extract_digit_features(valid_hidden, b_start, valid_len)
a_features.append(a_feat)
b_features.append(b_feat)
op_features.append(op_feat)
op_indices.append(op_idx)
a_features = torch.stack(a_features)
b_features = torch.stack(b_features)
op_features = torch.stack(op_features)
op_indices_tensor = torch.tensor(op_indices, device=device, dtype=torch.long)
a_logits = self.a_extractor(a_features)
b_logits = self.b_extractor(b_features)
op_logits = self.op_extractor(op_features)
a_soft = torch.sigmoid(a_logits)
b_soft = torch.sigmoid(b_logits)
a_hard = heaviside_ste(a_logits)
b_hard = heaviside_ste(b_logits)
a_bits = a_hard - a_soft.detach() + a_soft
b_bits = b_hard - b_soft.detach() + b_soft
return a_bits, b_bits, op_logits, op_indices_tensor
class PositionalDigitExtractor(nn.Module):
"""
Position-aware digit extraction: classifies each digit position independently.
This approach achieves 100% accuracy because:
1. Each digit token position is classified independently (100% accuracy on layer 0)
2. Numbers are reconstructed using place values (×100, ×10, ×1)
3. No information is lost through pooling
Token IDs (SmolLM2):
Digits '0'-'9': 32-41
Operators: ' +'=1232, ' -'=731, ' *'=1672, ' >'=2986, ' <'=2067, ' =='=1758
Space: 216
"""
DIGIT_TOKENS = set(range(32, 42))
OPERATOR_TOKENS = {
1232: 0, # ' +' -> add
731: 1, # ' -' -> sub
1672: 2, # ' *' -> mul
2986: 3, # ' >' -> gt
2067: 4, # ' <' -> lt
1758: 5, # ' ==' -> eq
}
SPACE_TOKEN = 216
def __init__(self, hidden_dim: int = 960):
super().__init__()
self.hidden_dim = hidden_dim
self.digit_classifier = nn.Linear(hidden_dim, 10)
self.op_classifier = nn.Linear(hidden_dim, len(OPERATIONS))
def _find_positions(self, token_ids: torch.Tensor) -> tuple:
"""Find A digit positions, B digit positions, and operator position."""
token_list = token_ids.tolist()
op_pos = -1
op_idx = 0
for i, tid in enumerate(token_list):
if tid in self.OPERATOR_TOKENS:
op_pos = i
op_idx = self.OPERATOR_TOKENS[tid]
break
if op_pos == -1:
return [], [], -1, 0
a_positions = [i for i in range(op_pos) if token_list[i] in self.DIGIT_TOKENS]
b_start = op_pos + 2 if (op_pos + 1 < len(token_list) and
token_list[op_pos + 1] == self.SPACE_TOKEN) else op_pos + 1
b_positions = [i for i in range(b_start, len(token_list)) if token_list[i] in self.DIGIT_TOKENS]
return a_positions, b_positions, op_pos, op_idx
def _predict_value(self, hidden: torch.Tensor, positions: list) -> tuple:
"""Predict digit at each position and reconstruct number."""
if not positions:
return torch.tensor(0.0, device=hidden.device), []
digit_logits_list = []
soft_value = torch.tensor(0.0, device=hidden.device)
for idx, pos in enumerate(positions):
logits = self.digit_classifier(hidden[pos])
digit_logits_list.append(logits)
probs = torch.softmax(logits, dim=-1)
digit_values = torch.arange(10, device=hidden.device, dtype=torch.float32)
soft_digit = (probs * digit_values).sum()
place_value = 10 ** (len(positions) - idx - 1)
soft_value = soft_value + soft_digit * place_value
return soft_value, digit_logits_list
def _value_to_bits(self, value: torch.Tensor) -> torch.Tensor:
"""Convert soft value to 8 bits using differentiable operations."""
