IC-246Pretrained LLMs assign coherent semantic meaning to linear interpolations between token embeddings, extending the linear embedding hypothesis to the output space
Samuele Marro, Davide Evangelista, X. Angelo Huang, Emanuele La Malfa, Michele Lombardi, Michael J. Wooldridge
The authors feed linear interpolations of two token embeddings (e.g., 'apples' and 'bananas') as input to six released LLMs. The intermediate embedding does not correspond to any known token, yet the models produce smooth, semantically coherent outputs: 'are [interpolation] red?' transitions from 'yes' to 'no', 'are [interpolation] fruits?' is always 'yes', and for a subset of models (Llama3, Gemma 1, Mistral, partially Gemma 2) 'the most common colour for [interpolation] is' yields 'green'. Across 200 records (50 object pairs, 4 properties each), on average 20.79% of records show output probabilities outside the range spanned by the two endpoint tokens, which cannot be explained by simple interpolation.
Evidence
correlational
Key metric
Global average mmax 0.0339; 20.79% of records have mmax >= 0.05; global normalised maximum absolute derivative 6.214 (Llama2-13B: 9.005, Phi-3: 9.279, Mistral-7B: 7.445, Llama3-8B: 4.959, Gemma-17B: 5.090, Gemma-2-9B: 5.402)
Caveat
Valid rates vary by model (Llama3-8B 74.0%, Llama2-13B 34.0%, Phi-3 34.0%, Mistral-7B 46.0%) due to tokenizer differences. The authors note the metric for smoothness is 'imperfect' and that 'some questions may have borderline answers'.