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API Reference

triadic_head

triadic_head

triadic-head — Drop-in triadic projection head for any HuggingFace transformer.

Adds interpretable prime-factor semantic signatures to language models at zero language cost. A single linear layer (n_embd -> n_bits) produces discrete prime composites that enable exact algebraic operations: subsumption, composition, analogy, and gap analysis.

Quick start

from triadic_head import TriadicWrapper

model = TriadicWrapper("gpt2", n_bits=64) sigs = model.encode(["king", "queen", "dog"]) result = model.compare("king", "queen")

Algebra Module

Pure Python module with zero external dependencies. Provides exact algebraic operations on prime-factor signatures.

triadic_head.algebra

Prime-factor algebra for neurosymbolic semantic operations.

Provides exact algebraic operations (subsumption, composition, gap analysis) on prime-factor signatures — things impossible with cosine similarity.

Zero external dependencies.

PrimeMapper

Maps continuous projections (tanh outputs in [-1, 1]) to composite prime integers.

Each bit position is assigned a unique prime. If projection[i] > 0, prime[i] is included in the composite product.

Example

projections = [0.5, -0.2, 0.8, 0.1] (4 bits) primes = [2, 3, 5, 7 ] composite = 2 * 5 * 7 = 70 (bits 0, 2, 3 are positive)

Source code in triadic-head-src/triadic-head/triadic_head/algebra.py 
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class PrimeMapper:
    """
    Maps continuous projections (tanh outputs in [-1, 1]) to composite prime integers.

    Each bit position is assigned a unique prime. If projection[i] > 0,
    prime[i] is included in the composite product.

    Example:
        projections = [0.5, -0.2, 0.8, 0.1]  (4 bits)
        primes      = [2,    3,    5,   7  ]
        composite   = 2 * 5 * 7 = 70  (bits 0, 2, 3 are positive)
    """

    def __init__(self, n_bits: int):
        self.n_bits = n_bits
        self.primes = [nth_prime(i + 1) for i in range(n_bits)]

    def encode(self, projections) -> int:
        """
        Convert projection values to a composite prime integer.

        Args:
            projections: sequence of floats (tanh outputs in [-1, 1])
                         or a 1D tensor.

        Returns:
            int — composite prime product.
        """
        composite = 1
        for proj, prime in zip(projections, self.primes):
            val = float(proj)
            if val > 0:
                composite *= prime
        # Return 1 (identity element) when all projections negative,
        # rather than prime 2 which has specific semantic meaning.
        return composite

    # Alias for compatibility with src/triadic.py which uses map()
    map = encode

    def get_bits(self, projections) -> List[int]:
        """Return binary bit pattern from projections."""
        return [1 if float(p) > 0 else 0 for p in projections]

    def explain(self, composite: int) -> Dict:
        """Decompose a composite into its constituent prime factors."""
        factors = []
        bit_indices = []
        for i, prime in enumerate(self.primes):
            if composite % prime == 0:
                factors.append(prime)
                bit_indices.append(i)
        return {
            'composite': composite,
            'factors': factors,
            'active_bits': bit_indices,
            'n_active': len(factors),
            'n_total': self.n_bits,
        }

    def similarity(self, a: int, b: int) -> float:
        """Jaccard similarity over prime factor sets."""
        return TriadicValidator.similarity(a, b)

encode(projections) -> int

Convert projection values to a composite prime integer.

Parameters:

Name Type Description Default
projections

sequence of floats (tanh outputs in [-1, 1]) or a 1D tensor.

 required

Returns:

Type Description
int

int — composite prime product.
Source code in triadic-head-src/triadic-head/triadic_head/algebra.py 
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def encode(self, projections) -> int:
    """
    Convert projection values to a composite prime integer.

    Args:
        projections: sequence of floats (tanh outputs in [-1, 1])
                     or a 1D tensor.

    Returns:
        int — composite prime product.
    """
    composite = 1
    for proj, prime in zip(projections, self.primes):
        val = float(proj)
        if val > 0:
            composite *= prime
    # Return 1 (identity element) when all projections negative,
    # rather than prime 2 which has specific semantic meaning.
    return composite

get_bits(projections) -> List[int]

Return binary bit pattern from projections.

Source code in triadic-head-src/triadic-head/triadic_head/algebra.py 
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def get_bits(self, projections) -> List[int]:
    """Return binary bit pattern from projections."""
    return [1 if float(p) > 0 else 0 for p in projections]

explain(composite: int) -> Dict

Decompose a composite into its constituent prime factors.

Source code in triadic-head-src/triadic-head/triadic_head/algebra.py 
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def explain(self, composite: int) -> Dict:
    """Decompose a composite into its constituent prime factors."""
    factors = []
    bit_indices = []
    for i, prime in enumerate(self.primes):
        if composite % prime == 0:
            factors.append(prime)
            bit_indices.append(i)
    return {
        'composite': composite,
        'factors': factors,
        'active_bits': bit_indices,
        'n_active': len(factors),
        'n_total': self.n_bits,
    }

similarity(a: int, b: int) -> float

Jaccard similarity over prime factor sets.

Source code in triadic-head-src/triadic-head/triadic_head/algebra.py 
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def similarity(self, a: int, b: int) -> float:
    """Jaccard similarity over prime factor sets."""
    return TriadicValidator.similarity(a, b)

TriadicValidator

Verifies semantic relationships using prime-factor algebra.

Three operations IMPOSSIBLE with cosine similarity
  1. Subsumption — Does concept A contain all features of B?
  2. Composition — Create a concept with features of A and B.
  3. Gap Analysis — Exactly WHICH features differ between A and B?
Source code in triadic-head-src/triadic-head/triadic_head/algebra.py 
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class TriadicValidator:
    """
    Verifies semantic relationships using prime-factor algebra.

    Three operations IMPOSSIBLE with cosine similarity:
      1. Subsumption — Does concept A contain all features of B?
      2. Composition — Create a concept with features of A and B.
      3. Gap Analysis — Exactly WHICH features differ between A and B?
    """

    @staticmethod
    def subsumes(a: int, b: int) -> bool:
        """Does concept A contain ALL semantic features of B?  (A % B == 0)"""
        if b == 0:
            return False
        return a % b == 0

    @staticmethod
    def compose(*concepts: int) -> int:
        """Combine features from multiple concepts (LCM)."""
        result = concepts[0]
        for c in concepts[1:]:
            result = (result * c) // math.gcd(result, c)
        return result

    @staticmethod
    def explain_gap(a: int, b: int) -> Dict:
        """Explain exactly WHY two concepts differ."""
        shared = math.gcd(a, b)
        only_a = a // shared
        only_b = b // shared
        return {
            'shared': shared,
            'shared_factors': prime_factors(shared),
            'only_in_a': only_a,
            'only_in_a_factors': prime_factors(only_a),
            'only_in_b': only_b,
            'only_in_b_factors': prime_factors(only_b),
            'a_contains_b': (a % b == 0) if b > 0 else False,
            'b_contains_a': (b % a == 0) if a > 0 else False,
        }

    @staticmethod
    def similarity(a: int, b: int) -> float:
        """Jaccard similarity over prime factor sets. Range: [0.0, 1.0]."""
        fa = set(prime_factors(a))
        fb = set(prime_factors(b))
        if not fa and not fb:
            return 1.0
        total = fa | fb
        return len(fa & fb) / len(total) if total else 0.0

    @staticmethod
    def analogy(a: int, b: int, c: int) -> int:
        """
        Analogy: A is to B as C is to ?

        Computes the transformation from A->B (factors removed/added),
        then applies it to C to find D.

        D = (C / GCD(C, only_in_a)) * only_in_b
        where only_in_a = A/GCD(A,B) and only_in_b = B/GCD(A,B)

        Two steps: (1) remove A-specific factors from C, (2) add B-specific.
        """
        shared_ab = math.gcd(a, b)
        only_in_a = a // shared_ab  # factors to remove
        only_in_b = b // shared_ab  # factors to add

        # Remove A-specific factors from C (where they overlap)
        c_reduced = c // math.gcd(c, only_in_a)
        # Add B-specific factors (avoiding duplicates via GCD)
        return (c_reduced * only_in_b) // math.gcd(c_reduced, only_in_b)

subsumes(a: int, b: int) -> bool staticmethod

Does concept A contain ALL semantic features of B? (A % B == 0)

Source code in triadic-head-src/triadic-head/triadic_head/algebra.py 
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@staticmethod
def subsumes(a: int, b: int) -> bool:
    """Does concept A contain ALL semantic features of B?  (A % B == 0)"""
    if b == 0:
        return False
    return a % b == 0

compose(*concepts: int) -> int staticmethod

Combine features from multiple concepts (LCM).

Source code in triadic-head-src/triadic-head/triadic_head/algebra.py 
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@staticmethod
def compose(*concepts: int) -> int:
    """Combine features from multiple concepts (LCM)."""
    result = concepts[0]
    for c in concepts[1:]:
        result = (result * c) // math.gcd(result, c)
    return result

explain_gap(a: int, b: int) -> Dict staticmethod

Explain exactly WHY two concepts differ.

Source code in triadic-head-src/triadic-head/triadic_head/algebra.py 
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@staticmethod
def explain_gap(a: int, b: int) -> Dict:
    """Explain exactly WHY two concepts differ."""
    shared = math.gcd(a, b)
    only_a = a // shared
    only_b = b // shared
    return {
        'shared': shared,
        'shared_factors': prime_factors(shared),
        'only_in_a': only_a,
        'only_in_a_factors': prime_factors(only_a),
        'only_in_b': only_b,
        'only_in_b_factors': prime_factors(only_b),
        'a_contains_b': (a % b == 0) if b > 0 else False,
        'b_contains_a': (b % a == 0) if a > 0 else False,
    }

similarity(a: int, b: int) -> float staticmethod

Jaccard similarity over prime factor sets. Range: [0.0, 1.0].

Source code in triadic-head-src/triadic-head/triadic_head/algebra.py 
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@staticmethod
def similarity(a: int, b: int) -> float:
    """Jaccard similarity over prime factor sets. Range: [0.0, 1.0]."""
    fa = set(prime_factors(a))
    fb = set(prime_factors(b))
    if not fa and not fb:
        return 1.0
    total = fa | fb
    return len(fa & fb) / len(total) if total else 0.0

analogy(a: int, b: int, c: int) -> int staticmethod

Analogy: A is to B as C is to ?

Computes the transformation from A->B (factors removed/added), then applies it to C to find D.

D = (C / GCD(C, only_in_a)) * only_in_b where only_in_a = A/GCD(A,B) and only_in_b = B/GCD(A,B)

Two steps: (1) remove A-specific factors from C, (2) add B-specific.

