Analyzed network weights for Pac-Man grid
Public
Analyzed network weights for Pac-Man grid
Agent
Codex
Model
GPT 6 Astra
Started
Nov 3, 3:08 AM
Messages3
Downloads0
Reviewed network input grid and channel definitions.
UnderstandAnalyzed weight patterns showing maze-shaped agent representation.
UnderstandTHE OBSERVATION The network sees a 10 x 10 grid. Rows are numbered 0 (top) to 9 (bottom) and columns 0 (left) to 9 (right). The outer ring of cells (row 0, row 9, column 0 and column 9) is a wall border; the playable area is the inner 8 x 8 cells (rows 1-8, columns 1-8). Each cell has 5 binary channels (0 or 1): channel 0 agent: the cells the player controls channel 1 moving objects: things other than the agent that move channel 2 reward targets: things that give reward channel 3 obstacles: cells the agent cannot enter or that end the episode (the wall border is always here) channel 4 previous frame: the cells that were in channel 0 or channel 1 on the previous step The observation is flattened to 500 numbers. Input number i = (row * 10 + column) * 5 + channel; for example input 0 is (row 0, column 0, channel 0), input 4 is (row 0, column 0, channel 4), input 5 is (row 0, column 1, channel 0) and input 499 is (row 9, column 9, channel 4).
THE ACTIONS The network outputs 5 numbers (logits), one per action; the action is sampled from the softmax of these logits: action 0 no-op action 1 up (toward row 0) action 2 down (toward row 9) action 3 left (toward column 0) action 4 right (toward column 9)
THE NETWORK A policy network (multilayer perceptron) with 500 inputs, two hidden layers of 32 units with tanh activations, and 5 outputs: h1 = tanh(x @ W1 + b1) W1: 500 x 32, b1: 32 h2 = tanh(h1 @ W2 + b2) W2: 32 x 32, b2: 32 logits = h2 @ W3 + b3 W3: 32 x 5, b3: 5 Row i of W1 holds the weights from input i to the 32 hidden units; column j of a weight matrix belongs to unit j of the next layer. 17,253 parameters in total. It was trained with reinforcement learning (PPO) to maximise the reward of a game played on this grid.
QUESTION. The weights below belong to one policy network that was trained with reinforcement learning to play a game on this grid. Which game was it trained on? Work from the weights. You have no tools: no code execution, no calculator, nothing to run. This is a single response.
Answer in this order: Observations: <what you see in the weights: for each input channel, where in the grid its weights are large or show structure and what that suggests; what the output layer and its biases show about the actions; quote the weights you rely on> Reasoning: <which kinds of game fit these observations, which are ruled out, and why> Game: <the game, as specifically as you can; if it resembles a well-known game, give that game's name> Description: <what the agent does and what gives reward, in one or two sentences> Confidence: <0-100>%
THE NETWORK'S WEIGHTS Policy network weights. Forward pass: h1 = tanh(x @ W1 + b1); h2 = tanh(h1 @ W2 + b2); logits = h2 @ W3 + b3. Values rounded to 3 decimals.
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-1.373 -0.068 -0.114 -0.904 -0.591 -0.212 -0.748 -0.710 -0.796 0.128 0.745 1.191 0.483 -1.493 -1.081 -0.927 -0.435 0.493 -0.235 -0.181 0.603 -0.142 0.625 -0.219 -0.377 -0.186 -0.275 -0.426 0.329 0.950 0.141 1.187 1.344 -0.778 0.935 0.017 0.470 1.101 0.247 -1.112 -0.989 1.639 0.511 -0.346 0.722 0.221 0.518 -0.735 -0.002 0.562 0.578 -0.806 -0.436 0.160 0.342 0.842 -0.984 0.089 1.007 -0.595 0.257 -0.070 -0.701 -0.514 -0.739 1.560 0.085 1.490 0.540 0.740 -0.380 -0.094 -2.381 -0.055 -0.267 -0.123 -1.059 0.520 0.257 -0.991 0.964 -1.284 0.172 1.184 -0.339 0.152 0.582 0.589 0.441 -0.241 -0.123 -0.929 -0.862 -0.829 -0.198 0.254 -0.688 0.187 -0.637 -0.037 -0.046 0.393 -0.558 0.332 0.222 0.335 -0.171 0.429 -0.685 -0.491
b2 (layer 2 biases), shape 32: -0.392 0.498 0.596 0.215 0.153 0.295 -0.119 -0.567 -0.248 -0.377 -0.039 -0.658 -0.190 -0.172 0.020 0.553 -0.024 0.309 -0.622 -0.029 0.322 0.389 0.256 0.168 0.261 -0.317 0.326 -0.356 -0.203 -0.057 0.613 0.001
