IC-063Llama 3 70B learns global graph structure via TD learning, building successor-representation-like geometry in its residual stream that is causally supported by TD latents
Can Demircan, Tankred Saanum, Akshay Kumar Jagadish, Marcel Binz, Eric Schulz
When prompted with a random walk on a latent community graph, Llama 3 70B reaches near-ceiling next-state prediction accuracy after about 100 transitions. MDS projections of its residual stream representations gradually converge to the 2D projection of the graph's successor representation across transformer blocks. SAE features correlate more strongly with the SR (max r = 0.62) than with the learned transition matrix (max r = 0.49), and with TD errors (max r = 0.60) than with a surprise signal (max r = 0.18). Bottleneck states are linearly decodable from block 20 onward, peaking mid-model. Lesioning the strongest TD latent in block 64 drops next-state accuracy from 24.3% to 18.9% and distorts the community structure in subsequent blocks.
Evidence
interventional
Key metric
SR correlation max r=0.62 vs transition matrix max r=0.49; TD error max r=0.60 vs surprise max r=0.18; next-state accuracy 24.3% to 18.9% after lesion in block 64; bottleneck decoding from block 20; ceiling accuracy 25%
Caveat
The SAEs are task-specific; the paper notes that a circuit-level understanding of how these representations arise remains unclear.