Source code in triadic-head-src/triadic-head/triadic_head/algebra.py 
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@staticmethod
def analogy(a: int, b: int, c: int) -> int:
    """
    Analogy: A is to B as C is to ?

    Computes the transformation from A->B (factors removed/added),
    then applies it to C to find D.

    D = (C / GCD(C, only_in_a)) * only_in_b
    where only_in_a = A/GCD(A,B) and only_in_b = B/GCD(A,B)

    Two steps: (1) remove A-specific factors from C, (2) add B-specific.
    """
    shared_ab = math.gcd(a, b)
    only_in_a = a // shared_ab  # factors to remove
    only_in_b = b // shared_ab  # factors to add

    # Remove A-specific factors from C (where they overlap)
    c_reduced = c // math.gcd(c, only_in_a)
    # Add B-specific factors (avoiding duplicates via GCD)
    return (c_reduced * only_in_b) // math.gcd(c_reduced, only_in_b)

sieve_primes(limit: int) -> List[int]

Return all primes up to limit via Sieve of Eratosthenes.

Source code in triadic-head-src/triadic-head/triadic_head/algebra.py 
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def sieve_primes(limit: int) -> List[int]:
    """Return all primes up to `limit` via Sieve of Eratosthenes."""
    if limit < 2:
        return []
    is_prime = [True] * (limit + 1)
    is_prime[0] = is_prime[1] = False
    for i in range(2, int(limit ** 0.5) + 1):
        if is_prime[i]:
            for j in range(i * i, limit + 1, i):
                is_prime[j] = False
    return [i for i in range(2, limit + 1) if is_prime[i]]

nth_prime(n: int) -> int

Return the nth prime (1-indexed: nth_prime(1) = 2).

Source code in triadic-head-src/triadic-head/triadic_head/algebra.py 
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def nth_prime(n: int) -> int:
    """Return the nth prime (1-indexed: nth_prime(1) = 2)."""
    if n <= 0:
        raise ValueError("n must be >= 1")
    while len(_PRIMES_CACHE) < n:
        candidate = _PRIMES_CACHE[-1] + 2
        while True:
            if all(candidate % p != 0 for p in _PRIMES_CACHE if p * p <= candidate):
                _PRIMES_CACHE.append(candidate)
                break
            candidate += 2
    return _PRIMES_CACHE[n - 1]

prime_factors(n: int) -> List[int]

Return sorted list of unique prime factors of n.

Source code in triadic-head-src/triadic-head/triadic_head/algebra.py 
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def prime_factors(n: int) -> List[int]:
    """Return sorted list of unique prime factors of n."""
    if n <= 1:
        return []
    factors = []
    d = 2
    temp = n
    while d * d <= temp:
        if temp % d == 0:
            factors.append(d)
            while temp % d == 0:
                temp //= d
        d += 1
    if temp > 1:
        factors.append(temp)
    return factors

Wrapper Module

PyTorch wrapper for HuggingFace transformers. Adds a triadic projection head to any causal language model.

triadic_head.wrapper

TriadicWrapper — Drop-in triadic projection head for any HuggingFace transformer.

Usage

from triadic_head import TriadicWrapper

model = TriadicWrapper("gpt2", n_bits=64) model.freeze_backbone()

... train phase 1 (triadic head only) ...

model.unfreeze_last_n(2)

... train phase 2 (joint optimization) ...

sigs = model.encode(["king", "queen", "dog"]) model.compare("king", "queen") # -> 0.89

TriadicHead

Bases: Module

Single linear projection: hidden_states -> tanh -> n_bits continuous values.

This is the only new parameter added to the backbone model. For GPT-2 (768D, 64 bits): 768 * 64 = 49,152 parameters.

Source code in triadic-head-src/triadic-head/triadic_head/wrapper.py 
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class TriadicHead(nn.Module):
    """
    Single linear projection: hidden_states -> tanh -> n_bits continuous values.

    This is the only new parameter added to the backbone model.
    For GPT-2 (768D, 64 bits): 768 * 64 = 49,152 parameters.
    """

    def __init__(self, n_embd: int, n_bits: int):
        super().__init__()
        self.proj = nn.Linear(n_embd, n_bits, bias=False)
        nn.init.normal_(self.proj.weight, mean=0.0, std=0.02)

    def forward(self, hidden_states: torch.Tensor) -> torch.Tensor:
        """(B, T, n_embd) -> (B, T, n_bits) in [-1, 1]."""
        return torch.tanh(self.proj(hidden_states))

forward(hidden_states: torch.Tensor) -> torch.Tensor

(B, T, n_embd) -> (B, T, n_bits) in [-1, 1].

Source code in triadic-head-src/triadic-head/triadic_head/wrapper.py 
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def forward(self, hidden_states: torch.Tensor) -> torch.Tensor:
    """(B, T, n_embd) -> (B, T, n_bits) in [-1, 1]."""
    return torch.tanh(self.proj(hidden_states))

TriadicWrapper

Bases: Module

Wraps any HuggingFace causal LM with a triadic projection head.

The wrapper adds a single linear layer (n_embd -> n_bits) that produces discrete prime-factor signatures alongside normal language model outputs. Training uses a multi-component triadic loss that transfers semantic structure from the model's own embeddings to the triadic head.

Parameters:

Name Type Description Default
model Union[str, Module]

HuggingFace model instance or model name string (e.g. "gpt2").

 required
n_bits int

Number of triadic bits (default 64). Each bit maps to a prime.

 64
align_mode str

Alignment loss type — "mse", "rank", or "infonce". Use "infonce" for pre-trained models, "mse" for from-scratch.

 'infonce'
device Optional[str]

Device to place model on (auto-detected if None).

 None
Source code in triadic-head-src/triadic-head/triadic_head/wrapper.py 
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class TriadicWrapper(nn.Module):
    """
    Wraps any HuggingFace causal LM with a triadic projection head.

    The wrapper adds a single linear layer (n_embd -> n_bits) that produces
    discrete prime-factor signatures alongside normal language model outputs.
    Training uses a multi-component triadic loss that transfers semantic
    structure from the model's own embeddings to the triadic head.

    Args:
        model: HuggingFace model instance or model name string (e.g. "gpt2").
        n_bits: Number of triadic bits (default 64). Each bit maps to a prime.
        align_mode: Alignment loss type — "mse", "rank", or "infonce".
                    Use "infonce" for pre-trained models, "mse" for from-scratch.
        device: Device to place model on (auto-detected if None).
    """

    def __init__(
        self,
        model: Union[str, nn.Module],
        n_bits: int = 64,
        align_mode: str = 'infonce',
        device: Optional[str] = None,
    ):
        super().__init__()

        # Load model from string if needed
        if isinstance(model, str):
            from transformers import AutoModelForCausalLM
            model = AutoModelForCausalLM.from_pretrained(model)

        self._arch = _detect_architecture(model)
        self.backbone_model = model
        self.n_bits = n_bits
        self.n_embd = self._arch['n_embd']
        self.align_mode = align_mode
        self.block_size = self._arch.get('block_size', 1024)

        # The one new thing: triadic projection head
        self.triadic_head = TriadicHead(self.n_embd, n_bits)

        if device:
            self.to(device)

    # ----------------------------------------------------------
    # Configuration — view and change settings
    # ----------------------------------------------------------

    def config(self, **kwargs) -> Dict:
        """
        View or update model configuration.

        Call with no arguments to view current config.
        Pass keyword arguments to update:

            model.config(align_mode='rank', n_bits=32)

        Changeable settings:
            align_mode: 'mse' | 'rank' | 'infonce'

        Read-only (shown but not changeable):
            n_bits, n_embd, backbone, block_size, triadic_params, total_params
        """
        VALID_ALIGN = ('mse', 'rank', 'infonce')

        if 'align_mode' in kwargs:
            mode = kwargs['align_mode']
            if mode not in VALID_ALIGN:
                raise ValueError(f"align_mode must be one of {VALID_ALIGN}, got {mode!r}")
            self.align_mode = mode

        return {
            'align_mode': self.align_mode,
            'n_bits': self.n_bits,
            'n_embd': self.n_embd,
            'backbone': type(self.backbone_model).__name__,
            'block_size': self.block_size,
            'triadic_params': self.triadic_params(),
            'total_params': self.num_params(),
        }

    # ----------------------------------------------------------
    # Freeze / unfreeze
    # ----------------------------------------------------------

    def freeze_backbone(self):
        """Freeze entire backbone. Only triadic head receives gradients."""
        for param in self.backbone_model.parameters():
            param.requires_grad = False
        for param in self.triadic_head.parameters():
            param.requires_grad = True

    def unfreeze_last_n(self, n: int = 2):
        """Unfreeze the last N transformer layers + final layer norm."""
        if 'ln_f' in self._arch:
            for param in self._arch['ln_f'].parameters():
                param.requires_grad = True
        layers = self._arch['layers']
        total = len(layers)
        for i in range(max(0, total - n), total):
            for param in layers[i].parameters():
                param.requires_grad = True

    def unfreeze_all(self):
        """Unfreeze everything."""
        for param in self.parameters():
            param.requires_grad = True

    # ----------------------------------------------------------
    # Forward pass
    # ----------------------------------------------------------

    def forward(
        self,
        input_ids: torch.Tensor,
        attention_mask: Optional[torch.Tensor] = None,
        labels: Optional[torch.Tensor] = None,
    ):
        """
        Forward pass through backbone + triadic head.

        Returns:
            logits:       (B, T, vocab_size)
            triadic_proj: (B, T, n_bits) in [-1, 1]
            lang_loss:    scalar or None
        """
        backbone = self._arch['backbone']
        outputs = backbone(
            input_ids=input_ids,
            attention_mask=attention_mask,
        )
        # Handle different return types
        if hasattr(outputs, 'last_hidden_state'):
            hidden = outputs.last_hidden_state
        elif isinstance(outputs, tuple):
            hidden = outputs[0]
        else:
            hidden = outputs

        # LM head
        lm_head = self._arch.get('lm_head')
        if lm_head is not None:
            logits = lm_head(hidden)
        else:
            logits = self.backbone_model.lm_head(hidden)

        # Triadic head
        triadic_proj = self.triadic_head(hidden)

        # Language loss
        lang_loss = None
        if labels is not None:
            shift_logits = logits[..., :-1, :].contiguous()
            shift_labels = labels[..., 1:].contiguous()
            lang_loss = F.cross_entropy(
                shift_logits.view(-1, shift_logits.size(-1)),
                shift_labels.view(-1),
                ignore_index=-100,
            )

        return logits, triadic_proj, lang_loss

    # ----------------------------------------------------------
    # Triadic loss
    # ----------------------------------------------------------

    def triadic_loss(
        self,
        triadic_proj: torch.Tensor,
        input_ids: Optional[torch.Tensor] = None,
        alpha: float = 0.05,
        entropy_weight: float = 1.0,
        align_weight: float = 5.0,
        align_mode: Optional[str] = None,
    ) -> torch.Tensor:
        """
        Compute multi-component triadic loss.

