In-context Learning and Induction Heads

### Contents

[Key Concepts](#key-concepts)
* [In-context Learning](#in-context-learning-key-concept)
* [Induction Heads](#definition-of-induction-heads)
* [Per-Token Loss Analysis](#per-token-loss-intro)

[Arguments Summary](#toc-arguments)
[Argument 1 (Macroscopic co-occurrence)](#argument-phase-change)
* [Looking at the Phase Change More Closely](#phase-change-more-closely)

[Argument 2 (Macroscopic co-perturbation)](#argument-architectural-requirements)
[Argument 3 (Direct ablation)](#argument-ablations)
[Argument 4 (Examples of generality)](#argument-induction-heads-can-implement-abstract-behaviors)
* [Behavior 1: Literal sequence copying](#copying-literal-text)
* [Behavior 2: Translation](#performing-translation)
* [Behavior 3: Pattern matching](#pattern-matching)

[Argument 5 (Mechanistic plausibility)](#argument-induction-head-mechanism)
[Argument 6 (Continuity)](#argument-extrapolation)
[Model Analysis Table](#model-analysis-table)

[Unexplained Curiosities](#curiosities)
[Discussion](#discussion)
[Related Work](#related-work)

[Comments & Replications](#comments-replications)
* [Adam Scherlis](#comment-redwood)
* [Tom Lieberum](#comment-lieberum)

[Acknowledgments](#acknowledgments)
[Author Contributions](#author-contributions)
[Citation Information](#citation)
[Additional Details](#where-are-induction-heads-located-in-models)

As Transformer generative models continue to scale and gain increasing real world use , addressing their associated safety problems becomes increasingly important. Mechanistic interpretability – attempting to reverse engineer the detailed computations performed by the model – offers one possible avenue for addressing these safety issues. If we can understand the internal structures that cause Transformer models to produce the outputs they do, then we may be able to address current safety problems more systematically, as well as anticipating safety problems in future more powerful models. Note that mechanistic interpretability is a subset of the broader field of interpretability, which encompasses many different methods for explaining the outputs of a neural network. Mechanistic interpretability is distinguished by a specific focus on trying to systematically characterize the internal circuitry of a neural net.

In the past, mechanistic interpretability has largely focused on CNN vision models, but recently, we [presented](https://transformer-circuits.pub/2021/framework/index.html) some very preliminary progress on mechanistic interpretability for Transformer language models. Specifically, in our prior work we developed a mathematical framework for decomposing the operations of transformers, which allowed us to make sense of small (1 and 2 layer attention-only) models and give a near-complete account of how they function. Perhaps the most interesting finding was the induction head, a circuit whose function is to look back over the sequence for previous instances of the current token (call it `A`), find the token that came after it last time (call it `B`), and then predict that the same completion will occur again (e.g. forming the sequence `[A][B] … [A] → [B]`). In other words, induction heads “complete the pattern” by copying and completing sequences that have occurred before. Mechanically, induction heads in our models are implemented by a circuit of two attention heads: the first head is a “previous token head” which copies information from the previous token into the next token, while the second head (the actual “induction head”) uses that information to find tokens preceded by the present token. For 2-layer attention-only models,Note that induction heads don’t occur in 1 layer models, because they require a composition of attention heads in different layers. we were able to show precisely that induction heads implement this pattern copying behavior and appear to be the primary source of in-context learning.

Ultimately, however, our goal is to reverse-engineer frontier language models (which often contain hundreds of layers and billions or trillions of parameters), not merely 2-layer attention-only models. Unfortunately, both the presence of many layers, and the presence of MLPs, makes it much more difficult to mathematically pin down the precise circuitry of these models. However, a different approach is possible: by empirically observing, perturbing, and studying the learning process and the formation of various structures, we can try to assemble an indirect case for what might be happening mechanistically inside the network. This is somewhat similar to how a neuroscientist might gain understanding of how part of the brain functions by looking at neural development over time, studying patients with an injury to that part of the brain, perturbing brain function in animals, or looking at a select small number of relevant neurons.