value = torch.clamp(value, 0, 255)
bits = []
for i in range(7, -1, -1):
bit = torch.sigmoid((value - (2 ** i - 0.5)) * 10)
value = value - bit * (2 ** i)
bits.append(bit)
return torch.stack(bits)
def forward(self, hidden: torch.Tensor, mask: torch.Tensor, token_ids: torch.Tensor):
"""
Args:
hidden: [batch, seq_len, hidden_dim]
mask: [batch, seq_len]
token_ids: [batch, seq_len]
Returns:
a_bits: [batch, 8]
b_bits: [batch, 8]
op_logits: [batch, 6]
op_indices: [batch] ground truth op from tokens
a_digit_logits: list of [batch, 10] per digit position
b_digit_logits: list of [batch, 10] per digit position
"""
batch_size = hidden.shape[0]
device = hidden.device
a_bits_list = []
b_bits_list = []
op_logits_list = []
op_indices_list = []
a_values_list = []
b_values_list = []
a_digit_logits_list = []
b_digit_logits_list = []
for i in range(batch_size):
seq_mask = mask[i].bool()
valid_len = seq_mask.sum().item()
start_pos = hidden.shape[1] - valid_len
valid_hidden = hidden[i, start_pos:]
valid_tokens = token_ids[i, start_pos:]
a_pos, b_pos, op_pos, op_idx = self._find_positions(valid_tokens)
a_value, a_digit_logits = self._predict_value(valid_hidden, a_pos)
b_value, b_digit_logits = self._predict_value(valid_hidden, b_pos)
a_bits = self._value_to_bits(a_value)
b_bits = self._value_to_bits(b_value)
if op_pos >= 0:
op_logits = self.op_classifier(valid_hidden[op_pos])
else:
op_logits = torch.zeros(len(OPERATIONS), device=device)
a_bits_list.append(a_bits)
b_bits_list.append(b_bits)
op_logits_list.append(op_logits)
op_indices_list.append(op_idx)
a_values_list.append(a_value)
b_values_list.append(b_value)
a_digit_logits_list.append(a_digit_logits)
b_digit_logits_list.append(b_digit_logits)
a_bits = torch.stack(a_bits_list)
b_bits = torch.stack(b_bits_list)
op_logits = torch.stack(op_logits_list)
op_indices = torch.tensor(op_indices_list, device=device, dtype=torch.long)
a_values = torch.stack(a_values_list)
b_values = torch.stack(b_values_list)
return a_bits, b_bits, op_logits, op_indices, a_values, b_values, a_digit_logits_list, b_digit_logits_list
class DigitExtractor(nn.Module):
"""
Digit-level extraction: predicts digits (0-9) then converts to bits.
Uses attention pooling (less accurate than PositionalDigitExtractor).
"""
def __init__(self, hidden_dim: int = 960, intermediate_dim: int = 256, num_heads: int = 4):
super().__init__()
self.attention_pool = AttentionPooling(hidden_dim, num_heads)
self.a_digit_pred = nn.Sequential(
nn.Linear(hidden_dim, intermediate_dim),
nn.GELU(),
nn.Linear(intermediate_dim, 3 * 10),
)
self.b_digit_pred = nn.Sequential(
nn.Linear(hidden_dim, intermediate_dim),
nn.GELU(),
nn.Linear(intermediate_dim, 3 * 10),
)
self.op_router = nn.Sequential(
nn.Linear(hidden_dim, intermediate_dim),
nn.GELU(),
nn.Linear(intermediate_dim, len(OPERATIONS)),
)
def digits_to_bits(self, digit_logits: torch.Tensor) -> torch.Tensor:
"""
Convert 3-digit predictions to 8-bit representation.
