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This research investigates how Large Language Models perform complex arithmetic by utilizing implicit discrete state representations within their hidden layers, effectively bypassing the need to generate intermediate chain-of-thought text. The study reveals that while these internal symbolic mechanisms exist in top-tier models, current open-source variants suffer from information loss during this process, leading to calculation errors. Understanding how LLMs encode and manipulate abstract numerical states provides critical insight into their emergent reasoning capabilities and potential failure modes.
States Hidden in Hidden States: Implicit Discrete State Representations Emerge in LLMs' Hidden States
arXiv:2407.11421v2 Announce Type: replace Abstract: Large Language Models (LLMs) exhibit emergent abilities that may reveal aspects of their internal mechanisms. We study one such capability: directly performing extended sequences of calculations without generating chain-of-thought solutions. The strongest models in our evaluation can directly output sums with up to 15 addends, where operands are sampled from 1 to 100. We hypothesize that models form Implicit Discrete State Representations (IDSRs) within their hidden states and use them for internal symbolic calculation. We test for these representations, characterize their formation from layer, digit, and sequence perspectives, and investigate their use in producing answers. We also find that these state representations are far from lossless in current open-source models, contributing to errors in final outputs. Our work offers an initial exploration of LLMs' symbolic calculation abilities and underlying mechanisms. Code and reproducibility artifacts are available at https://github.com/Junhaoo-Chen/IDSR.
Abstract:Large Language Models (LLMs) exhibit emergent abilities that may reveal aspects of their internal mechanisms. We study one such capability: directly performing extended sequences of calculations without generating chain-of-thought solutions. The strongest models in our evaluation can directly output sums with up to 15 addends, where operands are sampled from 1 to 100. We hypothesize that models form Implicit Discrete State Representations (IDSRs) within their hidden states and use them for internal symbolic calculation. We test for these representations, characterize their formation from layer, digit, and sequence perspectives, and investigate their use in producing answers. We also find that these state representations are far from lossless in current open-source models, contributing to errors in final outputs. Our work offers an initial exploration of LLMs' symbolic calculation abilities and underlying mechanisms. Code and reproducibility artifacts are available at this https URL.
12 pages, 12 figures. Revised manuscript with public code and reproducibility artifacts; clarified the evaluation protocol; corrected figure labels and chance baselines, the attention-bridge description, cross-references, and probe notation. No new experiments
Computation and Language (cs.CL)
arXiv:2407.11421 [cs.CL]
(or arXiv:2407.11421v2 [cs.CL] for this version)
Text integral sub licența deschisă a publicației · 184 cuvinte
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