In this paper, we take the first preliminary steps towards building such an indirect case. In particular, we present preliminary and indirect evidence for a tantalizing hypothesis: that induction heads might constitute the mechanism for the actual majority of all in-context learning in large transformer models. Specifically, the thesis is that there are circuits which have the same or similar mechanism to the 2-layer induction heads and which perform a “fuzzy” or “nearest neighbor” version of pattern completion, completing `[A*][B*] … [A] → [B]` , where  `A* ≈ A` and `B* ≈ B`are similar in some space; and furthermore, that these circuits implement most in-context learning in large models.

The primary way in which we obtain this evidence is via discovery and study of a phase change that occurs early in training for language models of every size (provided they have more than one layer), and which is visible as a bump in the training loss. During this phase change, the majority of in-context learning ability (as measured by difference in loss between tokens early and late in the sequence) is acquired, and simultaneously induction heads form within the model that are capable of implementing fairly abstract and fuzzy versions of pattern completion. We study this connection in detail to try to establish that it is causal, including showing that if we perturb the transformer architecture in a way that causes the induction bump to occur in a different place in training, then the formation of induction heads as well as formation of in-context learning simultaneously move along with it.

Specifically, the paper presents six complementary lines of evidence arguing that induction heads may be the mechanistic source of general in-context learning in transformer models of any size:

.argument {margin-left: 4px; font-weight: bold; border-bottom: none; display: inline-block;}

* [Argument 1](#argument-phase-change) (Macroscopic co-occurence): Transformer language models undergo a “phase change” early in training, during which induction heads form and simultaneously in-context learning improves dramatically.
* [Argument 2](#argument-architectural-requirements) (Macroscopic co-perturbation): When we change the transformer architecture in a way that shifts whether induction heads can form (and when), the dramatic improvement in in-context learning shifts in a precisely matching way.
* [Argument 3](#argument-ablations) (Direct ablation):  When we directly “knock out” induction heads at test-time in small models, the amount of in-context learning greatly decreases.
* [Argument 4](#argument-induction-heads-can-implement-abstract-behaviors) (Specific examples of induction head generality): Although we define induction heads very narrowly in terms of copying literal sequences, we empirically observe that these same heads also appear to implement more sophisticated types of in-context learning, including highly abstract behaviors, making it plausible they explain a large fraction of in-context learning.
* [Argument 5](#argument-induction-head-mechanism) (Mechanistic plausibility of induction head generality): For small models, we can explain mechanistically how induction heads work, and can show they contribute to in-context learning. Furthermore, the actual mechanism of operation suggests natural ways in which it could be re-purposed to perform more general in-context learning.
* [Argument 6](#argument-extrapolation) (Continuity from small to large models): In the previous 5 arguments, the case for induction heads explaining in-context learning is stronger for small models than for large ones. However, many behaviors and data related to both induction heads and in-context learning are smoothly continuous from small to large models, suggesting the simplest explanation is that mechanisms are the same.

Together the claims establish a circumstantial case that induction heads might be responsible for the majority of in-context learning in state-of-the-art transformer models. We emphasize that our results here are only the beginnings of evidence for such a case, and that like any empirical or interventional study, a large number of subtle confounds or alternative hypotheses are possible – which we discuss in the relevant sections. But we considered these results worth reporting, both because future work could build on our results to establish the claim more firmly, and because this kind of indirect evidence is likely to be common in interpretability as it advances, so we’d like to establish a norm of reporting it even when it is not fully conclusive.

Finally, in addition to being instrumental for tying induction heads to in-context learning, the phase change may have relevance to safety in its own right. Neural network capabilities — such as multi-digit addition — are known to sometimes abruptly form or change as models train or increase in scale, and are of particular concern for safety as they mean that undesired or dangerous behavior could emerge abruptly. For example reward hacking, a type of safety problem, can emerge in such a phase change. Thus, studying a phase change “up close” and better understanding its internal mechanics could contain generalizable lessons for addressing safety problems in future systems. In particular, the phase change we observe forms an interesting potential bridge between the microscopic domain of interpretability and the macroscopic domain of scaling laws and learning dynamics.

The rest of the paper is organized as follows. We start by clarifying several key concepts and definitions, including in-context learning, induction heads, and a “per-token loss analysis” method we use throughout. We then present the 6 arguments one by one, drawing on evidence from analysis of 34 transformers over the course of training, including more than 50,000 attention head ablations (the data of which is shown in the [Model Analysis Table](#model-analysis-table)). We then discuss some unexplained “curiosities” in our findings, as well as reviewing related work.