        Components:
          1. Diversity — each bit should fire ~50% of the time.
          2. Contrastive — different sequences should produce different signatures.
          3. Entropy — prevent dead bits (bits stuck at +1 or -1).
          4. Embedding alignment — transfer semantic structure from embeddings.

        Args:
            triadic_proj: (B, T, n_bits) from forward().
            input_ids: (B, T) needed for alignment loss.
            alpha: Weight of total triadic loss (default 0.05, DO NOT exceed 0.10).
            entropy_weight: Weight for entropy term (default 1.0).
            align_weight: Weight for alignment term (default 5.0).
            align_mode: Override self.align_mode for this call.

        Returns:
            Weighted triadic loss scalar (already multiplied by alpha).
        """
        mode = align_mode or self.align_mode

        if triadic_proj.size(1) < 2:
            return torch.tensor(0.0, device=triadic_proj.device)

        # Force float32 for numerical stability (critical under AMP/mixed precision)
        triadic_proj = triadic_proj.float()

        B, T, n_bits = triadic_proj.shape

        # 1. Diversity: push per-bit mean toward 0
        bit_means = triadic_proj.mean(dim=(0, 1))
        diversity = (bit_means ** 2).mean()

        # 2. Contrastive: push sequence-level projections apart
        if B > 1:
            seq_proj = F.normalize(triadic_proj.mean(dim=1), dim=-1)
            sim = seq_proj @ seq_proj.T
            mask = ~torch.eye(B, device=sim.device, dtype=torch.bool)
            contrastive = sim[mask].pow(2).mean()
        else:
            contrastive = torch.tensor(0.0, device=triadic_proj.device)

        # 3. Entropy: maximize per-bit entropy across the batch
        entropy = torch.tensor(0.0, device=triadic_proj.device)
        if entropy_weight > 0:
            flat = triadic_proj.reshape(-1, n_bits)
            probs = ((flat.mean(dim=0) + 1.0) / 2.0).clamp(1e-7, 1 - 1e-7)
            H = -(probs * probs.log() + (1 - probs) * (1 - probs).log())
            entropy = (1.0 - H / math.log(2)).mean()

        # 4. Embedding alignment
        alignment = torch.tensor(0.0, device=triadic_proj.device)
        if align_weight > 0 and input_ids is not None:
            with torch.no_grad():
                embeds = self._arch['embed_layer'](input_ids).detach().float()

            if mode == 'mse':
                alignment = self._align_mse(triadic_proj, embeds)
            elif mode == 'rank':
                alignment = self._align_rank(triadic_proj, embeds)
            elif mode == 'infonce':
                alignment = self._align_infonce(triadic_proj, embeds)

        raw = diversity + contrastive
        if entropy_weight > 0:
            raw = raw + entropy_weight * entropy
        if align_weight > 0:
            raw = raw + align_weight * alignment

        return alpha * raw

    # ----------------------------------------------------------
    # Alignment loss implementations
    # ----------------------------------------------------------

    def _align_mse(self, proj, embeds, n_pairs=64):
        """MSE on absolute cosine similarity values. Best for from-scratch."""
        B, T, n_bits = proj.shape
        idx = torch.randint(0, T, (B, n_pairs, 2), device=proj.device)
        i, j = idx[:, :, 0], idx[:, :, 1]

        e_i = torch.gather(embeds, 1, i.unsqueeze(-1).expand(-1, -1, embeds.size(-1)))
        e_j = torch.gather(embeds, 1, j.unsqueeze(-1).expand(-1, -1, embeds.size(-1)))
        embed_sim = F.cosine_similarity(e_i, e_j, dim=-1)

        p_i = torch.gather(proj, 1, i.unsqueeze(-1).expand(-1, -1, n_bits))
        p_j = torch.gather(proj, 1, j.unsqueeze(-1).expand(-1, -1, n_bits))
        tri_sim = F.cosine_similarity(p_i, p_j, dim=-1)

        return F.mse_loss(tri_sim, embed_sim)

    def _align_rank(self, proj, embeds, n_anchors=32, n_cands=16, margin=0.1):
        """Margin ranking: preserve similarity ORDERING. Best for analogies."""
        B, T, n_bits = proj.shape
        d = embeds.size(-1)

        a_idx = torch.randint(0, T, (B, n_anchors), device=proj.device)
        c_idx = torch.randint(0, T, (B, n_anchors, n_cands), device=proj.device)

        a_e = torch.gather(embeds, 1, a_idx.unsqueeze(-1).expand(-1, -1, d))
        c_e = torch.gather(
            embeds, 1, c_idx.reshape(B, -1).unsqueeze(-1).expand(-1, -1, d)
        ).reshape(B, n_anchors, n_cands, d)

        e_sim = F.cosine_similarity(a_e.unsqueeze(2), c_e, dim=-1)
        pos_local = e_sim.argmax(dim=-1)
        neg_local = e_sim.argmin(dim=-1)

        pos_idx = torch.gather(c_idx, 2, pos_local.unsqueeze(-1)).squeeze(-1)
        neg_idx = torch.gather(c_idx, 2, neg_local.unsqueeze(-1)).squeeze(-1)

        a_p = torch.gather(proj, 1, a_idx.unsqueeze(-1).expand(-1, -1, n_bits))
        pos_p = torch.gather(proj, 1, pos_idx.unsqueeze(-1).expand(-1, -1, n_bits))
        neg_p = torch.gather(proj, 1, neg_idx.unsqueeze(-1).expand(-1, -1, n_bits))

        pos_sim = F.cosine_similarity(a_p, pos_p, dim=-1)
        neg_sim = F.cosine_similarity(a_p, neg_p, dim=-1)

        return F.relu(margin - (pos_sim - neg_sim)).mean()

    def _align_infonce(self, proj, embeds, n_anchors=32, temperature=0.1):
        """InfoNCE with embedding-mined positives. Best for pre-trained models."""
        B, T, n_bits = proj.shape
        d = embeds.size(-1)

        a_idx = torch.randint(0, T, (B, n_anchors), device=proj.device)
        p_idx = torch.randint(0, T, (B, n_anchors), device=proj.device)

        a_e = F.normalize(
            torch.gather(embeds, 1, a_idx.unsqueeze(-1).expand(-1, -1, d)), dim=-1)
        p_e = F.normalize(
            torch.gather(embeds, 1, p_idx.unsqueeze(-1).expand(-1, -1, d)), dim=-1)

        e_sim = torch.bmm(a_e, p_e.transpose(1, 2))
        pos_labels = e_sim.argmax(dim=-1)

        a_p = F.normalize(
            torch.gather(proj, 1, a_idx.unsqueeze(-1).expand(-1, -1, n_bits)), dim=-1)
        p_p = F.normalize(
            torch.gather(proj, 1, p_idx.unsqueeze(-1).expand(-1, -1, n_bits)), dim=-1)

        logits = torch.bmm(a_p, p_p.transpose(1, 2)) / temperature
        return F.cross_entropy(logits.reshape(-1, n_anchors), pos_labels.reshape(-1))

    # ----------------------------------------------------------
    # Encode: text -> prime signatures
    # ----------------------------------------------------------

    @torch.no_grad()
    def encode(
        self,
        texts: Union[str, List[str]],
        tokenizer=None,
    ) -> Dict[str, dict]:
        """
        Encode text(s) to prime-factor signatures.

        Args:
            texts: Single string or list of strings.
            tokenizer: HuggingFace tokenizer. If None, uses AutoTokenizer
                       matching the backbone model.

        Returns:
            Dict mapping each text to:
              - 'composite': int (prime product)
              - 'bits': List[int] (binary pattern)
              - 'projection': List[float] (raw tanh values)
              - 'n_active': int (number of active bits)
        """
        from .algebra import PrimeMapper

        if isinstance(texts, str):
            texts = [texts]

        if tokenizer is None:
            from transformers import AutoTokenizer
            config = getattr(self.backbone_model, 'config', None)
            model_name = getattr(config, '_name_or_path', 'gpt2')
            tokenizer = AutoTokenizer.from_pretrained(model_name)
            if tokenizer.pad_token is None:
                tokenizer.pad_token = tokenizer.eos_token

        device = next(self.parameters()).device
        mapper = PrimeMapper(self.n_bits)
        results = {}

        for text in texts:
            tokens = tokenizer(text, return_tensors='pt', truncation=True,
                               max_length=self.block_size).to(device)
            _, triadic_proj, _ = self(tokens['input_ids'],
                                     attention_mask=tokens.get('attention_mask'))
            # Average across all token positions
            avg_proj = triadic_proj.mean(dim=1).squeeze(0)  # (n_bits,)
            proj_list = avg_proj.cpu().tolist()

            composite = mapper.encode(proj_list)
            bits = mapper.get_bits(proj_list)

            results[text] = {
                'composite': composite,
                'bits': bits,
                'projection': proj_list,
                'n_active': sum(bits),
                'factors': mapper.explain(composite)['factors'],
            }

        return results

    @torch.no_grad()
    def compare(
        self,
        text_a: str,
        text_b: str,
        tokenizer=None,
    ) -> Dict:
        """
        Compare two texts using prime-factor algebra.

        Returns:
            Dict with 'similarity', 'shared_factors', 'only_in_a', 'only_in_b'.
        """
        from .algebra import TriadicValidator

        sigs = self.encode([text_a, text_b], tokenizer=tokenizer)
        a = sigs[text_a]['composite']
        b = sigs[text_b]['composite']

        gap = TriadicValidator.explain_gap(a, b)
        gap['similarity'] = TriadicValidator.similarity(a, b)
        gap['a_text'] = text_a
        gap['b_text'] = text_b
        return gap

    # ----------------------------------------------------------
    # Validation — Is training working?
    # ----------------------------------------------------------

    @torch.no_grad()
    def validate(
        self,
        tokenizer=None,
        word_groups: Optional[Dict[str, List[str]]] = None,
        verbose: bool = True,
        training_steps: int = 0,
    ) -> Dict:
        """
        Run diagnostic checks to verify triadic head training quality.

