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# Copyright (C) 2026 SnapKitty Collective
# SPDX-License-Identifier: AGPL-3.0-or-later
"""Tiny transformer implemented from scratch in NumPy (forward + backward).
This is the empirical validation vehicle: a small teacher is trained on
synthetic data, then the ENTIRE Tensor Roll pipeline (roll -> compress ->
distill -> finetune -> quantize -> .trq -> sandboxed inference) runs on it.
Same code path as the 30B scale-up; only the config and data change.
No torch / transformers / llama.cpp anywhere in this file.
"""
from __future__ import annotations
import time
from dataclasses import dataclass
import numpy as np
DTYPE = np.float32
EPS = 1e-5
@dataclass
class Config:
vocab: int = 32
d: int = 48
heads: int = 3
layers: int = 2
dff: int = 96
seq: int = 16
@property
def dh(self) -> int:
assert self.d % self.heads == 0
return self.d // self.heads
def to_dict(self):
return {"vocab": self.vocab, "d": self.d, "heads": self.heads,
"layers": self.layers, "dff": self.dff, "seq": self.seq}
@staticmethod
def from_dict(d):
return Config(**d)
def count_params(params: dict) -> int:
return int(sum(v.size for v in params.values()))
def init_params(rng: np.random.Generator, cfg: Config) -> dict:
def xavier(shape):
fan = shape[0] + shape[1] if len(shape) == 2 else shape[0]
lim = np.sqrt(6.0 / fan)
return rng.uniform(-lim, lim, size=shape).astype(DTYPE)
p = {"emb": xavier((cfg.vocab, cfg.d))}
for l in range(cfg.layers):
p[f"L{l}.ln1g"] = np.ones(cfg.d, dtype=DTYPE)
p[f"L{l}.ln1b"] = np.zeros(cfg.d, dtype=DTYPE)
for nm in ("Wq", "Wk", "Wv", "Wo"):
p[f"L{l}.{nm}"] = xavier((cfg.d, cfg.d))
p[f"L{l}.b{nm[1:]}"] = np.zeros(cfg.d, dtype=DTYPE)
p[f"L{l}.ln2g"] = np.ones(cfg.d, dtype=DTYPE)
p[f"L{l}.ln2b"] = np.zeros(cfg.d, dtype=DTYPE)
p[f"L{l}.W1"] = xavier((cfg.d, cfg.dff))
p[f"L{l}.b1"] = np.zeros(cfg.dff, dtype=DTYPE)
p[f"L{l}.W2"] = xavier((cfg.dff, cfg.d))
p[f"L{l}.b2"] = np.zeros(cfg.d, dtype=DTYPE)
p["lnfg"] = np.ones(cfg.d, dtype=DTYPE)
p["lnfb"] = np.zeros(cfg.d, dtype=DTYPE)
p["Whead"] = xavier((cfg.d, cfg.vocab))
p["bhead"] = np.zeros(cfg.vocab, dtype=DTYPE)
return p
# ---------------------------------------------------------------------------
# Forward
# ---------------------------------------------------------------------------
def _ln_forward(x, g, b):
mean = x.mean(axis=-1, keepdims=True)
var = x.var(axis=-1, keepdims=True)
std = np.sqrt(var + EPS)
xh = (x - mean) / std
return g * xh + b, (x, xh, std, g)
def _ln_backward(dy, cache):
x, xh, std, g = cache
n_feat = x.shape[-1]
dxh = dy * g
dvar = np.sum(dxh * (x - x.mean(axis=-1, keepdims=True))
* -0.5 * (std ** -3), axis=-1, keepdims=True)
dmean = (np.sum(dxh * -1.0 / std, axis=-1, keepdims=True)
+ dvar * np.mean(-2.0 * (x - x.mean(axis=-1, keepdims=True)), axis=-1, keepdims=True))
dx = dxh / std + dvar * 2.0 * (x - x.mean(axis=-1, keepdims=True)) / n_feat + dmean / n_feat
dg = np.sum(dy * xh, axis=(0, 1))
db = np.sum(dy, axis=(0, 1))
return dx, dg, db
def _softmax(x, axis=-1):
x = x - x.max(axis=axis, keepdims=True)
e = np.exp(x)
return e / e.sum(axis=axis, keepdims=True)
def forward(params: dict, cfg: Config, ids: np.ndarray):
"""Returns (logits, cache). ids: (B,T) int."""