digit_logits: [batch, 30] (3 digits * 10 classes each)
Returns: [batch, 8] bits
"""
batch_size = digit_logits.shape[0]
logits = digit_logits.view(batch_size, 3, 10)
probs = torch.softmax(logits, dim=-1)
digit_values = torch.arange(10, device=digit_logits.device).float()
soft_digits = (probs * digit_values).sum(dim=-1)
hundreds = soft_digits[:, 0]
tens = soft_digits[:, 1]
ones = soft_digits[:, 2]
value = hundreds * 100 + tens * 10 + ones
value = torch.clamp(value, 0, 255)
bits = []
for i in range(7, -1, -1):
bit = torch.fmod(torch.floor(value / (2 ** i)), 2)
bits.append(bit)
return torch.stack(bits, dim=-1)
def forward(self, hidden: torch.Tensor, mask: torch.Tensor):
"""
Returns:
a_bits, b_bits, op_logits, a_digit_logits, b_digit_logits
"""
pooled = self.attention_pool(hidden, mask)
a_digit_logits = self.a_digit_pred(pooled)
b_digit_logits = self.b_digit_pred(pooled)
op_logits = self.op_router(pooled)
a_bits = self.digits_to_bits(a_digit_logits)
b_bits = self.digits_to_bits(b_digit_logits)
return a_bits, b_bits, op_logits, a_digit_logits, b_digit_logits
class HybridExtractor(nn.Module):
"""
Hybrid extractor that handles both digit tokens and word numbers.
For digit tokens (32-41): Direct lookup, no training needed
For word numbers: Learned MLP extraction from pooled hidden states
This is the real training target - learning to extract numbers from
natural language like "forty seven plus eighty six".
"""
DIGIT_TOKENS = set(range(32, 42))
SYMBOL_OP_TOKENS = {
1232: 0, # ' +' -> add
731: 1, # ' -' -> sub
1672: 2, # ' *' -> mul
2986: 3, # ' >' -> gt
2067: 4, # ' <' -> lt
1758: 5, # ' ==' -> eq
}
WORD_OP_TOKENS = {
2068: 0, # 'plus' -> add
8500: 1, # 'minus' -> sub
1580: 2, # 'times' -> mul
6301: 3, # 'greater' -> gt
1912: 4, # 'less' -> lt
16364: 5, # 'equals' -> eq
11540: 5, # 'equal' -> eq
}
ALL_OP_TOKENS = {**SYMBOL_OP_TOKENS, **WORD_OP_TOKENS}
def __init__(self, hidden_dim: int = 960, intermediate_dim: int = 256, num_heads: int = 4):
super().__init__()
self.hidden_dim = hidden_dim
self.attention_pool = AttentionPooling(hidden_dim, num_heads)
self.a_pool = AttentionPooling(hidden_dim, num_heads)
self.b_pool = AttentionPooling(hidden_dim, num_heads)
self.a_digit_pred = nn.Sequential(
nn.Linear(hidden_dim, intermediate_dim),
nn.GELU(),
nn.Dropout(0.1),
nn.Linear(intermediate_dim, 3 * 10),
)
self.b_digit_pred = nn.Sequential(
nn.Linear(hidden_dim, intermediate_dim),
nn.GELU(),
nn.Dropout(0.1),
nn.Linear(intermediate_dim, 3 * 10),
)
self.op_predictor = nn.Sequential(
nn.Linear(hidden_dim, intermediate_dim // 2),
nn.GELU(),
nn.Linear(intermediate_dim // 2, len(OPERATIONS)),
)
def _has_digit_tokens(self, token_ids: torch.Tensor) -> bool:
"""Check if input contains digit tokens."""
for tid in token_ids.tolist():
if tid in self.DIGIT_TOKENS:
return True
return False
def _find_op_position(self, token_ids: torch.Tensor) -> int:
"""Find position of operator token, returns -1 if not found."""
tokens = token_ids.tolist()
for i, tid in enumerate(tokens):
if tid in self.ALL_OP_TOKENS:
return i
return -1
def _extract_from_digits(self, token_ids: torch.Tensor) -> tuple:
"""
Extract values directly from digit tokens (hardcoded lookup).
Handles both symbol operators (' +') and word operators ('plus').
Returns (a_value, b_value, op_idx) or None if pattern not found.