---

[Key Concepts](#key-concepts)
-----------------------------

### [In-context Learning](#in-context-learning-key-concept)

In modern language models, tokens later in the context are easier to predict than tokens earlier in the context. As the context gets longer, loss goes down. In some sense this is just what a sequence model is designed to do (use earlier elements in the sequence to predict later ones), but as the ability to predict later tokens from earlier ones gets better, it can increasingly be used in interesting ways (such as specifying tasks, giving instructions, or asking the model to match a pattern) that suggest it can usefully be thought of as a phenomenon of its own. When thought of in this way, it is usually referred to as in-context learning.Or sometimes metalearning, although this term implicitly makes the stronger claim that the model is learning how to do a new ability (as opposed to “locating” an ability, i.e. learning what it is supposed to do), an implication which is both controversial and not entirely precise in its meaning.

Emergent in-context learning was noted in GPT-2 and gained significant attention in GPT-3. Simply by adjusting a “prompt”, transformers can be adapted to do many useful things without re-training, such as translation, question-answering, arithmetic, and many other tasks. Using “prompt engineering” to leverage in-context learning became a popular topic of study and discussion.

At least two importantly different ways of conceptualizing and measuring in-context learning exist in the literature. The first conception, represented in Brown et al., focuses on few-shot learning of specific tasks. The model is prompted with several instances of some “task” framed in a next-token-prediction format (such as few-digit addition, or English-to-French translation). The second conception of in-context learning, represented in Kaplan et al., focuses on observing the loss at different token indices, in order to measure how much better the model gets at prediction as it receives more context. The first conception can be thought of as a micro perspective (focusing on specific tasks), where as the second conception can be seen as a macro perspective (focusing on general loss, which on average correlates with these tasks).

The “few-shot learning” conception of in-context learning has tended to receive greater community attention. The ability to do many different tasks with one large model, even without further fine-tuning, is a notable change to the basic economics of model training. Moreover, it gives evidence of wide-ranging general capabilities and the ability to adapt on the fly, which nudges us to re-examine what it means for a model to “understand” or to “reason”.

However, for the purposes of this work, we focus instead on the Kaplan et al. conception: decreasing loss at increasing token indices. We do so because it's a more general framing of the phenomenon than “few-shot learning”. A drawback of this definition is it fails to isolate specific behaviors of interest. At the same time, it allows us to measure models’ overall ability to learn on-the-fly from the context, without depending on our specific choices of “task”.  We’ll also see that, starting from this definition, we are also able to study a couple classic few-shot learning examples (see [Argument 4](#argument-induction-heads-can-implement-abstract-behaviors)).

Throughout this work we compute a simple heuristic measure of in-context learning:

* In-context learning score: the loss of the 500th token in the context minus the average loss of the 50th token in the context, averaged over dataset examples.

We chose the 500th and 50th token indices somewhat arbitrarily. The 500th token is near the end of a length-512 context, and the 50th token is far enough into the context that some basic properties of the text have been established (such as language and document type) while still being near the start. We will also show that picking different numbers here does not change our conclusions.

Finally, it is worth noting that in-context learning is of potentially special relevance to safety. In-context learning makes it harder to anticipate how a model might behave after a long context. In the longer run, concepts such as mesa-optimization or inner-alignment postulate that meaningful learning or optimization could occur at test time (without changing the weights). In-context learning would be an obvious future mechanism for such hidden optimization to occur, whether or not it does so today. Thus, studying in-context learning seems valuable for the future.

(See [Related Work](#in-context-learning-related-work) for more on in-context learning, and [Discussion](#safety-implications) for more on the connection to safety.)

### [Induction Heads](#definition-of-induction-heads)

In our [previous paper](https://transformer-circuits.pub/2021/framework/index.html), we discovered a special kind of attention head – which we named induction heads – in two layer attention-only models. Induction heads are implemented by a circuit consisting of a pair of attention heads in different layers that work together to copy or complete patterns. The first attention head copies information from the previous token into each token. This makes it possible for the second attention head to attend to tokens based on what happened before them, rather than their own content. Specifically, the second head (which we call the "induction head") search for a previous place in the sequence where the present token `A` occurred and attends to the next token (call it `B`), copying it and causing the model to be more likely to output `B` as the next token. That is, the two heads working together cause the sequence `…[A][B]…[A]` to be more likely to be completed with `[B]`.