        Checks:
          1. Diversity — are signatures unique? (>75% = PASS)
          2. Active bits — are enough bits firing? (15-85% = PASS)
          3. Semantic ordering — related words more similar than unrelated? (gap > 0 = PASS)
          4. Random baseline — is the gap significantly above what random bits would produce?

        Also provides per-group breakdown so you can see which semantic
        categories the model handles well and which need more training.

        Args:
            tokenizer: HuggingFace tokenizer (auto-loaded if None).
            word_groups: Custom word groups to test, e.g.
                         {"animals": ["dog", "cat"], "colors": ["red", "blue"]}.
                         Uses built-in groups if None.
            verbose: Print results to console.
            training_steps: Total training steps completed (for guidance messages).

        Returns:
            Dict with check results, per-group breakdown, random baseline,
            overall PASS/FAIL, config snapshot, and all signatures.
        """
        import random as _random
        from .algebra import PrimeMapper, TriadicValidator as TV

        if word_groups is None:
            word_groups = {
                'royalty': ['king', 'queen', 'prince', 'throne'],
                'animals': ['dog', 'cat', 'fish', 'bird'],
                'emotions': ['happy', 'sad', 'angry', 'love'],
                'food': ['bread', 'water', 'rice', 'fruit'],
            }

        all_words = [w for group in word_groups.values() for w in group]
        sigs = self.encode(all_words, tokenizer=tokenizer)

        # --- Check 1: Diversity ---
        composites = [sigs[w]['composite'] for w in all_words]
        unique_ratio = len(set(composites)) / len(composites)

        # --- Check 2: Active bits ---
        active_counts = [sigs[w]['n_active'] for w in all_words]
        avg_active = sum(active_counts) / len(active_counts)
        active_frac = avg_active / self.n_bits

        # --- Check 3: Semantic ordering (global + per-group) ---
        groups = list(word_groups.values())
        intra_sims, inter_sims = [], []
        group_details = {}

        for gname, group in word_groups.items():
            g_intra = []
            for i, w1 in enumerate(group):
                for w2 in group[i + 1:]:
                    sim = TV.similarity(sigs[w1]['composite'], sigs[w2]['composite'])
                    g_intra.append(sim)
                    intra_sims.append(sim)
            # Inter: this group vs all other groups
            g_inter = []
            for other_name, other_group in word_groups.items():
                if other_name == gname:
                    continue
                for w1 in group:
                    for w2 in other_group:
                        sim = TV.similarity(sigs[w1]['composite'], sigs[w2]['composite'])
                        g_inter.append(sim)
                        inter_sims.append(sim)

            avg_gi = sum(g_intra) / len(g_intra) if g_intra else 0
            avg_ge = sum(g_inter) / len(g_inter) if g_inter else 0
            group_details[gname] = {
                'words': group,
                'intra_sim': avg_gi,
                'inter_sim': avg_ge,
                'gap': avg_gi - avg_ge,
                'pass': (avg_gi - avg_ge) > 0,
            }

        # Deduplicate inter_sims (each pair counted from both group perspectives)
        # Recalculate cleanly
        inter_sims_clean = []
        for gi, g1 in enumerate(groups):
            for g2 in groups[gi + 1:]:
                for w1 in g1:
                    for w2 in g2:
                        inter_sims_clean.append(
                            TV.similarity(sigs[w1]['composite'], sigs[w2]['composite'])
                        )

        avg_intra = sum(intra_sims) / len(intra_sims) if intra_sims else 0
        avg_inter = sum(inter_sims_clean) / len(inter_sims_clean) if inter_sims_clean else 0
        semantic_gap = avg_intra - avg_inter

        # --- Check 4: Random baseline ---
        # Generate random bit patterns and measure what gap you'd get by pure chance.
        # This tells the user how much of the measured gap is real signal vs noise.
        n_words = len(all_words)
        n_trials = 100  # average over 100 random assignments
        mapper = PrimeMapper(self.n_bits)
        random_gaps = []
        _random.seed(42)

        for _ in range(n_trials):
            # Generate random composites with similar active-bit ratio as model
            random_composites = []
            for _ in range(n_words):
                bits = [1 if _random.random() < active_frac else 0 for _ in range(self.n_bits)]
                proj = [(b * 2.0 - 1.0) for b in bits]  # convert to [-1, 1]
                random_composites.append(mapper.encode(proj))

            # Compute intra/inter using same group structure
            r_intra, r_inter = [], []
            word_idx = 0
            for group in groups:
                g_composites = random_composites[word_idx:word_idx + len(group)]
                word_idx += len(group)
                for ii in range(len(g_composites)):
                    for jj in range(ii + 1, len(g_composites)):
                        r_intra.append(TV.similarity(g_composites[ii], g_composites[jj]))

            # Inter: all cross-group pairs
            word_idx = 0
            group_composites = []
            for group in groups:
                group_composites.append(random_composites[word_idx:word_idx + len(group)])
                word_idx += len(group)

            for gi in range(len(group_composites)):
                for gj in range(gi + 1, len(group_composites)):
                    for c1 in group_composites[gi]:
                        for c2 in group_composites[gj]:
                            r_inter.append(TV.similarity(c1, c2))

            r_avg_intra = sum(r_intra) / len(r_intra) if r_intra else 0
            r_avg_inter = sum(r_inter) / len(r_inter) if r_inter else 0
            random_gaps.append(r_avg_intra - r_avg_inter)

        random_gap_mean = sum(random_gaps) / len(random_gaps)
        random_gap_std = (sum((g - random_gap_mean) ** 2 for g in random_gaps) / len(random_gaps)) ** 0.5
        signal_above_random = semantic_gap - random_gap_mean

        # The gap is meaningful if it's at least 2 standard deviations above random
        baseline_pass = signal_above_random > max(2 * random_gap_std, 0.01)

        baseline_info = {
            'random_gap_mean': random_gap_mean,
            'random_gap_std': random_gap_std,
            'model_gap': semantic_gap,
            'signal_above_random': signal_above_random,
            'pass': baseline_pass,
            'detail': (f"model gap {semantic_gap:+.1%} vs random baseline {random_gap_mean:+.1%} "
                       f"(signal {signal_above_random:+.1%}, random std {random_gap_std:.1%})"),
        }

        # --- Build results ---
        checks = {
            'diversity': {
                'value': unique_ratio,
                'pass': unique_ratio > 0.75,
                'detail': f"{len(set(composites))}/{len(composites)} unique signatures ({unique_ratio:.0%})",
            },
            'active_bits': {
                'value': active_frac,
                'pass': 0.15 < active_frac < 0.85,
                'detail': f"{avg_active:.1f}/{self.n_bits} bits active on avg ({active_frac:.0%})",
            },
            'semantic_ordering': {
                'intra': avg_intra,
                'inter': avg_inter,
                'gap': semantic_gap,
                'pass': semantic_gap > 0,
                'detail': f"within-group {avg_intra:.1%} vs between-group {avg_inter:.1%} (gap {semantic_gap:+.1%})",
            },
            'random_baseline': baseline_info,
        }

        overall = all(c['pass'] for c in checks.values())

        # --- Training guidance ---
        guidance = self._training_guidance(training_steps, semantic_gap, signal_above_random, baseline_pass)

        if verbose:
            print(f"\n{'=' * 60}")
            print("  TRIADIC HEAD — VALIDATION REPORT")
            print(f"{'=' * 60}")
            print(f"  Config: {self.n_bits} bits | align_mode={self.align_mode} | "
                  f"{self.triadic_params():,} triadic params")
            if training_steps > 0:
                print(f"  Training: {training_steps:,} steps completed")
            print(f"{'-' * 60}")

            for name, check in checks.items():
                status = "PASS" if check['pass'] else "FAIL"
                print(f"  [{status}] {name}: {check['detail']}")

            # Per-group breakdown
            print("\n  PER-GROUP BREAKDOWN:")
            for gname, gd in group_details.items():
                status = "PASS" if gd['pass'] else "FAIL"
                print(f"    [{status}] {gname}: intra {gd['intra_sim']:.0%} vs inter {gd['inter_sim']:.0%} "
                      f"(gap {gd['gap']:+.1%}) — {gd['words']}")

            # Per-word active bits
            print("\n  PER-WORD ACTIVE BITS:")
            for w in all_words:
                print(f"    {w:>12}: {sigs[w]['n_active']:2d}/{self.n_bits} bits active")

            print(f"{'-' * 60}")
            if overall:
                print("  RESULT: PASS — Triadic head is producing meaningful signatures.")
                print(f"  Signal above random: {signal_above_random:+.1%}")
            else:
                failed = [n for n, c in checks.items() if not c['pass']]
                print(f"  RESULT: FAIL — Issues detected: {', '.join(failed)}")
                if 'diversity' in failed:
                    print("    -> Signatures are too similar. Train longer or increase entropy_weight.")
                if 'active_bits' in failed:
                    if active_frac <= 0.15:
                        print("    -> Too few bits active. Increase entropy_weight to activate dead bits.")
                    else:
                        print("    -> Too many bits active. Decrease alpha or increase training steps.")
                if 'semantic_ordering' in failed:
                    print("    -> Related words aren't more similar than unrelated.")
                    print("       Try: increase align_weight, or use align_mode='infonce' for pre-trained models.")
                if 'random_baseline' in failed:
                    print("    -> Gap is not significantly above random chance.")
                    print("       The model may be producing hash-like signatures without real semantics.")
                    print("       This usually means MORE TRAINING is needed (see guidance below).")
                failing_groups = [g for g, d in group_details.items() if not d['pass']]
                if failing_groups:
                    print(f"    -> Weak groups: {', '.join(failing_groups)} — consider adding more training data for these domains.")

