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Everything here finishes in minutes. The long generation runs are in
paper_runs.py.
"""
from __future__ import annotations
import hashlib
import json
import os
import sys
import time
from typing import Dict, List
sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
REPO = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
def runs_path(name: str) -> str:
d = os.path.join(REPO, "paper", "runs")
os.makedirs(d, exist_ok=True)
return os.path.join(d, name)
R: Dict = {}
def sha(b: bytes) -> str:
return hashlib.sha256(b).hexdigest()
def family_files() -> List[str]:
files = [os.path.join(REPO, "neural_computer.safetensors")]
vdir = os.path.join(REPO, "variants")
files += sorted(os.path.join(vdir, f) for f in os.listdir(vdir)
if f.endswith(".safetensors"))
return files
# ---------------------------------------------------------------------------
def check_codec():
from selfrep import describe, describe_literal, decode
print("[1] Recipe language")
files = family_files()
total = 0
bad = 0
tape_total = 0
for p in files:
data = open(p, "rb").read()
r = describe(data)
if decode(r) != data:
bad += 1
total += len(data)
tape_total += len(r)
print(f" delta(describe(f)) = f on all {len(files)} artifact files "
f"({total:,} bytes -> {tape_total:,} bytes of recipe): "
f"{'all exact' if bad == 0 else f'{bad} FAILED'}")
# the length bound of the completeness lemma, with c1 = 1, c2 = 127, c3 = 1
worst = 0.0
lb = 0
for p in files:
data = open(p, "rb").read()
rl = describe_literal(data)
assert decode(rl) == data
bound = len(data) + -(-len(data) // 127) + 1
assert len(rl) == bound, (len(rl), bound)
lb += 1
# exhaustive on short strings
import random
rng = random.Random(0)
ebad = 0
for n in range(0, 600):
s = bytes(rng.randrange(256) for _ in range(n))
for enc in (describe, describe_literal):
r = enc(s)
if decode(r) != s:
ebad += 1
if len(describe_literal(s)) != len(s) + -(-len(s) // 127) + 1:
ebad += 1
print(f" literal encoding meets |r| = |f| + ceil(|f|/127) + 1 on all "
f"{len(files)} files and on 600 random strings: "
f"{'exact' if ebad == 0 else 'FAILED'}")
R["codec"] = {"files": len(files), "bytes": total, "recipe_bytes": tape_total,
"roundtrip_failures": bad, "bound_failures": ebad}
# ---------------------------------------------------------------------------
def check_framing():
from selfrep import ser, inst, M_STAR, M_P, read_host, tau_star, describe
print("[2] Framing")
sigma = read_host()
bad = 0
cases = [(sigma, M_STAR, tau_star(sigma, M_STAR)),
(sigma, M_P, describe(b"")),
(b"", M_P, b"\x00"),
(b"\x00" * 3, M_STAR, b"")]
for sg, m, tau in cases:
s = ser(sg, bytes(m), tau)
got = inst(s)
if got != (sg, bytes(m), tau):
bad += 1
print(f" inst(ser(Omega)) = Omega on {len(cases)} instances: "
f"{'exact' if bad == 0 else 'FAILED'}")
R["framing"] = {"cases": len(cases), "failures": bad}
# ---------------------------------------------------------------------------
def check_serialization():
"""Under the canonical specification, rebuilding the host from source
reproduces its distributed encoding byte for byte, and two independent
builds agree."""