Induction heads are named by analogy to inductive reasoning. In inductive reasoning, we might infer that if `A` is followed by `B` earlier in the context, `A` is more likely to be followed by `B` again later in the same context. Induction heads crystallize that inference. They search the context for previous instances of the present token, attend to the token which would come next if the pattern repeated, and increase its probability. Induction heads attend to tokens that would be predicted by basic induction (over the context, rather than over the training data).

Notice that induction heads are implementing a simple algorithm, and are not memorizing a fixed table of n-gram statistics. The rule `[A][B] … [A] → [B]` applies regardless of what `A` and `B` are.More specifically, induction heads seem to largely decouple `A` and `B`. While some induction heads may specialize on certain kinds of `A`s or `B`s, this significant decoupling of `A` and `B` means that they don't have a fixed table of bigram statistics they can update on, but rather can abstract to new patterns. This means that induction heads can in some sense work out of distribution, as long as local statistics early in the context are representative of statistics later. This hints that they may be capable of more general and abstract behavior.

Our previous paper focused on a few explorations of induction heads, including showing that these heads occur in 2-layer attention-only models (but not 1-layer models); tracking down how they operate mechanistically as part of our mathematical decomposition of transformers; and making an eigenvalue-based test for detecting their presence. However, we were a bit vague on the exact definition of induction heads: it was more like we found a cluster of behaviors and mechanisms that tended to occur together, and called heads in that cluster “induction heads”.

In this paper our goal is to provide evidence for something more expansive: that induction heads play a major role in general in-context learning (not just literal `[A][B]...[A]→[B]` copying), for large models and not just for small 2-layer attention only models.  To do this clearly and coherently, we need a more precise definition of induction heads. Mechanistic analysis of weights and eigenvalue analysis are much more complicated in large models with MLP’s, so for this paper we choose to define induction heads by their narrow empirical sequence copying behavior (the `[A][B]...[A]→[B]`), and then attempt to show that they (1) also serve a more expansive function that can be tied to in-context learning, and (2) coincide with the mechanistic picture for small models.

Formally, we define an induction head as one which exhibits the following two propertiesIn practice, induction heads don't exhibit these properties perfectly, and our measurements give us a continuum, but there is a clear subset of heads which exhibit these properties with much greater than random chance. on a repeated random sequenceBy defining induction heads in terms of their behavior on repeated copies of random sequences, we can be confident that it's actually relying on induction rather than, say, a simple copying head that heuristically attends to previous tokens which could plausibly slot in well after the next token, even if that hasn’t occurred yet in the current context. of tokens:

* Prefix matching: The head attends back to previous tokens that were followed by the current and/or recent tokens.The simplest induction heads match just one preceding token. But we also often observe induction heads that perform a fuzzy match over several preceding tokens. That is, it attends to the token which induction would suggest comes next.
* Copying: The head’s output increases the logit corresponding to the attended-to token.

In other words, induction heads are any heads that empirically increase the likelihood of `[B]` given `[A][B]...[A]` when shown a repeated sequence of completely random tokens. An illustration of induction heads’ behavior is shown here:

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Note that, as a consequence, induction heads will tend to be good at repeating sequences wholesale. For example, given “The cat sat on the mat. The cat …”, induction heads will promote the continuation “sat on the mat”. This gives a first hint of how they might be connected to general in-context learning and even few-shot learning: they learn to repeat arbitrary sequences, which is a (simple) form of few-shot learning.

One of things we’ll be trying to establish is that when induction heads occur in sufficiently large models and operate on sufficiently abstract representations, the very same heads that do this sequence copying also take on a more expanded role of analogical sequence copying or in-context nearest neighbors. By this we mean that they promote sequence completions like `[A*][B*] … [A] → [B]` where `A*` is not exactly the same token as `A` but similar in some embedding space, and also `B` is not exactly the same token as `B*`. For example, `A` and `A*` (as well as B and `B*`) might be the same word in different languages, and the induction head can then translate a sentence word by word by looking for “something like `A`”, finding `A*` followed by`B*`, and then completing with “something like `B*`” (which is `B`). We are not yet able to prove mechanistically that induction heads do this in general, but in [Argument 4](#argument-induction-heads-can-implement-abstract-behaviors) we show empirical examples of induction heads behaving in this way (including on translation), and in [Argument 5](#argument-induction-head-mechanism) we point out that the known copying mechanism of induction heads in small models can be naturally adapted to function in this way.

