Designed zero-weight 9x9 Go policy network
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Designed zero-weight 9x9 Go policy network
Agent
Codex
Model
GPT 6 Astra
Started
Nov 3, 3:09 AM
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Implemented zero-initialized policy network.
BuildSaved tensors and summarized design heuristics.
Verifyimport numpy as np
# Hand-designed policy circuit. No training, game simulation, or network execution.N = 81H = 512OFFSET = 128.0
params = {}for k in range(1, 7): params[f"L{k}.W"] = np.zeros((243 if k == 1 else H, H), np.float32) params[f"L{k}.b"] = np.zeros(H, np.float32)params["out.W"] = np.zeros((H, 82), np.float32)params["out.b"] = np.zeros(82, np.float32)
def unit(channel, point): return channel * N + point
def point(r, c): return r * 9 + c
coords = [divmod(p, 9) for p in range(N)]neighbors = []diagonals = []for r, c in coords: neighbors.append([ point(r + dr, c + dc) for dr, dc in ((-1, 0), (1, 0), (0, -1), (0, 1)) if 0 <= r + dr < 9 and 0 <= c + dc < 9 ]) diagonals.append([ point(r + dr, c + dc) for dr, dc in ((-1, -1), (-1, 1), (1, -1), (1, 1)) if 0 <= r + dr < 9 and 0 <= c + dc < 9 ])
# Density, friendly shape, and opponent approach kernels.kernels = { (0, 1): (1.000, 0.550, -0.650), (1, 1): (0.750, 0.700, 0.100), (0, 2): (0.700, 0.750, 0.250), (1, 2): (0.420, 0.450, 0.120), (2, 2): (0.180, 0.120, 0.000), (0, 3): (0.200, 0.200, 0.030), (1, 3): (0.120, 0.120, 0.020), (2, 3): (0.050, 0.040, 0.000), (3, 3): (0.025, 0.015, 0.000), (0, 4): (0.055, 0.030, 0.000), (1, 4): (0.035, 0.020, 0.000), (2, 4): (0.015, 0.000, 0.000),}
density = np.zeros((N, N), np.float32)friendly_shape = np.zeros((N, N), np.float32)enemy_shape = np.zeros((N, N), np.float32)
full_density_mass = 0.0for dr in range(-4, 5): for dc in range(-4, 5): full_density_mass += kernels.get( tuple(sorted((abs(dr), abs(dc)))), (0.0, 0.0, 0.0) )[0]
for p, (r, c) in enumerate(coords): for q, (s, t) in enumerate(coords): d, f, e = kernels.get( tuple(sorted((abs(r - s), abs(c - t)))), (0.0, 0.0, 0.0), ) density[p, q] = d friendly_shape[p, q] = f enemy_shape[p, q] = e factor = min( 1.65, np.sqrt(full_density_mass / float(density[p].sum())) ) density[p] *= factor
TOTAL, WHITE, OWN_COUNT, OPP_COUNT = 486, 487, 488, 489PHASE, LATE, AHEAD, BEHIND = 490, 491, 492, 493
# L1: stones, direct liberties on stones, and territorial density penalties.W, b = params["L1.W"], params["L1.b"]for p in range(N): W[3*p, unit(0, p)] = 1.0 W[3*p+1, unit(1, p)] = 1.0
for color, channel in ((0, 2), (1, 3)): j = unit(channel, p) b[j] = len(neighbors[p]) - 4.0 W[3*p+color, j] += 4.0 for q in neighbors[p]: W[3*q, j] -= 1.0 W[3*q+1, j] -= 1.0
j_own, j_opp = unit(4, p), unit(5, p) b[j_own], b[j_opp] = -2.4, -2.1 for q in range(N): d = density[p, q] if d: W[3*q, j_own] += d W[3*q+1, j_own] -= 0.7*d W[3*q+1, j_opp] += d W[3*q, j_opp] -= 0.7*d
W[3*p, TOTAL] = 1.0 W[3*p+1, TOTAL] = 1.0 W[3*p+2, WHITE] = 1.0 / N W[3*p, OWN_COUNT] = 1.0 W[3*p+1, OPP_COUNT] = 1.0