            # Always show training guidance
            if guidance:
                print("\n  TRAINING GUIDANCE:")
                for line in guidance:
                    print(f"    {line}")

            print(f"{'=' * 60}")

        return {
            'checks': checks,
            'overall_pass': overall,
            'group_details': group_details,
            'random_baseline': baseline_info,
            'guidance': guidance,
            'config': self.config(),
            'signatures': sigs,
        }

    @staticmethod
    def _training_guidance(training_steps: int, semantic_gap: float,
                           signal_above_random: float, baseline_pass: bool) -> List[str]:
        """Generate actionable training guidance based on current results."""
        lines = []

        # Recommended minimums (from 26 training runs in Triadic MicroGPT research)
        RECOMMENDED = {
            'smoke_test': 5_000,
            'minimum_viable': 20_000,
            'good_quality': 50_000,
            'production': 100_000,
        }

        if training_steps > 0 and training_steps < RECOMMENDED['minimum_viable']:
            lines.append(f"WARNING: {training_steps:,} steps is a quick smoke test, not a full training run.")
            lines.append(f"Minimum recommended: {RECOMMENDED['minimum_viable']:,} steps for meaningful results.")
            lines.append("")

        lines.append("Recommended training steps:")
        lines.append(f"  Smoke test:      {RECOMMENDED['smoke_test']:>8,} steps  (verify pipeline works)")
        lines.append(f"  Minimum viable:  {RECOMMENDED['minimum_viable']:>8,} steps  (basic semantic ordering)")
        lines.append(f"  Good quality:    {RECOMMENDED['good_quality']:>8,} steps  (reliable word relationships)")
        lines.append(f"  Production:      {RECOMMENDED['production']:>8,} steps+ (publish-ready signatures)")

        if not baseline_pass:
            lines.append("")
            lines.append(f"Your model's semantic gap ({semantic_gap:+.1%}) is close to random noise ({signal_above_random:+.1%} above random).")
            lines.append("This is expected with short training. The model needs more steps to")
            lines.append("learn real word relationships vs statistical coincidence.")
        elif signal_above_random > 0 and signal_above_random < 0.05:
            lines.append("")
            lines.append(f"Your model shows weak signal above random ({signal_above_random:+.1%}).")
            lines.append("More training will strengthen real semantic relationships.")
        elif signal_above_random >= 0.05:
            lines.append("")
            lines.append(f"Good signal above random: {signal_above_random:+.1%}")

        lines.append("")
        lines.append("For large models (LLaMA, Mistral, etc.), expect to need more steps.")
        lines.append("Monitor the semantic gap: it should grow steadily during training.")
        lines.append("If gap plateaus, try: increase align_weight or switch align_mode.")

        return lines

    # ----------------------------------------------------------
    # Explore — Discover relationships between words
    # ----------------------------------------------------------

    @torch.no_grad()
    def explore(
        self,
        words: List[str],
        tokenizer=None,
        top_k: int = 0,
        threshold: Optional[float] = None,
        show_factors: bool = False,
        verbose: bool = True,
    ) -> Dict:
        """
        Full audit of relationships between words with similarity matrix.

        Args:
            words: List of words/phrases to compare.
            tokenizer: HuggingFace tokenizer (auto-loaded if None).
            top_k: Show only top-K and bottom-K pairs (0 = show ALL pairs).
            threshold: If set, flag pairs above this similarity for review.
            show_factors: Show shared/unique prime factors for every pair.
            verbose: Print results to console.

        Returns:
            Dict with similarity matrix, ranked pairs, signatures, and flagged pairs.
        """
        from .algebra import TriadicValidator as TV

        sigs = self.encode(words, tokenizer=tokenizer)
        n = len(words)

        # Build similarity matrix
        matrix = [[0.0] * n for _ in range(n)]
        pairs = []

        for i in range(n):
            matrix[i][i] = 1.0
            for j in range(i + 1, n):
                sim = TV.similarity(
                    sigs[words[i]]['composite'],
                    sigs[words[j]]['composite'],
                )
                gap_info = TV.explain_gap(
                    sigs[words[i]]['composite'],
                    sigs[words[j]]['composite'],
                )
                matrix[i][j] = sim
                matrix[j][i] = sim
                pairs.append({
                    'similarity': sim,
                    'word_a': words[i],
                    'word_b': words[j],
                    'shared_factors': gap_info['shared_factors'],
                    'only_a_factors': gap_info['only_in_a_factors'],
                    'only_b_factors': gap_info['only_in_b_factors'],
                    'n_shared': len(gap_info['shared_factors']),
                    'n_only_a': len(gap_info['only_in_a_factors']),
                    'n_only_b': len(gap_info['only_in_b_factors']),
                })

        pairs.sort(key=lambda p: p['similarity'], reverse=True)

        # Flag pairs above threshold
        flagged = []
        if threshold is not None:
            flagged = [p for p in pairs if p['similarity'] >= threshold]

        if verbose:
            col_w = min(max(max(len(w) for w in words), 6), 10)

            print(f"\n{'=' * 60}")
            print("  SIMILARITY MATRIX")
            print(f"{'=' * 60}")

            # Header
            header = " " * (col_w + 2) + "".join(f"{w[:col_w]:>{col_w + 1}}" for w in words)
            print(header)

            for i, w in enumerate(words):
                row_vals = []
                for j in range(n):
                    if i == j:
                        row_vals.append(f"{'---':>{col_w + 1}}")
                    else:
                        row_vals.append(f"{matrix[i][j]:>{col_w}.0%} ")
                print(f"{w[:col_w]:>{col_w}}  {''.join(row_vals)}")

            # Pairs listing
            if top_k > 0 and len(pairs) > top_k * 2:
                print(f"\n  TOP {top_k} most similar:")
                for p in pairs[:top_k]:
                    line = f"    {p['word_a']} <-> {p['word_b']}: {p['similarity']:.0%} ({p['n_shared']} shared)"
                    if show_factors:
                        line += f" shared={p['shared_factors']}"
                    print(line)
                print(f"\n  TOP {top_k} least similar:")
                for p in pairs[-top_k:]:
                    line = f"    {p['word_a']} <-> {p['word_b']}: {p['similarity']:.0%}"
                    print(line)
            else:
                print("\n  ALL PAIRS (ranked by similarity):")
                for p in pairs:
                    line = f"    {p['word_a']:>12} <-> {p['word_b']:<12}: {p['similarity']:.0%} ({p['n_shared']} shared, {p['n_only_a']} only-a, {p['n_only_b']} only-b)"
                    if show_factors:
                        line += f"\n{'':>42}shared={p['shared_factors']}"
                        if p['only_a_factors']:
                            line += f"\n{'':>42}only-{p['word_a']}={p['only_a_factors']}"
                        if p['only_b_factors']:
                            line += f"\n{'':>42}only-{p['word_b']}={p['only_b_factors']}"
                    print(line)

            # Flagged pairs
            if threshold is not None:
                print(f"\n  FLAGGED (similarity >= {threshold:.0%}): {len(flagged)} pairs")
                if flagged:
                    for p in flagged:
                        print(f"    {p['word_a']} <-> {p['word_b']}: {p['similarity']:.0%}")
                else:
                    print("    (none)")

            # Per-word signature card
            print("\n  PER-WORD SIGNATURES:")
            for i, w in enumerate(words):
                sims_for_w = [matrix[i][j] for j in range(n) if i != j]
                avg = sum(sims_for_w) / len(sims_for_w)
                most_sim_j = max((j for j in range(n) if j != i), key=lambda j: matrix[i][j])
                least_sim_j = min((j for j in range(n) if j != i), key=lambda j: matrix[i][j])
                primes = sigs[w]['factors']
                print(f"    {w:>12}: {sigs[w]['n_active']} bits | avg sim {avg:.0%} "
                      f"| closest: {words[most_sim_j]} ({matrix[i][most_sim_j]:.0%}) "
                      f"| furthest: {words[least_sim_j]} ({matrix[i][least_sim_j]:.0%})")
                if show_factors:
                    print(f"{'':>16}primes={primes}")

            # Factor index: which words share each prime?
            if show_factors:
                from .algebra import nth_prime as _nth_prime
                factor_index = {}  # prime -> list of words
                for w in words:
                    for p in sigs[w]['factors']:
                        factor_index.setdefault(p, []).append(w)

                # Sort by number of words sharing the factor (most shared first)
                sorted_factors = sorted(factor_index.items(),
                                        key=lambda x: len(x[1]), reverse=True)

                print("\n  FACTOR INDEX (what each prime means):")
                print(f"    {'prime':>8}  {'bit':>3}  {'words':>5}  shared by")
                print(f"    {'-'*8}  {'-'*3}  {'-'*5}  {'-'*30}")
                for prime, sharing_words in sorted_factors:
                    # Find bit index for this prime
                    bit_idx = next(
                        (i for i in range(self.n_bits) if _nth_prime(i + 1) == prime),
                        -1
                    )
                    count = len(sharing_words)
                    label = ', '.join(sharing_words)
                    if count == len(words):
                        label += '  [UNIVERSAL]'
                    elif count == 1:
                        label += '  [UNIQUE]'
                    print(f"    {prime:>8}  {bit_idx:>3}  {count:>5}  {label}")

            print(f"{'=' * 60}")

        return {
            'matrix': matrix,
            'words': words,
            'pairs_ranked': pairs,
            'signatures': sigs,
            'flagged': flagged,
        }

    # ----------------------------------------------------------
    # Generation (pass-through to backbone)
    # ----------------------------------------------------------

    @torch.no_grad()
    def generate(self, input_ids, max_new_tokens=100, temperature=0.7, top_k=50):
        """Autoregressive text generation."""
        for _ in range(max_new_tokens):
            idx = input_ids[:, -self.block_size:]
            logits, _, _ = self(idx)
            logits = logits[:, -1, :] / temperature
            if top_k is not None:
                v, _ = torch.topk(logits, min(top_k, logits.size(-1)))
                logits[logits < v[:, [-1]]] = float('-inf')
            probs = F.softmax(logits, dim=-1)
            next_id = torch.multinomial(probs, num_samples=1)
            input_ids = torch.cat([input_ids, next_id], dim=1)
        return input_ids

    # ----------------------------------------------------------
    # Utilities
    # ----------------------------------------------------------

    def num_params(self, trainable_only=False) -> int:
        if trainable_only:
            return sum(p.numel() for p in self.parameters() if p.requires_grad)
        return sum(p.numel() for p in self.parameters())

    def triadic_params(self) -> int:
        """Number of parameters in the triadic head only."""
        return sum(p.numel() for p in self.triadic_head.parameters())

    def __repr__(self):
        return (
            f"TriadicWrapper(\n"
            f"  backbone={type(self.backbone_model).__name__},\n"
            f"  n_embd={self.n_embd}, n_bits={self.n_bits},\n"
            f"  align_mode='{self.align_mode}',\n"
            f"  triadic_params={self.triadic_params():,},\n"
            f"  total_params={self.num_params():,}\n"
            f")"
        )

config(**kwargs) -> Dict

View or update model configuration.

Call with no arguments to view current config. Pass keyword arguments to update:

model.config(align_mode='rank', n_bits=32)
Changeable settings

align_mode: 'mse' | 'rank' | 'infonce'

Read-only (shown but not changeable): n_bits, n_embd, backbone, block_size, triadic_params, total_params

Source code in triadic-head-src/triadic-head/triadic_head/wrapper.py 
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def config(self, **kwargs) -> Dict:
    """
    View or update model configuration.