print("[3] Canonical serialization")
import struct
from selfrep import read_host, sigma_host
from check_sigma import resigma
original = read_host()
rebuilt = sigma_host()
deterministic = sigma_host() == rebuilt
same = rebuilt == original
round_trip = resigma(original) == original
print(f" rebuild from source is byte-identical: {same} "
f"({len(original):,} bytes, sha {sha(original)[:16]})")
print(f" two independent builds agree: {deterministic}")
print(f" the netlist the encoding denotes serializes back to it: "
f"{round_trip}")
n = struct.unpack("<Q", original[:8])[0]
hdr = json.loads(original[8:8 + n])
meta = hdr.pop("__metadata__", {})
keys = list(hdr)
dtypes = sorted({v["dtype"] for v in hdr.values()})
order = {"F64": 0, "F32": 1, "F16": 2, "I64": 3, "I32": 4, "I16": 5,
"I8": 6, "U8": 7, "BOOL": 8}
by_dtype_name = keys == sorted(keys, key=lambda k: (order[hdr[k]["dtype"]], k))
pad = len(original[8:8 + n]) - len(original[8:8 + n].rstrip(b" "))
print(f" header {n:,} bytes, {len(keys)} tensors, dtypes {dtypes}, "
f"metadata keys {sorted(meta)}")
print(f" tensor entries ordered by (element type, name): {by_dtype_name}; "
f"data begins at {8+n:,}, 8-aligned: {(8 + n) % 8 == 0}, "
f"{pad} bytes of padding")
R["serialization"] = {"byte_identical": same, "deterministic": deterministic,
"round_trip": round_trip,
"bytes": len(original), "sha256": sha(original),
"header_bytes": n, "tensors": len(keys),
"dtypes": dtypes, "metadata_keys": sorted(meta),
"ordered_by_dtype_then_name": by_dtype_name,
"data_offset": 8 + n, "header_padding": pad}
# ---------------------------------------------------------------------------
def _batch_vectors(m, p, device):
"""State vectors for a batch of (memory image, counter) pairs."""
import torch
v = torch.zeros(len(p), 2057, device=device)
for k in range(8):
v[:, k] = ((p >> (7 - k)) & 1).float()
v[:, 9 + k::8] = ((m >> (7 - k)) & 1).float()
return v
def _bytes_of(v):
"""The counter and the 256 memory bytes of every state of a batch."""
import torch
pw = torch.tensor([1 << (7 - k) for k in range(8)], dtype=torch.long,
device=v.device)
q = v.detach().long()
pc = (q[:, :8] * pw).sum(1)
mem = (q[:, 9:].reshape(q.shape[0], 256, 8) * pw).sum(2)
return pc, mem
def _reference_batch(mem, pc):
"""One step of Definition 3.1 on a batch of memory images and counters."""
import torch
take = lambda idx: mem.gather(1, idx.unsqueeze(1)).squeeze(1)
A = take(pc)
B = take((pc + 1) & 0xFF)
C = take((pc + 2) & 0xFF)
r = (take(B) - take(A)) & 0xFF
out = mem.clone()
out.scatter_(1, B.unsqueeze(1), r.unsqueeze(1))
leq = (r == 0) | (r >= 0x80)
return out, torch.where(leq, C, (pc + 3) & 0xFF)
def check_host_datapath():
"""One step of the netlist that sigma(N_host) denotes, against
Definition 3.1, over all 2^16 operand pairs and all 2^16 (pc, C) pairs."""
