📝 SummarXiv

Abstract

We present cryptogram solving as an ideal testbed for studying neural network generalization in combinatorially complex domains. In this task, models must decrypt text encoded with substitution ciphers, choosing from 26! possible mappings without explicit access to the cipher. We develop ALICE (an Architecture for Learning Interpretable Cryptogram dEcipherment): a simple encoder-only Transformer that sets a new state-of-the-art for both accuracy and speed on this decryption problem. Surprisingly, ALICE generalizes to unseen ciphers after training on only ${\sim}1500$ unique ciphers, a minute fraction ($3.7 \times 10^{-24}$) of the possible cipher space. To enhance interpretability, we introduce a novel bijective decoding head that explicitly models permutations via the Gumbel-Sinkhorn method, enabling direct extraction of learned cipher mappings. Through early exit analysis, we reveal how ALICE progressively refines its predictions in a way that appears to mirror common human strategies for this task: early layers employ frequency-based heuristics, middle layers form word structures, and final layers correct individual characters. Our architectural innovations and analysis methods extend beyond cryptograms to any domain with bijective mappings and combinatorial structure, offering new insights into neural network generalization and interpretability.