    Call with no arguments to view current config.
    Pass keyword arguments to update:

        model.config(align_mode='rank', n_bits=32)

    Changeable settings:
        align_mode: 'mse' | 'rank' | 'infonce'

    Read-only (shown but not changeable):
        n_bits, n_embd, backbone, block_size, triadic_params, total_params
    """
    VALID_ALIGN = ('mse', 'rank', 'infonce')

    if 'align_mode' in kwargs:
        mode = kwargs['align_mode']
        if mode not in VALID_ALIGN:
            raise ValueError(f"align_mode must be one of {VALID_ALIGN}, got {mode!r}")
        self.align_mode = mode

    return {
        'align_mode': self.align_mode,
        'n_bits': self.n_bits,
        'n_embd': self.n_embd,
        'backbone': type(self.backbone_model).__name__,
        'block_size': self.block_size,
        'triadic_params': self.triadic_params(),
        'total_params': self.num_params(),
    }

freeze_backbone()

Freeze entire backbone. Only triadic head receives gradients.

Source code in triadic-head-src/triadic-head/triadic_head/wrapper.py 
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def freeze_backbone(self):
    """Freeze entire backbone. Only triadic head receives gradients."""
    for param in self.backbone_model.parameters():
        param.requires_grad = False
    for param in self.triadic_head.parameters():
        param.requires_grad = True

unfreeze_last_n(n: int = 2)

Unfreeze the last N transformer layers + final layer norm.

Source code in triadic-head-src/triadic-head/triadic_head/wrapper.py 
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def unfreeze_last_n(self, n: int = 2):
    """Unfreeze the last N transformer layers + final layer norm."""
    if 'ln_f' in self._arch:
        for param in self._arch['ln_f'].parameters():
            param.requires_grad = True
    layers = self._arch['layers']
    total = len(layers)
    for i in range(max(0, total - n), total):
        for param in layers[i].parameters():
            param.requires_grad = True

unfreeze_all()

Unfreeze everything.

Source code in triadic-head-src/triadic-head/triadic_head/wrapper.py 
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def unfreeze_all(self):
    """Unfreeze everything."""
    for param in self.parameters():
        param.requires_grad = True

forward(input_ids: torch.Tensor, attention_mask: Optional[torch.Tensor] = None, labels: Optional[torch.Tensor] = None)

Forward pass through backbone + triadic head.

Returns:

Name Type Description
logits

(B, T, vocab_size)
triadic_proj

(B, T, n_bits) in [-1, 1]
lang_loss

scalar or None
Source code in triadic-head-src/triadic-head/triadic_head/wrapper.py 
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def forward(
    self,
    input_ids: torch.Tensor,
    attention_mask: Optional[torch.Tensor] = None,
    labels: Optional[torch.Tensor] = None,
):
    """
    Forward pass through backbone + triadic head.

    Returns:
        logits:       (B, T, vocab_size)
        triadic_proj: (B, T, n_bits) in [-1, 1]
        lang_loss:    scalar or None
    """
    backbone = self._arch['backbone']
    outputs = backbone(
        input_ids=input_ids,
        attention_mask=attention_mask,
    )
    # Handle different return types
    if hasattr(outputs, 'last_hidden_state'):
        hidden = outputs.last_hidden_state
    elif isinstance(outputs, tuple):
        hidden = outputs[0]
    else:
        hidden = outputs

    # LM head
    lm_head = self._arch.get('lm_head')
    if lm_head is not None:
        logits = lm_head(hidden)
    else:
        logits = self.backbone_model.lm_head(hidden)

    # Triadic head
    triadic_proj = self.triadic_head(hidden)

    # Language loss
    lang_loss = None
    if labels is not None:
        shift_logits = logits[..., :-1, :].contiguous()
        shift_labels = labels[..., 1:].contiguous()
        lang_loss = F.cross_entropy(
            shift_logits.view(-1, shift_logits.size(-1)),
            shift_labels.view(-1),
            ignore_index=-100,
        )

    return logits, triadic_proj, lang_loss

triadic_loss(triadic_proj: torch.Tensor, input_ids: Optional[torch.Tensor] = None, alpha: float = 0.05, entropy_weight: float = 1.0, align_weight: float = 5.0, align_mode: Optional[str] = None) -> torch.Tensor

Compute multi-component triadic loss.

Components
  1. Diversity — each bit should fire ~50% of the time.
  2. Contrastive — different sequences should produce different signatures.
  3. Entropy — prevent dead bits (bits stuck at +1 or -1).
  4. Embedding alignment — transfer semantic structure from embeddings.

Parameters:

Name Type Description Default
triadic_proj Tensor

(B, T, n_bits) from forward().

 required
input_ids Optional[Tensor]

(B, T) needed for alignment loss.

 None
alpha float

Weight of total triadic loss (default 0.05, DO NOT exceed 0.10).

 0.05
entropy_weight float

Weight for entropy term (default 1.0).

 1.0
align_weight float

Weight for alignment term (default 5.0).

 5.0
align_mode Optional[str]

Override self.align_mode for this call.

 None

Returns:

Type Description
Tensor

Weighted triadic loss scalar (already multiplied by alpha).
Source code in triadic-head-src/triadic-head/triadic_head/wrapper.py 
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def triadic_loss(
    self,
    triadic_proj: torch.Tensor,
    input_ids: Optional[torch.Tensor] = None,
    alpha: float = 0.05,
    entropy_weight: float = 1.0,
    align_weight: float = 5.0,
    align_mode: Optional[str] = None,
) -> torch.Tensor:
    """
    Compute multi-component triadic loss.

    Components:
      1. Diversity — each bit should fire ~50% of the time.
      2. Contrastive — different sequences should produce different signatures.
      3. Entropy — prevent dead bits (bits stuck at +1 or -1).
      4. Embedding alignment — transfer semantic structure from embeddings.

    Args:
        triadic_proj: (B, T, n_bits) from forward().
        input_ids: (B, T) needed for alignment loss.
        alpha: Weight of total triadic loss (default 0.05, DO NOT exceed 0.10).
        entropy_weight: Weight for entropy term (default 1.0).
        align_weight: Weight for alignment term (default 5.0).
        align_mode: Override self.align_mode for this call.

    Returns:
        Weighted triadic loss scalar (already multiplied by alpha).
    """
    mode = align_mode or self.align_mode

    if triadic_proj.size(1) < 2:
        return torch.tensor(0.0, device=triadic_proj.device)

    # Force float32 for numerical stability (critical under AMP/mixed precision)
    triadic_proj = triadic_proj.float()

    B, T, n_bits = triadic_proj.shape

    # 1. Diversity: push per-bit mean toward 0
    bit_means = triadic_proj.mean(dim=(0, 1))
    diversity = (bit_means ** 2).mean()

    # 2. Contrastive: push sequence-level projections apart
    if B > 1:
        seq_proj = F.normalize(triadic_proj.mean(dim=1), dim=-1)
        sim = seq_proj @ seq_proj.T
        mask = ~torch.eye(B, device=sim.device, dtype=torch.bool)
        contrastive = sim[mask].pow(2).mean()
    else:
        contrastive = torch.tensor(0.0, device=triadic_proj.device)

    # 3. Entropy: maximize per-bit entropy across the batch
    entropy = torch.tensor(0.0, device=triadic_proj.device)
    if entropy_weight > 0:
        flat = triadic_proj.reshape(-1, n_bits)
        probs = ((flat.mean(dim=0) + 1.0) / 2.0).clamp(1e-7, 1 - 1e-7)
        H = -(probs * probs.log() + (1 - probs) * (1 - probs).log())
        entropy = (1.0 - H / math.log(2)).mean()

    # 4. Embedding alignment
    alignment = torch.tensor(0.0, device=triadic_proj.device)
    if align_weight > 0 and input_ids is not None:
        with torch.no_grad():
            embeds = self._arch['embed_layer'](input_ids).detach().float()

        if mode == 'mse':
            alignment = self._align_mse(triadic_proj, embeds)
        elif mode == 'rank':
            alignment = self._align_rank(triadic_proj, embeds)
        elif mode == 'infonce':
            alignment = self._align_infonce(triadic_proj, embeds)

    raw = diversity + contrastive
    if entropy_weight > 0:
        raw = raw + entropy_weight * entropy
    if align_weight > 0:
        raw = raw + align_weight * alignment

    return alpha * raw

encode(texts: Union[str, List[str]], tokenizer=None) -> Dict[str, dict]

Encode text(s) to prime-factor signatures.

Parameters:

Name Type Description Default
texts Union[str, List[str]]

Single string or list of strings.

 required
tokenizer

HuggingFace tokenizer. If None, uses AutoTokenizer matching the backbone model.

 None

Returns:

Type Description
Dict[str, dict]

Dict mapping each text to: - 'composite': int (prime product) - 'bits': List[int] (binary pattern) - 'projection': List[float] (raw tanh values) - 'n_active': int (number of active bits)
Source code in triadic-head-src/triadic-head/triadic_head/wrapper.py 
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@torch.no_grad()
def encode(
    self,
    texts: Union[str, List[str]],
    tokenizer=None,
) -> Dict[str, dict]:
    """
    Encode text(s) to prime-factor signatures.

    Args:
        texts: Single string or list of strings.
        tokenizer: HuggingFace tokenizer. If None, uses AutoTokenizer
                   matching the backbone model.

    Returns:
        Dict mapping each text to:
          - 'composite': int (prime product)
          - 'bits': List[int] (binary pattern)
          - 'projection': List[float] (raw tanh values)
          - 'n_active': int (number of active bits)
    """
    from .algebra import PrimeMapper

    if isinstance(texts, str):
        texts = [texts]

    if tokenizer is None:
        from transformers import AutoTokenizer
        config = getattr(self.backbone_model, 'config', None)
        model_name = getattr(config, '_name_or_path', 'gpt2')
        tokenizer = AutoTokenizer.from_pretrained(model_name)
        if tokenizer.pad_token is None:
            tokenizer.pad_token = tokenizer.eos_token

    device = next(self.parameters()).device
    mapper = PrimeMapper(self.n_bits)
    results = {}

    for text in texts:
        tokens = tokenizer(text, return_tensors='pt', truncation=True,
                           max_length=self.block_size).to(device)
        _, triadic_proj, _ = self(tokens['input_ids'],
                                 attention_mask=tokens.get('attention_mask'))
        # Average across all token positions
        avg_proj = triadic_proj.mean(dim=1).squeeze(0)  # (n_bits,)
        proj_list = avg_proj.cpu().tolist()

        composite = mapper.encode(proj_list)
        bits = mapper.get_bits(proj_list)

        results[text] = {
            'composite': composite,
            'bits': bits,
            'projection': proj_list,
            'n_active': sum(bits),
            'factors': mapper.explain(composite)['factors'],
        }

    return results

compare(text_a: str, text_b: str, tokenizer=None) -> Dict

Compare two texts using prime-factor algebra.