# L2: certified liberty evidence and strategic move scores.## In a same-color star, an individual liberty contributes at most eight# to the weighted liberty sum below. Thus sums >8 and >16 certify# at least two and three DISTINCT liberties, respectively.W, b = params["L2.W"], params["L2.b"]line_prior = [-1.30, -0.05, 0.75, 0.65, 0.55, 0.65, 0.75, -0.05, -1.30]
for p, (r, c) in enumerate(coords): W[unit(0, p), unit(0, p)] = 1.0 W[unit(1, p), unit(1, p)] = 1.0
# The orientation choice preserves rotations and reflections. if abs(r - 4) > abs(c - 4): vertical, horizontal = 3.0, 5.0 elif abs(r - 4) < abs(c - 4): vertical, horizontal = 5.0, 3.0 else: vertical = horizontal = 4.0
for color, source_lib, destination, threshold in ( (0, 2, 2, 8.0), (1, 3, 3, 8.0), (0, 2, 4, 16.0), ): j = unit(destination, p) b[j] = -threshold - 64.0 W[unit(color, p), j] += 64.0 W[unit(source_lib, p), j] += 8.0 for q in neighbors[p]: s, t = coords[q] coefficient = vertical if s != r else horizontal W[unit(source_lib, q), j] += coefficient
j = unit(5, p) positional = line_prior[r] + line_prior[c] if r in (2, 6) and c in (2, 6): positional += 0.35 if (r, c) == (4, 4): positional += 0.15 b[j] = OFFSET + positional
W[unit(4, p), j] -= 2.4 W[unit(5, p), j] -= 2.7 for q in range(N): W[unit(0, q), j] += friendly_shape[p, q] W[unit(1, q), j] += enemy_shape[p, q]
for g in (TOTAL, WHITE, OWN_COUNT, OPP_COUNT): W[g, g] = 1.0W[TOTAL, PHASE], b[PHASE] = 1.0, -18.0W[TOTAL, LATE], b[LATE] = 1.0, -52.0W[OWN_COUNT, AHEAD] = 1.0W[OPP_COUNT, AHEAD] = -1.0W[WHITE, AHEAD] = 7.5b[AHEAD] = -1.0W[OWN_COUNT, BEHIND] = -1.0W[OPP_COUNT, BEHIND] = 1.0W[WHITE, BEHIND] = -7.5b[BEHIND] = 1.0
def copy_globals(W): for g in range(TOTAL, BEHIND + 1): W[g, g] = 1.0
# L3: propagate certified liberty evidence through same-color stones.# A pair (z,g) encodes stone=z-g exactly and nonnegative evidence=g.W, b = params["L3.W"], params["L3.b"]M = 481.0for p in range(N): neighborhood = [p] + neighbors[p] for stone_channel, evidence_channel, z_channel, g_channel in ( (0, 2, 0, 1), (1, 3, 2, 3), ): for destination, subtraction in ((z_channel, 0.0), (g_channel, 1.0)): j = unit(destination, p) W[unit(stone_channel, p), j] += M + 1.0 for q in neighborhood: W[unit(evidence_channel, q), j] += 1.0 b[j] = -M - subtraction
j = unit(4, p) W[unit(0, p), j] += M for q in neighborhood: W[unit(4, q), j] += 1.0 b[j] = -M W[unit(5, p), unit(5, p)] = 1.0copy_globals(W)
# L4: another same-color propagation step.W, b = params["L4.W"], params["L4.b"]M = 2401.0for p in range(N): neighborhood = [p] + neighbors[p] for z_channel, g_channel in ((0, 1), (2, 3)): for destination, subtraction in ((z_channel, 0.0), (g_channel, 1.0)): j = unit(destination, p) W[unit(z_channel, p), j] += M + 1.0 W[unit(g_channel, p), j] -= M + 1.0 for q in neighborhood: W[unit(g_channel, q), j] += 1.0 b[j] = -M - subtraction
j = unit(4, p) W[unit(0, p), j] += M W[unit(1, p), j] -= M for q in neighborhood: W[unit(4, q), j] += 1.0 b[j] = -M W[unit(5, p), unit(5, p)] = 1.0copy_globals(W)