print("[4] Host datapath")
import torch
from selfrep import NetEvaluator, read_host
device = "cuda" if torch.cuda.is_available() else "cpu"
E = NetEvaluator(read_host(), device=device)
def sweep(mems, pcs, chunk=256):
bad = 0
for i in range(0, len(pcs), chunk):
m = mems[i:i + chunk].to(device)
p = pcs[i:i + chunk].to(device)
got_pc, got_mem = _bytes_of(E.step(_batch_vectors(m, p, device)))
want_mem, want_pc = _reference_batch(m, p)
bad += int(((got_mem != want_mem).any(1)
| (got_pc != want_pc)).sum())
return bad
a = torch.arange(65536) % 256
b = torch.arange(65536) // 256
mems = torch.zeros(65536, 256, dtype=torch.long)
mems[:, 0], mems[:, 1], mems[:, 2] = 0x90, 0x91, 0x30
mems[:, 0x90] = a
mems[:, 0x91] = b
bad_ops = sweep(mems, torch.zeros(65536, dtype=torch.long))
print(f" one step against Definition 3.1 over all 65,536 operand pairs: "
f"{'exact' if bad_ops == 0 else f'{bad_ops} FAILED'}")
pc = torch.arange(65536) // 256
c = torch.arange(65536) % 256
mems = torch.zeros(65536, 256, dtype=torch.long)
mems[:, 0xA0], mems[:, 0xA1] = 4, 5
rows = torch.arange(65536)
mems[rows, pc] = 0xA0
mems[rows, (pc + 1) % 256] = 0xA1
mems[rows, (pc + 2) % 256] = c
bad_ctr = sweep(mems, pc)
print(f" one step against Definition 3.1 over all 65,536 (pc, C) pairs, "
f"the counter wrapping across the top of memory: "
f"{'exact' if bad_ctr == 0 else f'{bad_ctr} FAILED'}")
R["datapath"] = {"operand_pairs": 65536, "operand_failures": bad_ops,
"counter_pairs": 65536, "counter_failures": bad_ctr}
# ---------------------------------------------------------------------------
def check_interpreter():
"""One-record semantics exhaustively over record fields, and the dependence
hypothesis of the size proposition."""
print("[5] Interpreter U")
import torch
from reflect import (Cfg, build_net, Leveled, encode_gate, encode_netlist,
pad, ref_step, state_to_vec, vec_to_state)
cfg = Cfg()
net, inputs, outputs = build_net(cfg)
lev = Leveled(net, inputs, outputs, device="cpu")
def U(sig, gp, halt=0):
v = state_to_vec(cfg, {"sig": sig, "gp": gp, "halt": halt}).unsqueeze(0)
out = lev.step(v[:, :len(inputs)])[0]
return vec_to_state(cfg, out)
ra, rb, ro = cfg.WORK_BASE, cfg.WORK_BASE + 1, cfg.WORK_BASE + 2
bad = total = 0
for w0 in (-1, 0, 1):
for w1 in (-1, 0, 1):
for bias in range(-(1 << (cfg.BB - 1)), 1 << (cfg.BB - 1)):
nl = encode_netlist(cfg, [([(ra, w0, 0), (rb, w1, 0)], bias, (ro, 0))])
for va in (0, 1):
for vb in (0, 1):
sig = [0] * cfg.S
sig[cfg.NET0:cfg.NET0 + len(nl)] = nl
sig[ra], sig[rb] = va, vb
g = U(sig, 0)
exp = 1 if w0 * va + w1 * vb + bias >= 0 else 0
total += 1
if g["sig"][ro] != exp or g["gp"] != 1:
bad += 1
print(f" one-record semantics over all {total} (w0,w1,bias,x0,x1) "
f"configurations: {'exact' if bad == 0 else f'{bad} FAILED'}")
# record counter advances modulo G
cbad = 0
nl = encode_netlist(cfg, [])
for gp in range(cfg.G):
sig = [0] * cfg.S
sig[cfg.NET0:cfg.NET0 + len(nl)] = nl
g = U(sig, gp)
if g["gp"] != (gp + 1) % cfg.G:
cbad += 1
print(f" record counter advances mod G on all {cfg.G} values: "
f"{'exact' if cbad == 0 else 'FAILED'}")