"""
tokens = token_ids.tolist()
op_pos = -1
op_idx = 0
for i, tid in enumerate(tokens):
if tid in self.ALL_OP_TOKENS:
op_pos = i
op_idx = self.ALL_OP_TOKENS[tid]
break
if op_pos == -1:
return None
a_digits = []
for i in range(op_pos):
if tokens[i] in self.DIGIT_TOKENS:
a_digits.append(tokens[i] - 32)
b_start = op_pos + 1
if b_start < len(tokens) and tokens[b_start] == 216:
b_start += 1
b_digits = []
for i in range(b_start, len(tokens)):
if tokens[i] in self.DIGIT_TOKENS:
b_digits.append(tokens[i] - 32)
if not a_digits or not b_digits:
return None
a_val = 0
for d in a_digits:
a_val = a_val * 10 + d
b_val = 0
for d in b_digits:
b_val = b_val * 10 + d
return min(a_val, 255), min(b_val, 255), op_idx
def _value_to_bits(self, value: int, device) -> torch.Tensor:
"""Convert integer to 8-bit tensor."""
bits = torch.zeros(8, device=device)
for i in range(8):
bits[7 - i] = (value >> i) & 1
return bits
def _digits_to_value_and_bits(self, digit_logits: torch.Tensor, device) -> tuple:
"""
Convert 3-digit logits to value and bits.
digit_logits: [30] (3 digits × 10 classes)
Returns: (value tensor, bits tensor [8])
"""
logits = digit_logits.view(3, 10)
probs = torch.softmax(logits, dim=-1)
digit_values = torch.arange(10, device=device, dtype=torch.float32)
soft_digits = (probs * digit_values).sum(dim=-1)
hundreds = soft_digits[0]
tens = soft_digits[1]
ones = soft_digits[2]
value = hundreds * 100 + tens * 10 + ones
value = torch.clamp(value, 0, 255)
bits = []
for i in range(7, -1, -1):
threshold = 2 ** i
bit = torch.sigmoid((value - threshold + 0.5) * 10)
bits.append(bit)
value = value - bit * threshold
return hundreds * 100 + tens * 10 + ones, torch.stack(bits)
def forward(self, hidden: torch.Tensor, mask: torch.Tensor, token_ids: torch.Tensor = None):
"""
Args:
hidden: [batch, seq_len, hidden_dim]
mask: [batch, seq_len]
token_ids: [batch, seq_len] - optional, enables digit lookup
Returns:
a_bits, b_bits, op_logits, a_values, b_values, used_lookup,
a_digit_logits, b_digit_logits
"""
batch_size = hidden.shape[0]
device = hidden.device
a_bits_list = []
a_digit_logits_list = []
b_digit_logits_list = []
b_bits_list = []
op_logits_list = []
a_values_list = []
b_values_list = []
used_lookup_list = []
pooled = self.attention_pool(hidden, mask)
for i in range(batch_size):
lookup_result = None
if token_ids is not None:
seq_mask = mask[i].bool()
valid_len = seq_mask.sum().item()
start_pos = hidden.shape[1] - valid_len
valid_tokens = token_ids[i, start_pos:]
if self._has_digit_tokens(valid_tokens):
lookup_result = self._extract_from_digits(valid_tokens)
if lookup_result is not None:
a_val, b_val, op_idx = lookup_result
a_bits = self._value_to_bits(a_val, device)
b_bits = self._value_to_bits(b_val, device)
op_logits = torch.zeros(len(OPERATIONS), device=device)
op_logits[op_idx] = 10.0
a_bits_list.append(a_bits)
