I see people use "in-context learning" in different ways.

Take the opening to "In-Context Learning Creates Task Vectors":

In-context learning (ICL) in Large Language Models (LLMs) has emerged as a powerful new learning paradigm. However, its underlying mechanism is still not well understood. In particular, it is challenging to map it to the “standard” machine learning framework, where one uses a training set $S$ to find a best-fitting function $f (x)$ in some hypothesis class.

In one Bayesian sense, training data and prompts are both just evidence. From a given model, prior (architecture + initial weight distribution), and evidence (training data), you get new model weights. From the new model weights and some more evidence (prompt input), you get a distribution of output text. But the "training step" $(prior, data) \to weights$ and "inference step" $(weights, input) \to output$ could be simplified to a single function: $(prior, data, input) \to output$ . An LLM trained on a distribution of text that always starts with "Once upon a time" is essentially similar to an LLM trained on the Internet but prompted to continue after "Once upon a time." If the second model performs better—e.g. because it generalizes information from the other text—this is explained by training data limitations or by the availability of more forward passes and therefore computation steps and space to store latent state.

A few days ago "How Transformers Learn Causal Structure with Gradient Descent" defined in-context learning as

the ability to learn from information present in the input context without needing to update the model parameters. For example, given a prompt of input-output pairs, in-context learning is the ability to predict the output corresponding to a new input.

Using this interpretation, ICL is simply updating the state of latent variables based on the context and conditioning on this when predicting the next output. In this case, there's no clear distinction between standard input conditioning and ICL.

However, it's still nice to know the level of abstraction at which the in-context "learning" (conditioning) mechanism operates. We can distinguish "task recognition" (identifying known mappings even with unpaired input and label distributions) from "task learning" (capturing new mappings not present in pre-training data). At least some tasks can be associated wi...

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