B, T = ids.shape
H, dh = cfg.heads, cfg.dh
cache: dict = {"ids": ids}
x = params["emb"][ids] # (B,T,d)
cmask = np.zeros((T, T), dtype=DTYPE)
cmask[np.triu_indices(T, k=1)] = -1e9
for l in range(cfg.layers):
c: dict = {"x_prev": x}
h, c["ln1"] = _ln_forward(x, params[f"L{l}.ln1g"], params[f"L{l}.ln1b"])
Q = (h @ params[f"L{l}.Wq"] + params[f"L{l}.bq"]).reshape(B, T, H, dh)
K = (h @ params[f"L{l}.Wk"] + params[f"L{l}.bk"]).reshape(B, T, H, dh)
V = (h @ params[f"L{l}.Wv"] + params[f"L{l}.bv"]).reshape(B, T, H, dh)
s = np.einsum("bthd,bshd->bhts", Q, K) / np.sqrt(dh) + cmask[None, None, :, :]
P = _softmax(s)
A = np.einsum("bhts,bshd->bthd", P, V).reshape(B, T, cfg.d)
O = A @ params[f"L{l}.Wo"] + params[f"L{l}.bo"]
y = x + O
z, c["ln2"] = _ln_forward(y, params[f"L{l}.ln2g"], params[f"L{l}.ln2b"])
u = z @ params[f"L{l}.W1"] + params[f"L{l}.b1"]
a = np.maximum(u, 0)
m_ = a @ params[f"L{l}.W2"] + params[f"L{l}.b2"]
x = y + m_
c.update({"h": h, "Q": Q, "K": K, "V": V, "P": P, "A": A,
"y": y, "z": z, "u": u, "a": a})
cache[f"L{l}"] = c
f, cache["lnf"] = _ln_forward(x, params["lnfg"], params["lnfb"])
cache["f"] = f
cache["x_pre_lnf"] = x
logits = f @ params["Whead"] + params["bhead"]
return logits, cache
def backward(params: dict, cfg: Config, cache: dict, dlogits: np.ndarray,
d_hiddens: dict | None = None, d_attn: dict | None = None) -> dict:
"""dlogits: (B,T,V). d_hiddens: {layer_idx: (B,T,d) upstream grad added
at that layer's output} for hidden-state matching. d_attn: {layer_idx:
(B,H,T,T) upstream grad added to attention probs} for attention matching."""