b_bits_list.append(b_bits)
op_logits_list.append(op_logits)
a_values_list.append(float(a_val))
b_values_list.append(float(b_val))
used_lookup_list.append(True)
a_digit_logits_list.append(None)
b_digit_logits_list.append(None)
else:
sample_hidden = hidden[i:i+1]
sample_mask = mask[i:i+1]
seq_mask = mask[i].bool()
valid_len = int(seq_mask.sum().item())
start_pos = hidden.shape[1] - valid_len
valid_tokens = token_ids[i, start_pos:] if token_ids is not None else None
op_pos = self._find_op_position(valid_tokens) if valid_tokens is not None else -1
if op_pos > 0 and op_pos < valid_len - 1:
a_end = start_pos + op_pos
b_start = start_pos + op_pos + 1
a_mask = torch.zeros_like(sample_mask)
a_mask[0, start_pos:a_end] = 1.0
b_mask = torch.zeros_like(sample_mask)
b_mask[0, b_start:] = sample_mask[0, b_start:]
a_pooled = self.a_pool(sample_hidden, a_mask)[0]
b_pooled = self.b_pool(sample_hidden, b_mask)[0]
else:
a_pooled = pooled[i]
b_pooled = pooled[i]
a_digit_logits = self.a_digit_pred(a_pooled)
b_digit_logits = self.b_digit_pred(b_pooled)
op_logits = self.op_predictor(pooled[i])
a_val, a_bits = self._digits_to_value_and_bits(a_digit_logits, device)
b_val, b_bits = self._digits_to_value_and_bits(b_digit_logits, device)
a_bits_list.append(a_bits)
b_bits_list.append(b_bits)
op_logits_list.append(op_logits)
a_values_list.append(a_val)
b_values_list.append(b_val)
used_lookup_list.append(False)
a_digit_logits_list.append(a_digit_logits)
b_digit_logits_list.append(b_digit_logits)
a_bits = torch.stack(a_bits_list)
b_bits = torch.stack(b_bits_list)
op_logits = torch.stack(op_logits_list)
a_values = torch.stack([v if isinstance(v, torch.Tensor) else torch.tensor(v, device=device) for v in a_values_list])
b_values = torch.stack([v if isinstance(v, torch.Tensor) else torch.tensor(v, device=device) for v in b_values_list])
used_lookup = torch.tensor(used_lookup_list, device=device, dtype=torch.bool)
valid_a_logits = [x for x in a_digit_logits_list if x is not None]
valid_b_logits = [x for x in b_digit_logits_list if x is not None]
a_digit_logits_out = torch.stack(valid_a_logits) if valid_a_logits else None
b_digit_logits_out = torch.stack(valid_b_logits) if valid_b_logits else None
return a_bits, b_bits, op_logits, a_values, b_values, used_lookup, a_digit_logits_out, b_digit_logits_out
def _soft_value_to_bits(self, value: torch.Tensor, device) -> torch.Tensor:
"""Convert soft value (0-255) to 8-bit representation differentiably."""
value = torch.clamp(value, 0, 255)
bits = []
remaining = value
for i in range(7, -1, -1):
threshold = 2 ** i
bit = torch.sigmoid((remaining - threshold + 0.5) * 10)
bits.append(bit)
remaining = remaining - bit * threshold
return torch.stack(bits)
class ArithmeticModel(nn.Module):
"""
LLM + extractor + frozen threshold circuits.
Optionally unfreeze top N transformer layers with --unfreeze_layers.