# dependence hypothesis of the size proposition: for every record-region
# coordinate q, exhibit a state x and a data coordinate s with
# U(x)_s != U(x xor e_q)_s. A random state rarely witnesses this, because a
# random output address lands in the 106-bit data region about one time in
# ten; the targeted pass of check_dependence forces the record under test to
# write into the data region and makes the tested field decisive.
import random
from check_dependence import targeted
def U1(sig, gp):
return U(sig, gp)["sig"]
rng = random.Random(20260910)
D0, D1 = cfg.WORK_BASE, cfg.NET0
Q0 = cfg.NET0
Qbits = list(range(Q0, Q0 + cfg.G * cfg.R))
influenced = set()
for q in Qbits:
g, r = divmod(q - Q0, cfg.R)
found = 0
for attempt in range(160):
slots = [(rng.randrange(D0, D1 - 1), rng.choice((-1, 0, 1)),
rng.randint(0, 1)) for _ in range(2)]
bias = rng.randrange(-(1 << (cfg.BB - 1)), 1 << (cfg.BB - 1))
out = (rng.randrange(D0, D1 - 1), rng.randint(0, 1))
rec = encode_gate(cfg, pad(cfg, slots), bias, out)
sig = [0] * cfg.S
for d in range(D0, D1):
sig[d] = rng.randint(0, 1)
ptr = rng.choice((0, 1, 2, 3))
for k in range(cfg.A):
sig[cfg.PTR_BASE + k] = (ptr >> (cfg.A - 1 - k)) & 1
base = cfg.bank_base(0) + g * cfg.R
sig[base:base + cfg.R] = rec
s0, s1 = list(sig), list(sig)
s1[q] ^= 1
a0, a1 = U1(s0, g), U1(s1, g)
if any(a0[d] != a1[d] for d in range(D0, D1)):
found = attempt + 1
break
if not found:
found = targeted(cfg, U1, rng, q, g, r, D0, D1)
if found:
influenced.add(q)
print(f" every one of the {len(Qbits)} record-region bits influences some "
f"data-region bit of U(x): {len(influenced)}/{len(Qbits)}"
f"{' (hypothesis holds)' if len(influenced) == len(Qbits) else ' FAILED'}")
R["interpreter"] = {
"onerecord_cases": total, "onerecord_failures": bad,
"counter_failures": cbad,
"Q_bits": len(Qbits), "influencing": len(influenced),
"S": cfg.S, "G": cfg.G, "R": cfg.R, "b": cfg.R,
"Q_size": cfg.G * cfg.R, "records_max": (cfg.G * cfg.R) // cfg.R,
"units_lower_bound": (cfg.G * cfg.R + 1) // 2,
}
print(f" |Q| = {cfg.G*cfg.R}, b = {cfg.R}: at most {(cfg.G*cfg.R)//cfg.R} "
f"records stored; any fan-in-2 netlist realising U has at least "
f"{(cfg.G*cfg.R+1)//2} units")
# ---------------------------------------------------------------------------
def check_lev_sparse_dense():
"""The sparse and dense evaluations of Lev(N_host) agree."""
print("[6] Lev(N_host): sparse vs dense")
import torch
from selfrep import LevEvaluator, NetEvaluator, read_host
sigma = read_host()
dense = LevEvaluator(sigma, device="cpu", dense=True)
sparse = LevEvaluator(sigma, device="cpu", dense=False)
netl = NetEvaluator(sigma, device="cpu")
gen = torch.Generator().manual_seed(4242)
V = (torch.rand(64, LevEvaluator.N, generator=gen) < 0.5).float()
a = dense.step(V)
b = sparse.step(V)
c = netl.step(V)
same = bool((a == b).all()) and bool((a == c).all())
print(f" identical next state on 64 uniformly random states: {same}")
print(f" dense: {dense.info['layers']} layers, max width "
f"{dense.info['max_width']}, {dense.info['total_weights']:,} entries")
R["lev"] = {"sparse_dense_agree": same,
"layers": dense.info["layers"],
"max_width": dense.info["max_width"],
"total_weights": dense.info["total_weights"]}
def main() -> int:
t0 = time.perf_counter()
check_codec()
check_framing()
check_serialization()
check_host_datapath()
check_interpreter()
check_lev_sparse_dense()
R["seconds"] = time.perf_counter() - t0
path = runs_path("paper_verify.json")
json.dump(R, open(path, "w"), indent=1)
print(f"\nwrote {path} ({R['seconds']:.0f}s)")
return 0
if __name__ == "__main__":
sys.exit(main())
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