W3 (output layer weights), shape 32 x 5: one line per row -0.027 -0.312 -1.843 1.628 -1.030 -2.055 0.992 -0.888 1.189 -0.306 0.469 0.459 2.307 -1.683 0.191 -0.007 0.182 2.057 -0.317 -1.147 1.007 -0.045 0.848 0.964 -2.200 0.543 -1.586 0.034 1.139 1.092 -1.045 1.888 -0.564 -0.036 -1.226 0.278 -0.321 -2.498 0.664 0.469 0.718 -0.094 0.302 1.088 -1.462 0.740 0.334 -3.070 1.267 0.856 0.593 -1.454 1.640 -0.284 -0.301 -0.117 -0.931 -0.578 1.452 -0.871 -1.649 -1.039 -0.972 1.325 0.710 0.147 -2.190 0.991 -1.094 1.858 0.262 1.662 -0.822 0.481 -1.710 -0.346 1.544 0.321 0.602 -1.490 -1.061 -1.254 0.200 2.490 -0.338 0.790 2.144 -1.525 -0.598 0.380 -0.192 1.341 -0.237 -0.699 -1.203 0.889 1.299 -2.927 -0.321 1.556 0.282 -0.788 1.134 1.461 -0.620 0.571 -1.351 0.655 1.414 -0.727 0.783 -1.474 1.958 0.603 -0.649 1.049 -1.081 0.525 1.486 -0.393 -0.304 0.034 2.502 -0.142 -0.073 0.209 1.893 -0.742 -2.491 -0.386 -1.000 -0.939 0.639 1.041 0.045 1.090 0.182 0.221 0.697 -1.311 -0.050 -1.608 -1.018 0.033 2.500 1.305 -0.997 0.585 -0.371 0.521 -0.501 1.326 -1.247 -1.168 2.223 1.439 2.019 -0.268 -0.516 -2.023
b3 (output layer biases), shape 5: -0.873 0.703 0.712 0.595 -0.092
Channel 0 — agent: Large, position-specific weights follow a maze-shaped pattern, not an unrestricted arena or a single paddle row. For example, at (1,1) weights include −3.242, 3.377, −3.734, 4.081; at (1,3), 4.742, −3.778, 3.890. In contrast, (2,2) and (2,3) have small, initialization-like weights. The apparent corridor layout is below (. = substantial learned agent weights; # = small weights):
.........##..##..#....#....##......##....#....#..##..##.........This strongly suggests a fixed, symmetric maze.
Channel 1 — moving objects: Strong weights occur throughout those same corridors. At (1,1), examples include 2.453, 1.978, −1.619; at (1,6), −3.386. Other moving entities therefore matter across the maze—consistent with ghosts or pursuing enemies.
Channel 2 — reward targets: Generally much smaller weights than the agent and moving-object channels, but clearly learned in some locations. Connections to first-layer unit 6 include −1.490 at (1,1), −2.361 at (1,2), −1.905 at (1,3), and −4.876 at (2,4). This fits collectible targets distributed through corridors, with uneven importance to the learned policy. Negative weights alone do not mean avoidance.
Channel 3 — obstacles: Mostly small weights, including at interior locations. For example, the obstacle vector at (1,1) begins 0.057, 0.106, 0.006, 0.008. Together with the sharp corridor pattern in other channels, this suggests constant maze walls, whose layout can be memorized rather than dynamically interpreted. The always-present border also shows shared structure, such as repeatedly negative connections to unit 6.
Channel 4 — previous frame: Meaningful, spatially structured weights occur along corridors. At (1,1), examples include −0.739, −1.316, 0.593; at (1,8), −2.849 to unit 9. The policy uses movement history, plausibly to track enemies and recent motion.
Outputs: All four movement actions have substantial, differentiated connections: examples include 2.144 for up, 2.502 for down, 2.490 for left, and 2.500 for right. Biases are [−0.873, 0.703, 0.712, 0.595, −0.092], discouraging no-op relative to movement, though actual preferences depend on hidden activations.
The combination of a fixed symmetric maze, collectibles, independently moving entities, and four-direction navigation is characteristic of Pac-Man.
Pong, Breakout, and falling-object catching would normally restrict the agent to a row or column. Open-arena chasing does not explain the maze-shaped inactive cells. Ordinary maze navigation does not explain the strong moving-object channel. Snake is less consistent with this fixed corridor geometry and the comparatively weak obstacle channel, which would otherwise need to represent changing collision hazards.
Pac-Man, or a simplified grid-based Pac-Man clone.
The agent navigates maze corridors, collecting pellets or other reward items while avoiding moving ghosts. Reward comes from collecting those items, potentially with a bonus for clearing the maze.
96%
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