💻 computer science

Testing History Dependence Between In-Context and In-Weights Learning

This study demonstrates that while the order of training (approaching a balanced mixture from different directions) creates a transient, measurable difference in the strength of in-context versus in-weights learning mechanisms, it does not result in persistent hysteresis or fundamentally different causal circuit organizations in small transformers.

Original authors: Zuo Yuchen

Published 2026-08-06

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Zuo Yuchen

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are teaching a robot to tell jokes. You can teach it in two ways. First, you can show it a few examples right before it speaks, like a reference sheet on the table. The robot reads the reference sheet and figures out the punchline based on what it sees right now. This is called In-Context Learning. It's like the robot is thinking on its feet. Second, you can practice with the robot for hours until it memorizes the jokes so well that it doesn't need the reference sheet anymore. The jokes are now hard-wired into its brain. This is In-Weights Learning.

For a long time, scientists wondered: if you give the robot the exact same mix of reference sheets and practice, does it always solve the problem the exact same way? Or does it matter how it got there? Did it start by memorizing and then learn to read the reference sheet? Or did it start by reading the reference sheet and then memorize the jokes? This question is about history dependence. In the world of physics, this is similar to hysteresis—like a magnet that remembers which way it was pulled, even after you stop pulling it. If a robot's brain has hysteresis, its current state isn't just about what it's seeing now; it's also about the path it took to get there. This matters because if AI models are like this, we might not be able to predict their behavior just by looking at their current data; we'd need to know their entire training history.

This paper takes a small, controlled robot (a tiny AI model) and puts it through a specific test to see if it has this kind of "memory of the path." The researchers set up a game where the robot has to guess a secret code. Sometimes the code depends on a clue given in the current sentence (the reference sheet), and sometimes it depends on a rule the robot learned long ago (the hard-wired memory). They trained two identical copies of the robot to reach the exact same point in the game, but they took them there via different routes. One copy started by focusing on the hard-wired rules and slowly shifted to the reference sheets. The other copy started with the reference sheets and slowly shifted to the hard-wired rules.

The researchers found that when both robots arrived at the exact same spot, they didn't act exactly the same. The one that came from the "hard-wired" side was slightly more likely to use the reference sheet than the one that came from the "reference sheet" side. It was as if the robot that started with rules was still a little bit "stuck" in that mindset, even though it was now looking at the same clues as the other robot. This difference was real and measurable: the gap in their behavior was about 0.098 points on a specific scale, and this happened in all five of the different training experiments they ran.

However, this memory of the path was very short-lived. The researchers kept the robots training at that same spot for a little while longer. After just 25 more steps, the difference started to flip and then disappear. By the time they took 100 steps, the two robots were acting almost identically. The "ghost" of the path they took had faded away.

To understand why this happened, the scientists looked inside the robot's brain. They found that both robots were using the exact same internal parts to solve the problem. They didn't switch to a different "circuit" or a new way of thinking. Instead, the robot that came from the "hard-wired" side just turned up the volume slightly on the part of its brain that reads the reference sheet. It was a temporary volume boost, not a permanent change in the wiring.

So, the paper suggests that while AI models can briefly remember how they got to a certain point, this isn't a permanent "hysteresis" loop where they get stuck in different states forever. It's more like a momentary lag, a quick overshoot that settles down as the model continues to learn. The study shows that to truly understand an AI's behavior, you have to look at its immediate history, but you don't need to worry that it will stay stuck in a weird state forever just because of how it was trained. The model eventually catches up and forgets the path, focusing only on the destination.

Technical Summary: Testing History Dependence Between In-Context and In-Weights Learning

Problem Statement

In-context learning (ICL) and in-weights learning (IWL) allow transformers to solve prediction tasks using either prompt-based associations or stable parameterized associations. While prior work has established that ICL can emerge and subsequently decline in favor of IWL during training, it remains unclear whether the current data distribution uniquely determines the model's mechanism. Specifically, it is unknown if the state of a model at a fixed mixture of ICL and IWL is unique, or if the model retains a "memory" of the training trajectory (history dependence) that influences its behavior and causal circuit organization. This study investigates whether a model arriving at an identical ICL/IWL mixture from opposite directions (increasing vs. decreasing mixture schedules) exhibits different behaviors or causal sensitivities, a phenomenon analogous to hysteresis in dynamical systems.