B, T = cache["ids"].shape
grads = {}
f = cache["f"]
grads["Whead"] = np.einsum("btd,btv->dv", f, dlogits)
grads["bhead"] = dlogits.sum(axis=(0, 1))
df = dlogits @ params["Whead"].T
dx, dg, db = _ln_backward(df, cache["lnf"])
grads["lnfg"], grads["lnfb"] = dg, db
for l in reversed(range(cfg.layers)):
c = cache[f"L{l}"]
if d_hiddens and l in d_hiddens:
dx = dx + d_hiddens[l]
# x = y + m ; m = a@W2+b2
dy = dx.copy()
dm = dx
A = c["A"]
grads[f"L{l}.W2"] = np.einsum("bti,btj->ij", c["a"], dm)
grads[f"L{l}.b2"] = dm.sum(axis=(0, 1))
da = dm @ params[f"L{l}.W2"].T
du = da * (c["u"] > 0)
grads[f"L{l}.W1"] = np.einsum("bti,btj->ij", c["z"], du)
grads[f"L{l}.b1"] = du.sum(axis=(0, 1))
dz = du @ params[f"L{l}.W1"].T
dy2, dg2, db2 = _ln_backward(dz, c["ln2"])
grads[f"L{l}.ln2g"], grads[f"L{l}.ln2b"] = dg2, db2
dy = dy + dy2
# y = x_prev + O ; O = A@Wo+bo
dx_prev = dy.copy()
dO = dy
grads[f"L{l}.Wo"] = np.einsum("bti,btj->ij", A, dO)
grads[f"L{l}.bo"] = dO.sum(axis=(0, 1))
dA = (dO @ params[f"L{l}.Wo"].T).reshape(B, T, cfg.heads, cfg.dh)
Q, K, V, P = c["Q"], c["K"], c["V"], c["P"]
dP = np.einsum("bthd,bshd->bhts", dA, V)
if d_attn is not None and l in d_attn:
dP = dP + d_attn[l]
dV = np.einsum("bhts,bthd->bshd", P, dA)
dS = P * (dP - (dP * P).sum(axis=-1, keepdims=True))
inv = 1.0 / np.sqrt(cfg.dh)
dQ = np.einsum("bhts,bshd->bthd", dS, K) * inv
dK = np.einsum("bhts,bthd->bshd", dS, Q) * inv
h = c["h"]
for nm, dM in (("Wq", dQ), ("Wk", dK), ("Wv", dV)):
dM2 = dM.reshape(B, T, cfg.d)
grads[f"L{l}.{nm}"] = np.einsum("bti,btj->ij", h, dM2)
grads[f"L{l}.b{nm[1:]}"] = dM2.sum(axis=(0, 1))
dx_prev = dx_prev + dM2 @ params[f"L{l}.{nm}"].T
dh, dg1, db1 = _ln_backward(dx_prev, c["ln1"])
grads[f"L{l}.ln1g"], grads[f"L{l}.ln1b"] = dg1, db1
dx = dh # grad w.r.t. this layer's input = next (previous) layer's output grad
dEmb = np.zeros_like(params["emb"])
np.add.at(dEmb, cache["ids"], dx)
grads["emb"] = dEmb
return grads
# ---------------------------------------------------------------------------
# Losses
# ---------------------------------------------------------------------------
def ce_loss(logits: np.ndarray, targets: np.ndarray):
"""Mean softmax cross-entropy. Returns (loss, dlogits)."""
B, T, V = logits.shape
x = logits.reshape(-1, V).astype(np.float64)
t = targets.reshape(-1)
x = x - x.max(axis=1, keepdims=True)
logp = x - np.log(np.exp(x).sum(axis=1, keepdims=True))
loss = float(-logp[np.arange(t.size), t].mean())
d = np.exp(logp)
d[np.arange(t.size), t] -= 1.0
d /= t.size
return loss, d.reshape(B, T, V).astype(DTYPE)
def kl_loss(s_logits: np.ndarray, t_logits: np.ndarray, tau: float = 2.0):
"""tau^2 * mean KL(softmax(t/tau) || softmax(s/tau)). Returns (loss, dlogits_s)."""
B, T, V = s_logits.shape
s = (s_logits / tau).reshape(-1, V).astype(np.float64)
t = (t_logits / tau).reshape(-1, V).astype(np.float64)
s = s - s.max(1, keepdims=True)
t = t - t.max(1, keepdims=True)
log_q = s - np.log(np.exp(s).sum(1, keepdims=True))
log_p = t - np.log(np.exp(t).sum(1, keepdims=True))
p = np.exp(log_p)
kl = (p * (log_p - log_q)).sum(1).mean()
loss = float(tau * tau * kl)
d = (np.exp(log_q) - p) * tau / p.shape[0]
return loss, d.reshape(B, T, V).astype(DTYPE)
def kl_divergence_mean(t_logits: np.ndarray, s_logits: np.ndarray) -> float:
"""Mean KL(teacher || student) at tau=1 — teacher-divergence metric."""