### [Per-Token Loss Analysis](#per-token-loss-intro)

To better understand how models evolve during training, we analyze what we call the "per-token loss vectors." The core idea traces back to a method used by Erhan et al. , and more generally to the idea of "function spaces" in mathematics.In mathematics, one sometimes thinks of a function as an infinite dimensional vector of the values it would give for different inputs. For neural networks, this can be a nice way to abstract away the fact that functionally identical models can have very different parameter vectors. Of course, we can't directly represent these infinite dimensional vectors, but we can approximate them by sampling.

We start with a collection of models. (In our use, we'll train several different model architectures, saving dozens of “snapshots” of each over the course of training. We’ll use this set of snapshots as our collection of models.) Next, we collect the log-likelihoods each model assigns to a consistent set of 10,000 random tokens, each taken from a different example sequence. We combine these log-likelihoods into a "per-token loss vector" and apply Principal Component Analysis (PCA):

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A more detailed discussion of technical details can be found in the [Appendix](#per-token-losses).

By applying this method to snapshots over training for multiple models, we can visualize and compare how different models' training trajectories evolve in terms of their outputs. Since we're using PCA, each direction can be thought of as a vector of log-likelihoods that models are moving along. We particularly focus on the first two principal components, since we can easily visualize those. Of course, models also move in directions not captured by the first two principal components, but it's a useful visualization for capturing the highest-level story of training.

---

[Arguments that induction heads are the mechanism for the majority of in-context learning.](#toc-arguments)
-----------------------------------------------------------------------------------------------------------

Now we’ll proceed to the main part of the paper, which makes the case that induction heads may provide the primary mechanism for the majority of in-context learning for transformer models in general. As stated in the introduction, this is a very broad hypothesis and much of our evidence is indirect, but nevertheless we believe that all the lines of evidence together make a relatively strong, though not conclusive, case.

Before we go through the arguments, it’s useful to delineate where the evidence is more conclusive vs. less conclusive. This is shown in the table below. For small, attention-only models, we believe we have strong evidence that attention heads are the mechanism for the majority of in-context learning, as we have evidence supported by ablations and mechanistic reverse engineering. Conversely, for all models, we can make a strong case that induction heads play some role in in-context learning, as we can demonstrate examples and show suggestive correlations. However, the larger the models get, the harder it is to establish that induction heads account for the actual majority of in-context learning. For large models with MLP’s, we must therefore rely on mainly correlational evidence, which could be confounded. We explore alternate hypotheses throughout, including at the end of [Argument 1](#assessing-the-evidence) and again briefly in [Argument 6](#argument-extrapolation).

Summary of Evidence for Sub-Claims (Strongest Argument for Each)
 Small Attention-Only Small with MLPs Large Models
Contributes Some Strong, Causal Strong, Causal Medium, Correlational & Mechanistic
Contributes Majority Strong, Causal Medium, Causal Medium, Correlational

Here is the list of arguments we’ll be making, one per section, repeated from the introduction:

.argument {margin-left: 4px; font-weight: bold; border-bottom: none; display: inline-block;}

* [Argument 1](#argument-phase-change) (Macroscopic co-occurrence): Transformer language models undergo a “phase change” early in training, during which induction heads form and simultaneously in-context learning improves dramatically.
* [Argument 2](#argument-architectural-requirements) (Macroscopic co-perturbation): When we change the transformer architecture in a way that shifts whether induction heads can form (and when), the dramatic improvement in in-context learning shifts in a precisely matching way.
* [Argument 3](#argument-ablations)  (Direct ablation):  When we directly “knock out” induction heads at test-time in small models, the amount of in-context learning greatly decreases.
* [Argument 4](#argument-induction-heads-can-implement-abstract-behaviors) (Specific examples of induction head generality): Although we define induction heads very narrowly in terms of copying literal sequences, we empirically observe that these same heads also appear to implement more sophisticated types of in-context learning, including highly abstract behaviors, making it plausible they explain a large fraction of in-context learning.
* [Argument 5](#argument-induction-head-mechanism) (Mechanistic plausibility of induction head generality): For small models, we can explain mechanistically how induction heads work, and can show they contribute to in-context learning.  Furthermore, the actual mechanism of operation suggests natural ways in which it could be repurposed to perform more general in-context learning.
* [Argument 6](#argument-extrapolation) (Continuity from small to large models): In the previous 5 arguments, the case for induction heads explaining in-context learning is stronger for small models than for large ones.  However, many behaviors and data related to both induction heads and in-context learning are smoothly continuous from small to large models, suggesting the simplest explanation is that mechanisms are the same.