Returns:

Type Description
Dict

Dict with 'similarity', 'shared_factors', 'only_in_a', 'only_in_b'.
Source code in triadic-head-src/triadic-head/triadic_head/wrapper.py 
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@torch.no_grad()
def compare(
    self,
    text_a: str,
    text_b: str,
    tokenizer=None,
) -> Dict:
    """
    Compare two texts using prime-factor algebra.

    Returns:
        Dict with 'similarity', 'shared_factors', 'only_in_a', 'only_in_b'.
    """
    from .algebra import TriadicValidator

    sigs = self.encode([text_a, text_b], tokenizer=tokenizer)
    a = sigs[text_a]['composite']
    b = sigs[text_b]['composite']

    gap = TriadicValidator.explain_gap(a, b)
    gap['similarity'] = TriadicValidator.similarity(a, b)
    gap['a_text'] = text_a
    gap['b_text'] = text_b
    return gap

validate(tokenizer=None, word_groups: Optional[Dict[str, List[str]]] = None, verbose: bool = True, training_steps: int = 0) -> Dict

Run diagnostic checks to verify triadic head training quality.

Checks
  1. Diversity — are signatures unique? (>75% = PASS)
  2. Active bits — are enough bits firing? (15-85% = PASS)
  3. Semantic ordering — related words more similar than unrelated? (gap > 0 = PASS)
  4. Random baseline — is the gap significantly above what random bits would produce?

Also provides per-group breakdown so you can see which semantic categories the model handles well and which need more training.

Parameters:

Name Type Description Default
tokenizer

HuggingFace tokenizer (auto-loaded if None).

 None
word_groups Optional[Dict[str, List[str]]]

Custom word groups to test, e.g. {"animals": ["dog", "cat"], "colors": ["red", "blue"]}. Uses built-in groups if None.

 None
verbose bool

Print results to console.

 True
training_steps int

Total training steps completed (for guidance messages).

 0

Returns:

Type Description
Dict

Dict with check results, per-group breakdown, random baseline,
Dict

overall PASS/FAIL, config snapshot, and all signatures.
Source code in triadic-head-src/triadic-head/triadic_head/wrapper.py 
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@torch.no_grad()
def validate(
    self,
    tokenizer=None,
    word_groups: Optional[Dict[str, List[str]]] = None,
    verbose: bool = True,
    training_steps: int = 0,
) -> Dict:
    """
    Run diagnostic checks to verify triadic head training quality.

    Checks:
      1. Diversity — are signatures unique? (>75% = PASS)
      2. Active bits — are enough bits firing? (15-85% = PASS)
      3. Semantic ordering — related words more similar than unrelated? (gap > 0 = PASS)
      4. Random baseline — is the gap significantly above what random bits would produce?

    Also provides per-group breakdown so you can see which semantic
    categories the model handles well and which need more training.

    Args:
        tokenizer: HuggingFace tokenizer (auto-loaded if None).
        word_groups: Custom word groups to test, e.g.
                     {"animals": ["dog", "cat"], "colors": ["red", "blue"]}.
                     Uses built-in groups if None.
        verbose: Print results to console.
        training_steps: Total training steps completed (for guidance messages).

    Returns:
        Dict with check results, per-group breakdown, random baseline,
        overall PASS/FAIL, config snapshot, and all signatures.
    """
    import random as _random
    from .algebra import PrimeMapper, TriadicValidator as TV

    if word_groups is None:
        word_groups = {
            'royalty': ['king', 'queen', 'prince', 'throne'],
            'animals': ['dog', 'cat', 'fish', 'bird'],
            'emotions': ['happy', 'sad', 'angry', 'love'],
            'food': ['bread', 'water', 'rice', 'fruit'],
        }

    all_words = [w for group in word_groups.values() for w in group]
    sigs = self.encode(all_words, tokenizer=tokenizer)

    # --- Check 1: Diversity ---
    composites = [sigs[w]['composite'] for w in all_words]
    unique_ratio = len(set(composites)) / len(composites)

    # --- Check 2: Active bits ---
    active_counts = [sigs[w]['n_active'] for w in all_words]
    avg_active = sum(active_counts) / len(active_counts)
    active_frac = avg_active / self.n_bits

    # --- Check 3: Semantic ordering (global + per-group) ---
    groups = list(word_groups.values())
    intra_sims, inter_sims = [], []
    group_details = {}

    for gname, group in word_groups.items():
        g_intra = []
        for i, w1 in enumerate(group):
            for w2 in group[i + 1:]:
                sim = TV.similarity(sigs[w1]['composite'], sigs[w2]['composite'])
                g_intra.append(sim)
                intra_sims.append(sim)
        # Inter: this group vs all other groups
        g_inter = []
        for other_name, other_group in word_groups.items():
            if other_name == gname:
                continue
            for w1 in group:
                for w2 in other_group:
                    sim = TV.similarity(sigs[w1]['composite'], sigs[w2]['composite'])
                    g_inter.append(sim)
                    inter_sims.append(sim)

        avg_gi = sum(g_intra) / len(g_intra) if g_intra else 0
        avg_ge = sum(g_inter) / len(g_inter) if g_inter else 0
        group_details[gname] = {
            'words': group,
            'intra_sim': avg_gi,
            'inter_sim': avg_ge,
            'gap': avg_gi - avg_ge,
            'pass': (avg_gi - avg_ge) > 0,
        }

    # Deduplicate inter_sims (each pair counted from both group perspectives)
    # Recalculate cleanly
    inter_sims_clean = []
    for gi, g1 in enumerate(groups):
        for g2 in groups[gi + 1:]:
            for w1 in g1:
                for w2 in g2:
                    inter_sims_clean.append(
                        TV.similarity(sigs[w1]['composite'], sigs[w2]['composite'])
                    )

    avg_intra = sum(intra_sims) / len(intra_sims) if intra_sims else 0
    avg_inter = sum(inter_sims_clean) / len(inter_sims_clean) if inter_sims_clean else 0
    semantic_gap = avg_intra - avg_inter

    # --- Check 4: Random baseline ---
    # Generate random bit patterns and measure what gap you'd get by pure chance.
    # This tells the user how much of the measured gap is real signal vs noise.
    n_words = len(all_words)
    n_trials = 100  # average over 100 random assignments
    mapper = PrimeMapper(self.n_bits)
    random_gaps = []
    _random.seed(42)

    for _ in range(n_trials):
        # Generate random composites with similar active-bit ratio as model
        random_composites = []
        for _ in range(n_words):
            bits = [1 if _random.random() < active_frac else 0 for _ in range(self.n_bits)]
            proj = [(b * 2.0 - 1.0) for b in bits]  # convert to [-1, 1]
            random_composites.append(mapper.encode(proj))

        # Compute intra/inter using same group structure
        r_intra, r_inter = [], []
        word_idx = 0
        for group in groups:
            g_composites = random_composites[word_idx:word_idx + len(group)]
            word_idx += len(group)
            for ii in range(len(g_composites)):
                for jj in range(ii + 1, len(g_composites)):
                    r_intra.append(TV.similarity(g_composites[ii], g_composites[jj]))

        # Inter: all cross-group pairs
        word_idx = 0
        group_composites = []
        for group in groups:
            group_composites.append(random_composites[word_idx:word_idx + len(group)])
            word_idx += len(group)

        for gi in range(len(group_composites)):
            for gj in range(gi + 1, len(group_composites)):
                for c1 in group_composites[gi]:
                    for c2 in group_composites[gj]:
                        r_inter.append(TV.similarity(c1, c2))

        r_avg_intra = sum(r_intra) / len(r_intra) if r_intra else 0
        r_avg_inter = sum(r_inter) / len(r_inter) if r_inter else 0
        random_gaps.append(r_avg_intra - r_avg_inter)

    random_gap_mean = sum(random_gaps) / len(random_gaps)
    random_gap_std = (sum((g - random_gap_mean) ** 2 for g in random_gaps) / len(random_gaps)) ** 0.5
    signal_above_random = semantic_gap - random_gap_mean

    # The gap is meaningful if it's at least 2 standard deviations above random
    baseline_pass = signal_above_random > max(2 * random_gap_std, 0.01)

    baseline_info = {
        'random_gap_mean': random_gap_mean,
        'random_gap_std': random_gap_std,
        'model_gap': semantic_gap,
        'signal_above_random': signal_above_random,
        'pass': baseline_pass,
        'detail': (f"model gap {semantic_gap:+.1%} vs random baseline {random_gap_mean:+.1%} "
                   f"(signal {signal_above_random:+.1%}, random std {random_gap_std:.1%})"),
    }

    # --- Build results ---
    checks = {
        'diversity': {
            'value': unique_ratio,
            'pass': unique_ratio > 0.75,
            'detail': f"{len(set(composites))}/{len(composites)} unique signatures ({unique_ratio:.0%})",
        },
        'active_bits': {
            'value': active_frac,
            'pass': 0.15 < active_frac < 0.85,
            'detail': f"{avg_active:.1f}/{self.n_bits} bits active on avg ({active_frac:.0%})",
        },
        'semantic_ordering': {
            'intra': avg_intra,
            'inter': avg_inter,
            'gap': semantic_gap,
            'pass': semantic_gap > 0,
            'detail': f"within-group {avg_intra:.1%} vs between-group {avg_inter:.1%} (gap {semantic_gap:+.1%})",
        },
        'random_baseline': baseline_info,
    }

    overall = all(c['pass'] for c in checks.values())

    # --- Training guidance ---
    guidance = self._training_guidance(training_steps, semantic_gap, signal_above_random, baseline_pass)

    if verbose:
        print(f"\n{'=' * 60}")
        print("  TRIADIC HEAD — VALIDATION REPORT")
        print(f"{'=' * 60}")
        print(f"  Config: {self.n_bits} bits | align_mode={self.align_mode} | "
              f"{self.triadic_params():,} triadic params")
        if training_steps > 0:
            print(f"  Training: {training_steps:,} steps completed")
        print(f"{'-' * 60}")

        for name, check in checks.items():
            status = "PASS" if check['pass'] else "FAIL"
            print(f"  [{status}] {name}: {check['detail']}")

        # Per-group breakdown
        print("\n  PER-GROUP BREAKDOWN:")
        for gname, gd in group_details.items():
            status = "PASS" if gd['pass'] else "FAIL"
            print(f"    [{status}] {gname}: intra {gd['intra_sim']:.0%} vs inter {gd['inter_sim']:.0%} "
                  f"(gap {gd['gap']:+.1%}) — {gd['words']}")