t = t_logits.reshape(-1, t_logits.shape[-1]).astype(np.float64)
s = s_logits.reshape(-1, s_logits.shape[-1]).astype(np.float64)
t = t - t.max(1, keepdims=True)
s = s - s.max(1, keepdims=True)
log_p = t - np.log(np.exp(t).sum(1, keepdims=True))
log_q = s - np.log(np.exp(s).sum(1, keepdims=True))
p = np.exp(log_p)
return float((p * (log_p - log_q)).sum(1).mean())
# ---------------------------------------------------------------------------
# Optimizer
# ---------------------------------------------------------------------------
class Adam:
def __init__(self, params: dict, lr: float = 3e-3,
beta1: float = 0.9, beta2: float = 0.999, eps: float = 1e-8):
self.lr = lr
self.b1, self.b2, self.eps = beta1, beta2, eps
self.m = {k: np.zeros_like(v) for k, v in params.items()}
self.v = {k: np.zeros_like(v) for k, v in params.items()}
self.t = 0
def step(self, params: dict, grads: dict):
self.t += 1
for k in params:
g = grads[k].astype(np.float64)
self.m[k] = self.b1 * self.m[k] + (1 - self.b1) * g
self.v[k] = self.b2 * self.v[k] + (1 - self.b2) * g * g
mh = self.m[k] / (1 - self.b1 ** self.t)
vh = self.v[k] / (1 - self.b2 ** self.t)
params[k] = (params[k].astype(np.float64)
- self.lr * mh / (np.sqrt(vh) + self.eps)).astype(DTYPE)
# ---------------------------------------------------------------------------
# Synthetic data + training
# ---------------------------------------------------------------------------
def gen_data(rng: np.random.Generator, n: int, cfg: Config) -> np.ndarray:
"""Deterministic grammar: x[t] = (3*x[t-1] + 5*x[t-2] + 7) mod V."""
ids = np.zeros((n, cfg.seq), dtype=np.int64)
ids[:, 0] = rng.integers(0, cfg.vocab, size=n)
ids[:, 1] = rng.integers(0, cfg.vocab, size=n)
for t in range(2, cfg.seq):
ids[:, t] = (3 * ids[:, t - 1] + 5 * ids[:, t - 2] + 7) % cfg.vocab
return ids
def train_teacher(cfg: Config, *, steps: int, batch: int, lr: float,
seed: int, log_every: int = 100):
rng = np.random.default_rng(seed)
params = init_params(rng, cfg)
opt = Adam(params, lr=lr)
history = []
t0 = time.perf_counter()
for step in range(1, steps + 1):
ids = gen_data(rng, batch, cfg)
logits, cache = forward(params, cfg, ids[:, :-1])
loss, dl = ce_loss(logits, ids[:, 1:])
grads = backward(params, cfg, cache, dl)
opt.step(params, grads)
if step % log_every == 0 or step == steps:
history.append({"step": step, "loss": loss,
"elapsed_s": time.perf_counter() - t0})
return params, history
def eval_metrics(params: dict, cfg: Config, *, batches: int = 8,
batch: int = 256, seed: int = 999):
"""Real held-out accuracy + loss on the synthetic grammar."""
rng = np.random.default_rng(seed)
tot_loss, tot_correct, tot_n = 0.0, 0, 0
for _ in range(batches):
ids = gen_data(rng, batch, cfg)
logits, _ = forward(params, cfg, ids[:, :-1])
loss, _ = ce_loss(logits, ids[:, 1:])
pred = logits.argmax(axis=-1)
tot_loss += loss
tot_correct += int((pred == ids[:, 1:]).sum())
tot_n += batch
return {"loss": tot_loss / batches, "accuracy": tot_correct / (tot_n * (cfg.seq - 1))}
def _act_input(name: str, cache: dict, cfg: Config):
"""Input activation feeding the op that owns tensor `name`, taken from
a real forward cache. Returns None when not attributable."""
