A machine learning engineer is training a soft prompt, σ, to replace a lengthy context, c. They use the following optimization formula, where s(·,·) is a function measuring the difference between two predictions:

hat(σ) = argmin_σ s(hat(y), hat(y)_σ)

Here, hat(y) is the model's prediction with the full context c, and hat(y)_σ is the prediction with the soft prompt σ. After training, the engineer observes that for many inputs, the value of s(hat(y), hat(y)_σ) is consistently high. What does this observation most directly imply about the outcome of the training process?

Impact of the Similarity Function in Soft Prompt Optimization

In the context of learning a compressed representation of a long text, consider the optimization formula: hat(σ) = argmin_σ s(hat(y), hat(y)_σ), where hat(y) is the prediction from the full text and hat(y)_σ is the prediction from the compressed representation σ. If the function s(·,·) were changed from a dissimilarity measure (e.g., a loss function) to a similarity measure (e.g., a cosine similarity score), the argmin operator should be replaced with argmax to correctly identify the optimal compressed representation hat(σ).