For each argument, we’ll have a similar table to the one in this section, showing the strength of the evidence provided by that claim as it applies to large/small models and some/most of context learning. The table above is the sum of the evidence from all six lines of reasoning.

---

[Argument 1: Transformer language models undergo a “phase change” during training, during which induction heads form and simultaneously in-context learning improves dramatically.](#argument-phase-change)
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Our first line of evidence comes from correlating measures of in-context learning and measures of induction head presence over the course of training. Specifically, we observe a tight co-variation between them across dozens of models, of different sizes, trained on different datasets (See [Model Analysis Table](#model-analysis-table) for more on the models in which we observe this co-occurrence.).

The table below summarizes the quality of this evidence for the models we have studied: it applies to both large and small models, and is the expected outcome if induction heads were responsible for the majority of in-context learning, but it is only correlational and so could be confounded (discussed more below).

Strength of Argument for Sub-Claims
 Small Attention-Only Small with MLPs Large Models
Contributes Some Medium, Correlational Medium, Correlational Medium, Correlational
Contributes Majority Medium, Correlational Medium, Correlational Medium, Correlational

Our first observation is that if we measure in-context learning for transformer models over the course of training (defined as the 50th token loss minus the 500th token loss as described in [Key Concepts](#in-context-learning-key-concept)), it develops abruptly in a narrow window early in training (roughly 2.5 to 5 billion tokens) and then is constant for the rest of training (see figure below).  Before this window there is less than 0.15 nats of in-context learning, after it there is roughly 0.4 nats, an amount that remains constant for the rest of training and is also constant across many different model sizes (except for the one layer model where not much in-context learning ever forms).  This seems surprising – naively, one might expect in-context learning to improve gradually over training, and improve with larger model sizes,Although see [later discussion](#seemingly-constant) for a way in which a constant 0.4 nats can be viewed as a “larger” improvement for a more-powerful model, because attaining the same magnitude of improvement starting from a better baseline is more challenging. as most things in machine learning do.

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Although we only show three models above, the pattern holds true very generally: many examples are shown in the [Model Analysis Table](#model-analysis-table) later in the paper, including models of varying model architecture and size.

One might wonder if the sudden increase is somehow an artifact of the choice to define in-context learning in terms of the difference between the 500th and 50th tokens. We'll discuss this in more depth [later](#seemingly-constant). But for now, an easy way to see that this is a robust phenomenon is to look at the derivative of loss with respect to the logarithm token index in context. You can think of this as measuring something like "in-context learning per ε% increase in context length." We can visualize this on a 2D plot, where one axis is the amount of training that has elapsed, the other is the token index being predicted. Before the phase change, loss largely stops improving around token 50, but after the phase change, loss continues to improve past that point.

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It turns out that a sudden improvement in in-context learning isn't the only thing that changes in this window. If we go through the attention heads of a model and and score them for whether they are induction heads (using a prefix matching score which measures their ability to perform the task we used to define induction heads in [Key Concepts](#definition-of-induction-heads)), we find that induction heads form abruptly during exactly the same window where in-context learning develops (figure below). Again we show only a few models here, but a full set is shown in the [Model Analysis Table](#model-analysis-table). The exception is the one-layer model, where induction heads never form – just as in-context learning never substantially develops for the one-layer model.

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This already strongly suggests some connection between induction heads and in-context learning, but beyond just that, it appears this window is a pivotal point for the training process in general: whatever's occurring is visible as a bump on the training curve (figure below). It is in fact the only place in training where the loss is not convex (monotonically decreasing in slope).

That might not sound significant, but the loss curve is averaging over many thousands of tokens. Many behaviors people find interesting in language models, such as the emergence of arithmetic, would be microscopic on the loss curve. For something to be visible at that scale suggests it's a widespread, major change in model behavior. This shift also appears to be the first point where, at least for small models, the loss curve diverges from a one-layer model – which does not display the bump, just as it does not display the other abrupt changes.