if name == "emb":
return cache["L0"]["x_prev"]
if name in ("Whead", "bhead"):
return cache["f"]
if name in ("lnfg", "lnfb"):
return cache["x_pre_lnf"]
if name.startswith("L"):
_, rest = name.split(".", 1)
l = name[1:].split(".")[0]
c = cache[f"L{l}"]
if rest in ("Wq", "Wk", "Wv", "bq", "bk", "bv"):
return c["h"]
if rest in ("Wo", "bo"):
return c["A"]
if rest in ("W1", "b1"):
return c["z"]
if rest in ("W2", "b2"):
return c["a"]
if rest in ("ln1g", "ln1b"):
return c["x_prev"]
if rest in ("ln2g", "ln2b"):
return c["y"]
return None
def measure_tensor_stats(params: dict, cfg: Config, batches: int = 4,
batch: int = 64, seed: int = 0) -> dict:
"""Measured per-tensor contributions over real forward/backward passes.
activation contribution: RMS of the input activation feeding each
tensor's op, averaged over batches (from the forward cache).
gradient contribution: mean Frobenius norm of the tensor's gradient,
plus the relative ||grad|| / ||W||.
Returns {tensor_name: {"act_rms": float, "grad_norm": float,
"grad_rel": float}}.
"""
rng = np.random.default_rng(seed)
acc_a, acc_g, n = {}, {}, 0
for _ in range(batches):
ids = gen_data(rng, batch, cfg)
logits, cache = forward(params, cfg, ids[:, :-1])
_, dlogits = ce_loss(logits, ids[:, 1:])
grads = backward(params, cfg, cache, dlogits)
n += 1
for k, W in params.items():
ai = _act_input(k, cache, cfg)
if ai is not None:
v = float(np.sqrt(np.mean(np.asarray(ai, dtype=np.float64) ** 2)))
acc_a[k] = acc_a.get(k, 0.0) + v
g = grads.get(k)
if g is not None:
acc_g[k] = acc_g.get(k, 0.0) + float(np.linalg.norm(g))
stats = {}
for k, W in params.items():
wn = float(np.linalg.norm(W))
gn = acc_g.get(k, 0.0) / n
stats[k] = {
"act_rms": acc_a.get(k, 0.0) / n if k in acc_a else None,
"grad_norm": gn,
"grad_rel": gn / (wn + 1e-12),
}
return stats
# ---------------------------------------------------------------------------
# Generation (greedy; streaming-capable)
# ---------------------------------------------------------------------------
def generate(params: dict, cfg: Config, prompt, max_tokens: int,
seed: int = 0):
"""Greedy generation. Returns (tokens, tokens_per_sec, elapsed_s)."""
return _generate_impl(params, cfg, prompt, max_tokens, on_token=None)
def generate_stream(params: dict, cfg: Config, prompt, max_tokens: int,
seed: int = 0, on_token=None):
"""Greedy generation, yielding each token as produced (true streaming).
Returns (tokens, tokens_per_sec, elapsed_s)."""
return _generate_impl(params, cfg, prompt, max_tokens, on_token=on_token)
def _generate_impl(params: dict, cfg: Config, prompt, max_tokens: int,
on_token):
ids = np.array([list(prompt)], dtype=np.int64)
out = []
t0 = time.perf_counter()
for _ in range(max_tokens):
ctx = ids[:, -cfg.seq:]
logits, _ = forward(params, cfg, ctx)
nxt = int(logits[0, -1].argmax())
out.append(nxt)
if on_token is not None:
on_token(nxt)
ids = np.concatenate([ids, [[nxt]]], axis=1)
dt = time.perf_counter() - t0
tps = len(out) / dt if dt > 0 else 0.0
return out, tps, dt
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