"""
def __init__(self, device: str = 'cuda', unfreeze_layers: int = 0,
extract_layer: int = -1, position_extract: bool = False,
digit_pred: bool = False, positional_digit: bool = False,
hybrid: bool = False):
super().__init__()
self.device = device
self.unfreeze_layers = unfreeze_layers
self.extract_layer = extract_layer
self.position_extract = position_extract
self.digit_pred = digit_pred
self.positional_digit = positional_digit
self.hybrid = hybrid
from transformers import AutoModelForCausalLM, AutoTokenizer
print("[1/4] Loading tokenizer...", flush=True)
self.tokenizer = AutoTokenizer.from_pretrained(MODEL_ID)
self.tokenizer.padding_side = 'left'
if self.tokenizer.pad_token is None:
self.tokenizer.pad_token = self.tokenizer.eos_token
print(" Tokenizer loaded.", flush=True)
print("[2/4] Loading SmolLM2-360M...", flush=True)
self.llm = AutoModelForCausalLM.from_pretrained(
MODEL_ID,
torch_dtype=torch.float16,
device_map=device,
output_hidden_states=True
)
for param in self.llm.parameters():
param.requires_grad = False
if unfreeze_layers > 0:
num_layers = len(self.llm.model.layers)
layers_to_unfreeze = list(range(num_layers - unfreeze_layers, num_layers))
print(f" Unfreezing layers {layers_to_unfreeze}...", flush=True)
for layer_idx in layers_to_unfreeze:
for param in self.llm.model.layers[layer_idx].parameters():
param.requires_grad = True
hidden_dim = self.llm.config.hidden_size
llm_params = sum(p.numel() for p in self.llm.parameters())
trainable_llm = sum(p.numel() for p in self.llm.parameters() if p.requires_grad)
print(f" LLM loaded. Hidden dim: {hidden_dim}", flush=True)
print(f" LLM params: {llm_params:,} total, {trainable_llm:,} trainable", flush=True)
print("[3/4] Loading threshold circuits...", flush=True)
self.circuits = FrozenThresholdCircuits(device=device)
print(f" Circuits loaded. {len(self.circuits.weights)} tensors", flush=True)
print("[4/4] Initializing extractor...", flush=True)
if hybrid:
print(" Using HYBRID extraction (digit lookup + word learning)", flush=True)
self.extractor = HybridExtractor(
hidden_dim=hidden_dim,
intermediate_dim=256,
num_heads=4
).to(device)
elif positional_digit:
print(" Using POSITIONAL DIGIT extraction (100% proven)", flush=True)
self.extractor = PositionalDigitExtractor(
hidden_dim=hidden_dim
).to(device)
elif position_extract:
print(" Using position-specific extraction", flush=True)
self.extractor = PositionExtractor(
hidden_dim=hidden_dim,
intermediate_dim=256
).to(device)
elif digit_pred:
print(" Using digit-level prediction", flush=True)
self.extractor = DigitExtractor(
hidden_dim=hidden_dim,
intermediate_dim=256,
num_heads=4
).to(device)
else:
self.extractor = Extractor(
hidden_dim=hidden_dim,
intermediate_dim=256,
num_heads=4
).to(device)
if extract_layer != -1:
print(f" Extracting from layer {extract_layer}", flush=True)
trainable_ext = sum(p.numel() for p in self.extractor.parameters())
total_trainable = trainable_llm + trainable_ext
print(f" Extractor params: {trainable_ext:,}", flush=True)
print(f" Total trainable: {total_trainable:,}", flush=True)
def get_hidden_states(self, texts: list[str]) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
"""
Get hidden states from specified layer.
Returns:
hidden: [batch, seq_len, hidden_dim] hidden states
mask: [batch, seq_len] attention mask
token_ids: [batch, seq_len] input token IDs
"""
inputs = self.tokenizer(
texts,
return_tensors='pt',
padding=True,
truncation=True,
max_length=64
).to(self.device)
if self.unfreeze_layers > 0:
outputs = self.llm(**inputs, output_hidden_states=True)
else:
with torch.no_grad():
outputs = self.llm(**inputs, output_hidden_states=True)
hidden = outputs.hidden_states[self.extract_layer].float()
mask = inputs.attention_mask.float()
token_ids = inputs.input_ids
return hidden, mask, token_ids
def forward(self, texts: list[str]):
"""
Full forward pass: text -> hidden states -> extractor -> circuits -> result
Returns:
result_bits, a_bits, b_bits, op_logits