# L5: recover stones and bounded tactical classifications.# "Unsafe" means no two-liberty certificate reached this stone.# These flags deliberately err toward noticing threats.W, b = params["L5.W"], params["L5.b"]for p in range(N): neighborhood = [p] + neighbors[p] for z_channel, g_channel, stone_channel, unsafe_channel in ( (0, 1, 0, 2), (2, 3, 1, 3), ): j = unit(stone_channel, p) W[unit(z_channel, p), j] += 1.0 W[unit(g_channel, p), j] -= 1.0
j = unit(unsafe_channel, p) W[unit(z_channel, p), j] += 1.0 W[unit(g_channel, p), j] -= 1.0 for q in neighborhood: W[unit(g_channel, q), j] -= 1.0
j = unit(4, p) # Friendly stone lacking a three-liberty certificate. W[unit(0, p), j] += 1.0 W[unit(1, p), j] -= 1.0 for q in neighborhood: W[unit(4, q), j] -= 1.0
W[unit(5, p), unit(5, p)] = 1.0copy_globals(W)
# L6: move-level capture/rescue, shape, eyes, self-atari, and safe contact.W, b = params["L6.W"], params["L6.b"]for p, (r, c) in enumerate(coords): degree = len(neighbors[p])
for q in neighbors[p]: W[unit(2, q), unit(0, p)] += 1.0 # Rescue urgency. W[unit(3, q), unit(1, p)] += 1.0 # Capture urgency.
j = unit(2, p) W[unit(5, p), j] = 1.0 edge_phase_weight = 0.0 for d in (min(r, 8-r), min(c, 8-c)): if d == 0: edge_phase_weight += 0.030 elif d == 1: edge_phase_weight += 0.012 W[PHASE, j] += edge_phase_weight for q in neighbors[p]: W[unit(1, q), j] += 1.1
# True-eye preservation, with diagonal false-eye exceptions. j = unit(3, p) b[j] = 1.0 - degree for q in neighbors[p]: W[unit(0, q), j] += 1.0 diagonal_penalty = 0.5 if degree == 4 else 1.0 for q in diagonals[p]: W[unit(1, q), j] -= diagonal_penalty
# Conservative self-atari / futile-extension penalty. # Capturing or connecting to a certified strong group exempts a move. j = unit(4, p) b[j] = 2.0 - 1.6 * degree for q in neighbors[p]: W[unit(0, q), j] += -3.2 W[unit(1, q), j] += 1.6 W[unit(2, q), j] += 1.4 W[unit(3, q), j] -= 4.0 W[unit(4, q), j] += 4.0
# Enemy contact is rewarded primarily when backed by a strong group. j = unit(5, p) for q in neighbors[p]: W[unit(1, q), j] += 1.0 W[unit(0, q), j] -= 2.0 W[unit(4, q), j] += 2.0
copy_globals(W)
# Output policy.W, b = params["out.W"], params["out.b"]for p in range(N): b[p] = -OFFSET for channel, coefficient in ( (0, 4.6), (1, 7.1), (2, 1.0), (3, -64.0), (4, -9.0), (5, -1.6), ): W[unit(channel, p), p] = coefficient
# Passing remains unlikely while constructive moves exist.b[81] = -5.6W[PHASE, 81] = 0.050W[LATE, 81] = 0.045W[AHEAD, 81] = 0.025W[BEHIND, 81] = -0.035W[WHITE, 81] = 0.150
# Only inspect and save weights; do not evaluate the policy.for name, array in params.items(): assert array.dtype == np.float32 assert np.isfinite(array).all() save(name, array)
print("Saved all 14 tensors.")print("Parameters:", sum(a.size for a in params.values()))print("Nonzero parameters:", sum(np.count_nonzero(a) for a in params.values()))print("Design: certified local liberty propagation, capture/rescue priorities,")print("self-atari filtering, eye preservation, territorial shape, and late passing.")Saved all 14 tensors.Parameters: 1480274Nonzero parameters: 34190Design: certified local liberty propagation, capture/rescue priorities,self-atari filtering, eye preservation, territorial shape, and late passing.