"""Compile text into a Llama-format autocomplete model. No training. Every weight is set by a closed-form rule from n-gram counts; nothing is fit by gradient descent and no other model is used. The result is an exact transformer implementation of an interpolated n-gram language model (Witten-Bell or Kneser-Ney) over the source text. Residual stream layout (hidden_size = 1 + (n_prev + 1) * CODE_DIM + vocab): [0] constant 1 (acts as a bias, Llama has none) cur slot (CODE_DIM) code of the current token <- embedding prev1..n (CODE_DIM) codes of the 1..n previous tokens <- attention out slot (vocab) next-token logits, scaled by OUT_SCALE <- MLP Token codes are seeded random unit vectors (nearly orthogonal). Attention head a (a = 1..n_prev) has constant query/key vectors whose RoPE phases make the score peak at exactly a positions back; its value copies that token's code into slot prev_a. Positions before the start fall back to position 0 (BOS). The MLP has one neuron per kept context (1..n_prev+1 tokens) plus one always-on unigram neuron. A neuron's gate sums code matches across slots minus (k - 0.5), so it fires only when all k tokens match. It writes log p(next | ctx) - log p(next | shorter ctx) into the out slot. All suffixes of the true context fire together, so the sum telescopes to the log probability under the longest kept context. Compile settings live in compile_settings.json ("hf" for this dense model, "web" for the sparse browser export written by export_web.py). """ import json import math import zlib from collections import Counter, defaultdict from dataclasses import dataclass from pathlib import Path import numpy as np import torch from safetensors.torch import save_file from tokenizers import Tokenizer, decoders, models, normalizers, pre_tokenizers, processors from transformers import GenerationConfig, LlamaConfig, PreTrainedTokenizerFast ROOT = Path(__file__).parent PHRASE_DIR = ROOT / "phrases" # hand-written everyday phrases DATA_DIR = ROOT / "data" # human-written prompts/replies (scripts/fetch_coding_prompts.py) SETTINGS_PATH = ROOT / "compile_settings.json" EOS, UNK = "<|endoftext|>", "" # EOS doubles as BOS and pad, like GPT-2 EOS_ID, UNK_ID = 0, 1 SEED = 1234 CODE_DIM = 384 MAX_POS = 128 ATTN_MARGIN = 30.0 # min attention logit gap (nats) between target and any other position BETA = 100.0 # gate sharpness; matched neurons sit at z = BETA / 2 OUT_SCALE = 1e-5 # keeps the out slot tiny so the final RMSNorm scale stays fixed UNK_LOGIT = -30.0 ROPE_THETA_CANDIDATES = [2.0, 4.0, 8.0, 16.0, 32.0, 64.0, 128.0, 256.0, 1000.0, 10000.0] NORMALIZER = normalizers.Sequence([normalizers.NFKC(), normalizers.Lowercase()]) PRE_TOKENIZER = pre_tokenizers.ByteLevel(add_prefix_space=True) @dataclass(frozen=True) class Settings: n_prev: int = 3 # previous tokens attended to; context = n_prev + current token smoothing: str = "wb" # "wb" (Witten-Bell) or "kn" (interpolated Kneser-Ney) discount: float = 0.75 # Kneser-Ney absolute discount phrase_weight: float = 5.0 # weight of one hand-written phrase (phrases/*.txt) prompt_weight: float = 1.0 # weight of one user prompt (data/prompts.txt) reply_weight: float = 1.0 # weight of one assistant reply sentence (data/replies.txt) max_vocab: int = 3000 min_word_count: float = 3 min_count: float | None = None # None: smallest context count that fits param_target param_target: int = 400_000_000 @property def order(self) -> int: return self.n_prev + 1 def load_settings(name: str) -> Settings: return Settings(**json.loads(SETTINGS_PATH.read_text())[name]) # ---------- text ---------- def pieces(text: str) -> list[str]: return [p for p, _ in PRE_TOKENIZER.pre_tokenize_str(NORMALIZER.normalize_str(text))] def load_lines(paths: list[Path]) -> list[list[str]]: seen, out = set(), [] for path in paths: for line