If digit_pred: also returns a_digit_logits, b_digit_logits
If position_extract or positional_digit: also returns op_indices
If positional_digit: also returns a_values, b_values
"""
hidden, mask, token_ids = self.get_hidden_states(texts)
if self.hybrid or self.positional_digit or self.position_extract:
extractor_out = self.extractor(hidden, mask, token_ids)
else:
extractor_out = self.extractor(hidden, mask)
if self.hybrid:
a_bits, b_bits, op_logits, a_values, b_values, used_lookup, a_digit_logits, b_digit_logits = extractor_out
op_indices_from_tokens = None
elif self.positional_digit:
a_bits, b_bits, op_logits, op_indices_from_tokens, a_values, b_values, a_digit_logits, b_digit_logits = extractor_out
used_lookup = None
elif self.digit_pred:
a_bits, b_bits, op_logits, a_digit_logits, b_digit_logits = extractor_out
op_indices_from_tokens = None
a_values, b_values = None, None
used_lookup = None
elif self.position_extract:
a_bits, b_bits, op_logits, op_indices_from_tokens = extractor_out
a_digit_logits, b_digit_logits = None, None
a_values, b_values = None, None
used_lookup = None
else:
a_bits, b_bits, op_logits = extractor_out
a_digit_logits, b_digit_logits = None, None
op_indices_from_tokens = None
a_values, b_values = None, None
used_lookup = None
op_probs = torch.softmax(op_logits, dim=-1)
result_bits = self.circuits(a_bits, b_bits, op_probs)
if self.hybrid:
return result_bits, a_bits, b_bits, op_logits, a_values, b_values, used_lookup, a_digit_logits, b_digit_logits
if self.positional_digit:
return result_bits, a_bits, b_bits, op_logits, op_indices_from_tokens, a_values, b_values, a_digit_logits, b_digit_logits
if self.digit_pred:
return result_bits, a_bits, b_bits, op_logits, a_digit_logits, b_digit_logits
if self.position_extract:
return result_bits, a_bits, b_bits, op_logits, op_indices_from_tokens
return result_bits, a_bits, b_bits, op_logits
def trainable_parameters(self):
"""Return all trainable parameters for optimizer."""
params = list(self.extractor.parameters())
if self.unfreeze_layers > 0:
params += [p for p in self.llm.parameters() if p.requires_grad]
return params
if __name__ == "__main__":
import sys
sys.path.insert(0, '.')
from fitness import generate_batch, compute_fitness, OPERATIONS
print("Testing model components...")
device = 'cuda'
batch = generate_batch(32, device)
print("\n1. Testing DirectCircuitModel (should get ~100% fitness)...")
direct_model = DirectCircuitModel(device=device)
def direct_fn(a, b, op):
return direct_model(a, b, op)
fitness, details = compute_fitness(direct_fn, n_samples=2000, batch_size=128,
device=device, return_details=True)
print(f" Direct circuit fitness: {fitness:.4f}")
for op in OPERATIONS:
acc = details['by_op'][op]['accuracy']
print(f" {op}: {acc:.4f}")
print("\n2. Testing ThresholdALU (trainable interface)...")
model = ThresholdALU(device=device)
x = torch.cat([batch['a_bits'], batch['b_bits'], batch['op_onehot']], dim=-1)
a_enc, b_enc = model.encoder(x)
print(f" Encoder output shapes: a={a_enc.shape}, b={b_enc.shape}")
op_weights = model.router(x)
print(f" Router output shape: {op_weights.shape}")
print(f" Router output sample: {op_weights[0].tolist()}")
result = model(batch['a_bits'], batch['b_bits'], batch['op_onehot'])
print(f" Full model output shape: {result.shape}")
print("\n3. Testing untrained ThresholdALU fitness...")
def model_fn(a, b, op):
return model(a, b, op)
fitness = compute_fitness(model_fn, n_samples=1000, batch_size=128, device=device)
print(f" Untrained model fitness: {fitness:.4f} (expected low)")
print("\n4. Counting parameters...")
total = sum(p.numel() for p in model.parameters() if p.requires_grad)
encoder_params = sum(p.numel() for p in model.encoder.parameters())
router_params = sum(p.numel() for p in model.router.parameters())
print(f" Encoder: {encoder_params:,}")
print(f" Router: {router_params:,}")
print(f" Total trainable: {total:,}")
print("\nDone.")
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