IC-220In Pythia-6.9B, the bag-of-heuristics mechanism emerges gradually during training and is the primary arithmetic mechanism from the earliest checkpoint showing good performance (23k steps)

Yaniv Nikankin, Anja Reusch, Aaron Mueller, Yonatan Belinkov

SourceArithmetic Without Algorithms: Language Models Solve Math with a Bag of Heuristics

Analyzing Pythia-6.9B training checkpoints from 23k to 143k steps, the authors show that the final heuristic neurons first appear early and gradually converge. The heuristic neurons mutual with the final checkpoint account for an average of 79% of the total heuristics' contribution to accuracy at each intermediate checkpoint, indicating that non-mutual heuristics are less important and become vestigial. Prompt-guided neuron knockout at each checkpoint shows that ablating 25 associated heuristic neurons per layer causes near-zero accuracy at all training stages, confirming the causal link between heuristics and correct completion exists throughout training, not just at the end.

Evidence
interventional
Key metric
final heuristics explain 79% of total heuristics' contribution at each checkpoint; ablating 25 heuristic neurons per layer causes near-zero accuracy at all stages from 23k to 143k steps
Caveat
Analysis is limited to Pythia-6.9B due to public availability of its training checkpoints; the 23k checkpoint is the earliest showing 'good arithmetic performance' but the exact threshold is not defined.
Model
Pythia Pythia-6.9B
Methods
Activation patching / Activation replacement / Cross-model activation patching (CMap) [primary], Mean Ablation / direct effect mean ablation / Mean token ablation [primary]
Related findings
IC-218, IC-219
Extraction
automatic-extraction