        # Per-word active bits
        print("\n  PER-WORD ACTIVE BITS:")
        for w in all_words:
            print(f"    {w:>12}: {sigs[w]['n_active']:2d}/{self.n_bits} bits active")

        print(f"{'-' * 60}")
        if overall:
            print("  RESULT: PASS — Triadic head is producing meaningful signatures.")
            print(f"  Signal above random: {signal_above_random:+.1%}")
        else:
            failed = [n for n, c in checks.items() if not c['pass']]
            print(f"  RESULT: FAIL — Issues detected: {', '.join(failed)}")
            if 'diversity' in failed:
                print("    -> Signatures are too similar. Train longer or increase entropy_weight.")
            if 'active_bits' in failed:
                if active_frac <= 0.15:
                    print("    -> Too few bits active. Increase entropy_weight to activate dead bits.")
                else:
                    print("    -> Too many bits active. Decrease alpha or increase training steps.")
            if 'semantic_ordering' in failed:
                print("    -> Related words aren't more similar than unrelated.")
                print("       Try: increase align_weight, or use align_mode='infonce' for pre-trained models.")
            if 'random_baseline' in failed:
                print("    -> Gap is not significantly above random chance.")
                print("       The model may be producing hash-like signatures without real semantics.")
                print("       This usually means MORE TRAINING is needed (see guidance below).")
            failing_groups = [g for g, d in group_details.items() if not d['pass']]
            if failing_groups:
                print(f"    -> Weak groups: {', '.join(failing_groups)} — consider adding more training data for these domains.")

        # Always show training guidance
        if guidance:
            print("\n  TRAINING GUIDANCE:")
            for line in guidance:
                print(f"    {line}")

        print(f"{'=' * 60}")

    return {
        'checks': checks,
        'overall_pass': overall,
        'group_details': group_details,
        'random_baseline': baseline_info,
        'guidance': guidance,
        'config': self.config(),
        'signatures': sigs,
    }

explore(words: List[str], tokenizer=None, top_k: int = 0, threshold: Optional[float] = None, show_factors: bool = False, verbose: bool = True) -> Dict

Full audit of relationships between words with similarity matrix.

Parameters:

Name Type Description Default
words List[str]

List of words/phrases to compare.

 required
tokenizer

HuggingFace tokenizer (auto-loaded if None).

 None
top_k int

Show only top-K and bottom-K pairs (0 = show ALL pairs).

 0
threshold Optional[float]

If set, flag pairs above this similarity for review.

 None
show_factors bool

Show shared/unique prime factors for every pair.

 False
verbose bool

Print results to console.

 True

Returns:

Type Description
Dict

Dict with similarity matrix, ranked pairs, signatures, and flagged pairs.
Source code in triadic-head-src/triadic-head/triadic_head/wrapper.py 
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@torch.no_grad()
def explore(
    self,
    words: List[str],
    tokenizer=None,
    top_k: int = 0,
    threshold: Optional[float] = None,
    show_factors: bool = False,
    verbose: bool = True,
) -> Dict:
    """
    Full audit of relationships between words with similarity matrix.

    Args:
        words: List of words/phrases to compare.
        tokenizer: HuggingFace tokenizer (auto-loaded if None).
        top_k: Show only top-K and bottom-K pairs (0 = show ALL pairs).
        threshold: If set, flag pairs above this similarity for review.
        show_factors: Show shared/unique prime factors for every pair.
        verbose: Print results to console.

    Returns:
        Dict with similarity matrix, ranked pairs, signatures, and flagged pairs.
    """
    from .algebra import TriadicValidator as TV

    sigs = self.encode(words, tokenizer=tokenizer)
    n = len(words)

    # Build similarity matrix
    matrix = [[0.0] * n for _ in range(n)]
    pairs = []

    for i in range(n):
        matrix[i][i] = 1.0
        for j in range(i + 1, n):
            sim = TV.similarity(
                sigs[words[i]]['composite'],
                sigs[words[j]]['composite'],
            )
            gap_info = TV.explain_gap(
                sigs[words[i]]['composite'],
                sigs[words[j]]['composite'],
            )
            matrix[i][j] = sim
            matrix[j][i] = sim
            pairs.append({
                'similarity': sim,
                'word_a': words[i],
                'word_b': words[j],
                'shared_factors': gap_info['shared_factors'],
                'only_a_factors': gap_info['only_in_a_factors'],
                'only_b_factors': gap_info['only_in_b_factors'],
                'n_shared': len(gap_info['shared_factors']),
                'n_only_a': len(gap_info['only_in_a_factors']),
                'n_only_b': len(gap_info['only_in_b_factors']),
            })

    pairs.sort(key=lambda p: p['similarity'], reverse=True)

    # Flag pairs above threshold
    flagged = []
    if threshold is not None:
        flagged = [p for p in pairs if p['similarity'] >= threshold]

    if verbose:
        col_w = min(max(max(len(w) for w in words), 6), 10)

        print(f"\n{'=' * 60}")
        print("  SIMILARITY MATRIX")
        print(f"{'=' * 60}")

        # Header
        header = " " * (col_w + 2) + "".join(f"{w[:col_w]:>{col_w + 1}}" for w in words)
        print(header)

        for i, w in enumerate(words):
            row_vals = []
            for j in range(n):
                if i == j:
                    row_vals.append(f"{'---':>{col_w + 1}}")
                else:
                    row_vals.append(f"{matrix[i][j]:>{col_w}.0%} ")
            print(f"{w[:col_w]:>{col_w}}  {''.join(row_vals)}")

        # Pairs listing
        if top_k > 0 and len(pairs) > top_k * 2:
            print(f"\n  TOP {top_k} most similar:")
            for p in pairs[:top_k]:
                line = f"    {p['word_a']} <-> {p['word_b']}: {p['similarity']:.0%} ({p['n_shared']} shared)"
                if show_factors:
                    line += f" shared={p['shared_factors']}"
                print(line)
            print(f"\n  TOP {top_k} least similar:")
            for p in pairs[-top_k:]:
                line = f"    {p['word_a']} <-> {p['word_b']}: {p['similarity']:.0%}"
                print(line)
        else:
            print("\n  ALL PAIRS (ranked by similarity):")
            for p in pairs:
                line = f"    {p['word_a']:>12} <-> {p['word_b']:<12}: {p['similarity']:.0%} ({p['n_shared']} shared, {p['n_only_a']} only-a, {p['n_only_b']} only-b)"
                if show_factors:
                    line += f"\n{'':>42}shared={p['shared_factors']}"
                    if p['only_a_factors']:
                        line += f"\n{'':>42}only-{p['word_a']}={p['only_a_factors']}"
                    if p['only_b_factors']:
                        line += f"\n{'':>42}only-{p['word_b']}={p['only_b_factors']}"
                print(line)

        # Flagged pairs
        if threshold is not None:
            print(f"\n  FLAGGED (similarity >= {threshold:.0%}): {len(flagged)} pairs")
            if flagged:
                for p in flagged:
                    print(f"    {p['word_a']} <-> {p['word_b']}: {p['similarity']:.0%}")
            else:
                print("    (none)")

        # Per-word signature card
        print("\n  PER-WORD SIGNATURES:")
        for i, w in enumerate(words):
            sims_for_w = [matrix[i][j] for j in range(n) if i != j]
            avg = sum(sims_for_w) / len(sims_for_w)
            most_sim_j = max((j for j in range(n) if j != i), key=lambda j: matrix[i][j])
            least_sim_j = min((j for j in range(n) if j != i), key=lambda j: matrix[i][j])
            primes = sigs[w]['factors']
            print(f"    {w:>12}: {sigs[w]['n_active']} bits | avg sim {avg:.0%} "
                  f"| closest: {words[most_sim_j]} ({matrix[i][most_sim_j]:.0%}) "
                  f"| furthest: {words[least_sim_j]} ({matrix[i][least_sim_j]:.0%})")
            if show_factors:
                print(f"{'':>16}primes={primes}")

        # Factor index: which words share each prime?
        if show_factors:
            from .algebra import nth_prime as _nth_prime
            factor_index = {}  # prime -> list of words
            for w in words:
                for p in sigs[w]['factors']:
                    factor_index.setdefault(p, []).append(w)

            # Sort by number of words sharing the factor (most shared first)
            sorted_factors = sorted(factor_index.items(),
                                    key=lambda x: len(x[1]), reverse=True)

            print("\n  FACTOR INDEX (what each prime means):")
            print(f"    {'prime':>8}  {'bit':>3}  {'words':>5}  shared by")
            print(f"    {'-'*8}  {'-'*3}  {'-'*5}  {'-'*30}")
            for prime, sharing_words in sorted_factors:
                # Find bit index for this prime
                bit_idx = next(
                    (i for i in range(self.n_bits) if _nth_prime(i + 1) == prime),
                    -1
                )
                count = len(sharing_words)
                label = ', '.join(sharing_words)
                if count == len(words):
                    label += '  [UNIVERSAL]'
                elif count == 1:
                    label += '  [UNIQUE]'
                print(f"    {prime:>8}  {bit_idx:>3}  {count:>5}  {label}")

        print(f"{'=' * 60}")

    return {
        'matrix': matrix,
        'words': words,
        'pairs_ranked': pairs,
        'signatures': sigs,
        'flagged': flagged,
    }

generate(input_ids, max_new_tokens=100, temperature=0.7, top_k=50)

Autoregressive text generation.

Source code in triadic-head-src/triadic-head/triadic_head/wrapper.py 
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@torch.no_grad()
def generate(self, input_ids, max_new_tokens=100, temperature=0.7, top_k=50):
    """Autoregressive text generation."""
    for _ in range(max_new_tokens):
        idx = input_ids[:, -self.block_size:]
        logits, _, _ = self(idx)
        logits = logits[:, -1, :] / temperature
        if top_k is not None:
            v, _ = torch.topk(logits, min(top_k, logits.size(-1)))
            logits[logits < v[:, [-1]]] = float('-inf')
        probs = F.softmax(logits, dim=-1)
        next_id = torch.multinomial(probs, num_samples=1)
        input_ids = torch.cat([input_ids, next_id], dim=1)
    return input_ids

triadic_params() -> int

Number of parameters in the triadic head only.

Source code in triadic-head-src/triadic-head/triadic_head/wrapper.py 
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def triadic_params(self) -> int:
    """Number of parameters in the triadic head only."""
    return sum(p.numel() for p in self.triadic_head.parameters())