in path.read_text().splitlines(): line = line.strip() if not line or line.startswith("#"): continue toks = pieces(line) if tuple(toks) not in seen: seen.add(tuple(toks)) out.append(toks) return out def load_phrases() -> list[list[str]]: return load_lines(sorted(PHRASE_DIR.glob("*.txt"))) def load_sources() -> dict[str, list[list[str]]]: return { "phrases": load_phrases(), "prompts": load_lines([DATA_DIR / "prompts.txt"]), "replies": load_lines([DATA_DIR / "replies.txt"]), } def heldout_split(lines: list[list[str]], pct: int = 10) -> tuple[list, list]: """Deterministic split by content hash: (train, test).""" test = [t for t in lines if zlib.crc32(" ".join(t).encode()) % 100 < pct] train = [t for t in lines if zlib.crc32(" ".join(t).encode()) % 100 >= pct] return train, test # ---------- counting ---------- def weighted_sources(s: Settings, sources: dict) -> list[tuple[list[list[str]], float]]: weights = {"phrases": s.phrase_weight, "prompts": s.prompt_weight, "replies": s.reply_weight} return [(sources[name], w) for name, w in weights.items() if w > 0 and name in sources] def build_vocab(s: Settings, sources: dict) -> list[str]: freq = Counter() for lines, w in weighted_sources(s, sources): for toks in lines: for p in toks: freq[p] += w by_freq = lambda p: (-freq[p], p) # noqa: E731 hand = {p for t in sources["phrases"] for p in t} if s.phrase_weight > 0 else set() rest = sorted((p for p in freq if p not in hand and freq[p] >= s.min_word_count), key=by_freq) words = hand | set(rest[: max(0, s.max_vocab - 2 - len(hand))]) return [EOS, UNK] + sorted(words, key=by_freq) def padded_events(seq: list[int], order: int): """(contexts of length 0..order, next token) for every position of a sequence.""" # `order` BOS tokens: the last one is the real BOS position the model sees. padded = [EOS_ID] * order + seq + [EOS_ID] for i in range(order - 1, len(padded) - 1): yield [tuple(padded[i - k + 1 : i + 1]) if k else () for k in range(order + 1)], padded[i + 1] def count_ngrams(weighted: list[tuple[list[int], float]], order: int) -> list[defaultdict]: counts = [defaultdict(Counter) for _ in range(order + 1)] for seq, weight in weighted: for ctxs, nxt in padded_events(seq, order): if nxt == UNK_ID: # never learn to predict continue for k, ctx in enumerate(ctxs): counts[k][ctx][nxt] += weight return counts class NGram: """Interpolated n-gram over the kept contexts; the reference the weights must reproduce. Witten-Bell: p_k(j) = (c_j + u * p_{k-1}(j)) / (c + u) Kneser-Ney: p_k(j) = (c_j - d_j) / c + (sum_j d_j / c) * p_{k-1}(j), d_j = min(D, c_j), with continuation counts below the top order (KenLM-style) Both have the form p_k(j) = A_j + gamma * p_{k-1}(j), so each context's neuron can write log p_k(j) - log(gamma * p_{k-1}(j)) for its seen tokens and 0 elsewhere. """ def __init__(self, raw: list[dict], keep: list[set], vocab_size: int, s: Settings): self.s, self.V, self.order = s, vocab_size, s.order self.support = {ctx: sum(raw[k][ctx].values()) for k in range(1, self.order + 1) for ctx in keep[k]} if s.smoothing == "kn": cont = [defaultdict(Counter) for _ in range(self.order)] for k in range(self.order): for ctx, table in raw[k + 1].items(): for j in table: cont[k][ctx[1:]][j] += 1 self.tables = [cont[0][()]] + [{c: cont[k][c] for c in keep[k]} for k in range(1, self.order)] self.tables.append({c: raw[self.order][c] for c in keep[self.order]}) elif s.smoothing == "wb": self.tables = [raw[0][()]] + [{c: raw[k][c] for c in keep[k]} for k in range(1, self.order + 1)] else: raise ValueError(s.smoothing) for k in range(2, self.order + 1): assert all(c[1:] in self.tables[k - 1] for c in self.tables[k]), "backoff chain broken" uni = np.zeros(vocab_size) for j, c in self.tables[0].items(): uni[j] = c logits = np.log(uni + 1.0) # add-one smoothing