Handcrafting a Network to Predict Next Token Probabilities for the Random-Random-XOR Process

For this hackathon, we handcrafted a network to perfectly predict next token probabilities for the Random-Random-XOR process. The network takes existing tokens from the process's output, computes several features on these tokens, and then uses these features to calculate next token probabilities. These probabilities match those from a process simulator (also coded for this hackathon). The handcrafted network is our core contribution and we describe it in Section 3 of this writeup.

Prior work has demonstrated that a network trained on the Random-Random-XOR process approximates the 36 possible belief states. Our network does not directly calculate these belief states, demonstrating that networks trained on Hidden Markov Models may not need to comprehend all belief states. Our hope is that this work will aid in the interpretability of neural networks trained on Hidden Markov Models by demonstrating potential shortcuts that neural networks can take.