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We can also apply principal components analysis (PCA) to the per-token losses, as described in [per-token-loss analysis](#per-token-loss-intro), which allows us to summarize the main dimensions of variation in how several models' predictions vary over the course of training.

Below we show the first two principal components of these models’ predictions, with the golden outline highlighting the same interval shown above, when in-context learning abruptly improved. We see that the training trajectories pivot during exactly the same window where the other changes happen. In some sense, whatever is occurring when in-context learning improves is the primary deviation from the basic trajectory our transformers follow during the course of their training.  Once again the only exception is the one-layer model – where induction heads cannot form and in-context learning does not improve.

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)
In summary, the following things all co-occur during the same abrupt window:

* Capacity for in-context learning sharply improves (as measured via the [in-context learning score](#in-context-learning-key-concept)).
* Induction heads form.
* Loss undergoes a small “bump” (that is, the loss curve undergoes a period of visibly steeper improvement than the parts of the curve before and after).
* The model’s trajectory abruptly changes (in the space of per-token losses, as visualized with PCA).

Collectively these results suggest that some important transition is happening during the 2.5e9 to 5e9 token window early in training (for large models this is maybe 1-2% of the way through training). We call this transition “the phase change”, in that it’s an abrupt change that alters the model’s behavior and has both macroscopic (loss and in-context learning curves) and microscopic (induction heads) manifestations, perhaps analogous to e.g. ice melting. As we'll see, many other [curious phenomena](#curiosities) occur during the phase change as well.

### [Looking at the Phase Change More Closely](#phase-change-more-closely)

A natural explanation would be that for all these models, the induction heads implement in-context learning: their formation is what drives all the other changes observed. To strengthen this hypothesis a bit, we check a few things. First, the window where the phase change happens doesn’t appear to correspond to a scheduled change in learning rate, warmup, or weight decay; there is not some known exogenous factor precipitating everything. Second, we tried out training some of the small models on a different dataset, and we observed the phase change develop in the same way (see [Model Analysis Table](#model-analysis-table) for more details). That said, it’s also the case that aside from the experiments varying the dataset, all these models were trained on the same tokens in the same order

Third, to strengthen the connection a little more, we look qualitatively and anecdotally at what’s going on with the model’s behavior during the phase change. One way to do this is to look at specific tokens the model gets better and worse at predicting. The model's loss is an average of billions of log-likelihood losses for individual tokens. By pulling them apart, we can get a sense for what's changed.

Concretely, let's pick a piece of text – for fun, we'll use the first paragraph of Harry Potter – and look at the differences in log-likelihoods comparing the start and the end of the phase change.Of course, this passage is merely a single piece of anecdata, shown here to provide a qualitative intuition rather than meant as systematic evidence. For a more comprehensive analysis of the observed behavioral change before and after the phase change, consult the “ablation to before-and-after vector” analyses in the [Model Analysis Table](#model-analysis-table) We'll notice that the majority of the changes occur when tokens are repeated multiple times in the text. If a sequence of tokens occurs multiple times, the model is better at predicting the sequence the second time it shows up. On the other hand, if a token is followed by a different token than it previously was, the post-phase-change model is worse at predicting it:

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We can also do this same analysis over the course of model training. The loss curve is the average of millions of per-token loss curves. We can break this apart and look at the loss curves for individual tokens.

In particular, let’s take a look at per-token loss trajectories for two tokens in the first paragraph of Harry Potter. In red, we show a token whose prediction gets dramatically better during the phase change: it’s the last of four tokens in “ The Dursleys”, a sequence that appears several times in the text. In blue, we show a token that gets meaningfully worse during the phase change: it’s the first-ever appearance of “ Mrs Potter”, after both previous instances of “ Mrs” were followed by “ Dursley” instead.

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Catherine Olsson
Nelson Elhage
Neel Nanda
Nicholas Joseph
Nova DasSarma
Tom Henighan
Ben Mann
Amanda Askell
Yuntao Bai
Anna Chen
Tom Conerly
Dawn Drain
Deep Ganguli
Zac Hatfield-Dodds
Danny Hernandez
Scott Johnston
Andy Jones
Jackson Kernion
Liane Lovitt
Kamal Ndousse
Dario Amodei
Tom Brown
Jack Clark
Jared Kaplan
Sam McCandlish
Chris Olah