logits[UNK_ID] = UNK_LOGIT self.base_logits = logits - logits[2:].mean() # constant shift; softmax-invariant p0 = np.exp(self.base_logits - self.base_logits.max()) self.p0 = p0 / p0.sum() self._prob, self._delta, self._stats = {}, {}, {} def _table_stats(self, ctx: tuple): if ctx not in self._stats: table = self.tables[len(ctx)][ctx] total = sum(table.values()) if self.s.smoothing == "wb": u = len(table) self._stats[ctx] = (table, {j: c / (total + u) for j, c in table.items()}, u / (total + u)) else: d = {j: min(self.s.discount, c) for j, c in table.items()} self._stats[ctx] = (table, {j: (c - d[j]) / total for j, c in table.items()}, sum(d.values()) / total) return self._stats[ctx] def prob(self, j: int, ctx: tuple) -> float: key = (j, ctx) if key not in self._prob: if not ctx: p = self.p0[j] else: lower = self.prob(j, ctx[1:]) if ctx in self.tables[len(ctx)]: _, a, gamma = self._table_stats(ctx) p = a.get(j, 0.0) + gamma * lower else: p = lower self._prob[key] = p return self._prob[key] def delta(self, ctx: tuple) -> dict[int, float]: """log p_k - log p_{k-1}, minus the constant log(gamma) shared by unseen tokens.""" if ctx not in self._delta: table, a, gamma = self._table_stats(ctx) out = {} for j in table: q = gamma * self.prob(j, ctx[1:]) out[j] = math.log(a[j] + q) - math.log(q) self._delta[ctx] = out return self._delta[ctx] def delta_arrays(self, ctx: tuple) -> tuple[np.ndarray, np.ndarray]: d = self.delta(ctx) return np.fromiter(d.keys(), dtype=np.int64, count=len(d)), np.fromiter(d.values(), dtype=np.float64, count=len(d)) def contexts(self) -> list[tuple]: return [ctx for k in range(1, self.order + 1) for ctx in sorted(self.tables[k])] def window(self, ids: list[int]) -> tuple: """Last order tokens (oldest .. current); positions before 0 read BOS like the attention heads.""" t = len(ids) - 1 return tuple(ids[max(t - a, 0)] for a in range(self.s.n_prev, -1, -1)) def predict(self, ids: list[int]) -> tuple[np.ndarray, float, int]: """(logits up to a constant, support of the longest matched context, its length).""" window = self.window(ids) logits = self.base_logits.copy() support, length = 0.0, 0 for k in range(1, self.order + 1): ctx = window[-k:] if ctx in self.tables[k]: idx, vals = self.delta_arrays(ctx) logits[idx] += vals support, length = self.support[ctx], k return logits, support, length def reference_logits(self, ids: list[int]) -> torch.Tensor: return torch.from_numpy(self.predict(ids)[0]) def compile_tables(s: Settings, sources: dict): """vocab, NGram and stats for settings s (min_count=None fits the dense param budget).""" vocab = build_vocab(s, sources) index = {p: i for i, p in enumerate(vocab)} weighted = [([index.get(p, UNK_ID) for p in toks], w) for lines, w in weighted_sources(s, sources) for toks in lines] raw = count_ngrams(weighted, s.order) forced = set() if s.phrase_weight > 0: for toks in sources["phrases"]: for ctxs, _ in padded_events([index[p] for p in toks], s.order): forced.update(ctxs[1:]) totals = {ctx: sum(t.values()) for k in range(1, s.order + 1) for ctx, t in raw[k].items()} min_count = s.min_count if min_count is None: # Smallest count threshold whose kept neurons (forced + total >= threshold) fit the budget. hist = Counter(0 if ctx in forced else c for ctx, c in totals.items()) thresholds = sorted(c for c in hist if c > 0) running, kept_at = hist[0], {} for c in reversed(thresholds): running += hist[c] kept_at[c] = running fits = [c for c in thresholds if dense_params(len(vocab), s.n_prev, 1 + kept_at[c]) <= s.param_target] if not fits: raise SystemExit("hand-written contexts alone exceed param_target; lower max_vocab") min_count = fits[0] keep = [set()] + [{c for c in raw[k] if c in forced or totals[c] >= min_count} for k in range(1, s.order + 1)] ngram = NGram(raw, keep, len(vocab), s) stats = { "vocab": len(vocab), "min_context_count": min_count, "contexts_seen": len(totals), "contexts_kept": sum(len(k) for k in keep), } return vocab, ngram, stats # ---------- dense transformer ---------- def hidden_size(V: int, n_prev: int) -> int: # transformers validates hidden_size % num_heads == 0; pad with unused zero dims. raw = 1 + (n_prev + 1) * CODE_DIM + V return -(-raw // (8 * n_prev)) * (8 * n_prev) def dense_params(V: int, n_prev: int, neurons: int) -> int: D, h = hidden_size(V, n_prev), CODE_DIM return 2 * V * D + (2 * n_prev + 2) * h * D + 3 * neurons * D + 3 * D def rope_attention_scale(head_dim: int, n_prev: int) -> tuple[float, torch.Tensor, float]: """Pick rope_theta maximizing the worst-case attention margin; return (theta, inv_freq, q_amp).""" best = None for theta in ROPE_THETA_CANDIDATES: inv_freq = 1.0 / (theta ** (torch.arange(0, head_dim, 2, dtype=torch.int64).double() / head_dim)) offsets = torch.arange(-MAX_POS, MAX_POS + 1, dtype=torch.float64) kernel = torch.cos(offsets[:, None] * inv_freq[None, :]).sum(1) # K(x), index x + MAX_POS worst = math.inf for lag in range(1, n_prev + 1): for t in range(MAX_POS): s_target = max(t - lag, 0) xs = torch.tensor([t - s - lag for s in range(t + 1)]) + MAX_POS scores = kernel[xs] others = torch.cat([scores[:s_target], scores[s_target + 1 :]]) if len(others): worst = min(worst, (scores[s_target] - others.max()).item()) if best is None or worst > best[0]: best = (worst, theta, inv_freq) worst, theta, inv_freq = best assert worst > 0, "no rope_theta separates positions" # score = q_amp * sum_i cos(...) / sqrt(head_dim) (key amplitude 1) q_amp = ATTN_MARGIN * math.sqrt(head_dim) / worst return theta, inv_freq, q_amp def build_dense(vocab: list[str], ngram: NGram, s: Settings): V, m, n_prev = len(vocab), CODE_DIM, s.n_prev contexts = ngram.contexts() N = 1 + len(contexts) CONST, CUR = 0, 1 prev_slot = [1 + a * m for a in range(n_prev + 1)] # prev_slot[0] is the cur slot OUT = 1 + (n_prev + 1) * m n_heads, h = n_prev, m D = hidden_size(V, n_prev) gen = torch.Generator().manual_seed(SEED) codes = torch.randn(V, m, generator=gen, dtype=torch.float64) codes /= codes.norm(dim=1, keepdim=True) gram = codes @ codes.T gram.fill_diagonal_(0) max_coherence = gram.abs().max().item() assert max_coherence < 0.4, max_coherence embed = torch.zeros(V, D, dtype=torch.float64) embed[:, CONST] = 1.0 embed[:, CUR : CUR + m] = codes theta, inv_freq, q_amp = rope_attention_scale(h, n_prev) half = h // 2 q_proj = torch.zeros(n_heads * h, D, dtype=torch.float64) for a in range(n_heads): lag = a + 1 q_proj[a * h : a * h + half, CONST] = q_amp * torch.cos(lag * inv_freq) q_proj[a * h + half : (a + 1) * h, CONST] = -q_amp * torch.sin(lag * inv_freq) k_proj = torch.zeros(h, D, dtype=torch.float64) k_proj[:half, CONST] = 1.0 v_proj = torch.zeros(h, D, dtype=torch.float64) v_proj[:, CUR : CUR + m] = torch.eye(m, dtype=torch.float64) o_proj = torch.zeros(D, n_heads * h, dtype=torch.float64) for a in range(n_heads): o_proj[prev_slot[a + 1] : prev_slot[a + 1] + m, a * h : (a + 1) * h] = torch.eye(m, dtype=torch.float64) # The MLP matrices dominate memory, so they are built directly in float32. gate = torch.zeros(N, D, dtype=torch.float32) up = torch.zeros(N, D, dtype=torch.float32) down = torch.zeros(D, N, dtype=torch.float32) on = (BETA / 2) * torch.sigmoid(torch.tensor(BETA / 2, dtype=torch.float64)).item() # silu(BETA/2) up[:, CONST] = 1.0 gate[0, CONST] = BETA / 2 # always-on unigram neuron down[OUT : OUT + V, 0] = torch.from_numpy(OUT_SCALE * ngram.base_logits / on).float() for n, ctx in enumerate(contexts, start=1): k = len(ctx) for a, tok in enumerate(reversed(ctx)): # a = 0 current, a = 1 previous, ... gate[n, prev_slot[a] : prev_slot[a] + m] = BETA * codes[tok] gate[n, CONST] = -BETA * (k - 0.5) for j, d in ngram.delta(ctx).items(): down[OUT + j, n] = OUT_SCALE * d / on lm_head = torch.zeros(V, D, dtype=torch.float64) lm_head[torch.arange(V), OUT + torch.arange(V)] = 1.0 / OUT_SCALE # RMSNorm weights undo the norm for the (fixed) input norms: |x|^2 = 2 before # attention, 1 + 1 + n_prev after it. attn_norm = math.sqrt(2 / D) mlp_norm = math.sqrt((2 + n_prev) / D) state = { "model.embed_tokens.weight": embed, "model.layers.0.input_layernorm.weight": torch.full((D,), attn_norm), "model.layers.0.self_attn.q_proj.weight": q_proj, "model.layers.0.self_attn.k_proj.weight": k_proj, "model.layers.0.self_attn.v_proj.weight": v_proj, "model.layers.0.self_attn.o_proj.weight": o_proj, "model.layers.0.post_attention_layernorm.weight": torch.full((D,), mlp_norm), "model.layers.0.mlp.gate_proj.weight": gate, "model.layers.0.mlp.up_proj.weight": up, "model.layers.0.mlp.down_proj.weight": down, "model.norm.weight": torch.full((D,), mlp_norm), "lm_head.weight": lm_head, } state = {k: v.to(torch.float32).contiguous() for k, v in state.items()} config = LlamaConfig( vocab_size=V, hidden_size=D, intermediate_size=N, num_hidden_layers=1, num_attention_heads=n_heads, num_key_value_heads=1, head_dim=h, hidden_act="silu", max_position_embeddings=MAX_POS, rms_norm_eps=1e-10, rope_theta=theta, tie_word_embeddings=False, bos_token_id=0, eos_token_id=0, pad_token_id=0, ) info = { "hidden": D, "neurons": N, "rope_theta": theta, "max_code_coherence": round(max_coherence, 3), "params": sum(t.numel() for t in state.values()), } return state, config, info def build_tokenizer(vocab: list[str]) -> PreTrainedTokenizerFast: tok = Tokenizer(models.WordLevel({p: i for i, p in enumerate(vocab)}, unk_token=UNK)) tok.normalizer = NORMALIZER tok.pre_tokenizer = PRE_TOKENIZER tok.decoder = decoders.ByteLevel() tok.post_processor = processors.TemplateProcessing(single=f"{EOS} $A", special_tokens=[(EOS, 0)]) return PreTrainedTokenizerFast( tokenizer_object=tok, bos_token=EOS, eos_token=EOS, unk_token=UNK, pad_token=EOS, clean_up_tokenization_spaces=False, model_max_length=MAX_POS, ) def compile_model(): """Build the dense ("hf") model in memory (used by the tests for the n-gram reference).""" s = load_settings("hf") sources = load_sources() vocab, ngram, stats = compile_tables(s, sources) state, config, info = build_dense(vocab, ngram, s) lines = {name: len(v) for name, v in sources.items()} return lines, vocab, ngram, state, config, {**stats, **info} def main() -> None: lines, vocab, _, state, config, info = compile_model() assert info["params"] <= 1_000_000_000, info save_file(state, ROOT / "model.safetensors", metadata={"format": "pt"}) config.save_pretrained(ROOT) cfg_path = ROOT / "config.json" cfg = json.loads(cfg_path.read_text()) cfg["architectures"] = ["LlamaForCausalLM"] cfg["rope_theta"] = info["rope_theta"] # transformers 4.x reads this key, 5.x reads rope_parameters cfg["torch_dtype"] = "float32" cfg_path.write_text(json.dumps(cfg, indent=2, sort_keys=True) + "\n") GenerationConfig(bos_token_id=0, eos_token_id=0, pad_token_id=0, do_sample=False, max_new_tokens=16).save_pretrained(ROOT) build_tokenizer(vocab).save_pretrained(ROOT) # transformers 5 writes "TokenizersBackend", which 4.x can't resolve; # PreTrainedTokenizerFast loads on both. 4.x also emits token_type_ids # by default, which Llama's generate() rejects, and overrides the # pre-tokenizer's add_prefix_space unless the config states it. tok_cfg_path = ROOT / "tokenizer_config.json" tok_cfg = json.loads(tok_cfg_path.read_text()) tok_cfg["tokenizer_class"] = "PreTrainedTokenizerFast" tok_cfg["add_prefix_space"] = True tok_cfg["model_input_names"] = ["input_ids", "attention_mask"] tok_cfg_path.write_text(json.dumps(tok_cfg, indent=2) + "\n") print(json.dumps({"lines": lines, **info}, indent=2)) if __name__ == "__main__": main()