Methodology

The author designed a controlled, counterbalanced causal study using a small decoder-only transformer (2 layers, 4 heads, 72k parameters) on an ambiguous associative-recall task.

Task Design: The task involves predicting a value for a query key. Two competing rules exist: a contextual rule (based on the current prompt's key-value pairs) and a fixed rule (a global permutation learned in weights). A mixture parameter $p_{ICL}$ controls the probability that the training target follows the contextual rule. Crucially, the input distribution remains fixed while $p_{ICL}$ varies, ensuring that changes in behavior are driven by the target distribution, not input statistics.
Counterbalanced Training Schedules:
- An "anchor" model is trained to convergence at a target mixture $p_0$ .
- The model and optimizer state are cloned.
- Two branches traverse triangular mixture schedules with identical update counts, identical multisets of training examples, and identical cumulative exposure, but in opposite orders:
  - From Below: $p_0 \to p_0 + \delta \to p_0 - \delta \to p_0$ (approaching the target from the IWL-favoring side).
  - From Above: $p_0 \to p_0 - \delta \to p_0 + \delta \to p_0$ (approaching the target from the ICL-favoring side).
- This design isolates the effect of order and final approach direction while matching training age, optimizer state, and data exposure.
Evaluation Metrics:
- Behavioral: The logit margin between the contextual and fixed answers on conflict trials.
- Causal Interventions:
  - Activation Patching: Replacing internal states between clean and corrupted runs to trace information flow.
  - Mean Replacement: Replacing attention head outputs with their checkpoint-specific means to measure the contribution of example-specific information.
- Relaxation Control: Evaluating models after 0, 25, and 100 additional updates at the fixed target mixture to distinguish transient lag from persistent hysteresis.

Key Contributions

Counterbalanced Schedule Design: A novel experimental setup that compares opposite arrival directions at identical mixture, update count, optimizer age, and cumulative component exposure.
Behaviorally Identifiable Task: A task where contextual and weight-based answers directly conflict, allowing strategy preference to be measured as a continuous logit margin rather than aggregate accuracy.
Paired Behavioral and Causal Tests: Integration of residual-stream patching and head/MLP mean replacements across independent training seeds to localize the source of history dependence.
Relaxation Control: A protocol to separate persistent history effects from models that are merely slow to track a changing data mixture.

Results

Immediate History Dependence: At the balanced mixture ( $p_0 = 0.5$ ), models arriving from below (IWL-favoring side) showed a higher contextual-minus-fixed logit margin ( $+0.0976$ ) compared to those arriving from above. This difference was consistent across all five independent seeds (all positive), yielding the smallest attainable exact two-sided sign-flip $p$ -value of 0.0625. The author describes this common sign and interval rather than making a binary significance claim.
Transient Nature: The behavioral gap reversed slightly after 25 common updates and vanished (near zero) after 100 updates. This indicates the effect is a transient overshoot rather than a stable branch or quasi-static hysteresis.
Causal Mechanism:
- Replacing all query-position attention-head outputs with checkpoint-specific means attenuated 86.8% of the immediate behavioral gap.
- Despite the behavioral difference, the identity of the dominant attention head and the topology of activation patching routes were nearly identical (correlations > 0.999) between the two histories.
- The results suggest that training order modulates the gain of a shared contextual route rather than selecting a distinct, alternative circuit.

Significance and Claims

The paper concludes that while small transformers exhibit finite-rate path dependence at a matched ICL/IWL mixture, they do not exhibit quasi-static hysteresis.

Modest Claim on Hysteresis: The author explicitly states that the observed effect is a "transient memory of training order" that relaxes quickly. They argue that curriculum order effects should not automatically be labeled as hysteresis without demonstrating a persistent branch gap under slow sweeps.
Developmental Interpretability: The study highlights that a model's snapshot (parameters and current data mixture) may not uniquely predict its immediate computation; closely matched models can retain short-lived information about their training history.
Circuit Identity vs. Engagement: A key finding is the distinction between circuit topology and circuit engagement strength. The same causal circuit (the contextual route via specific attention heads) was used in both histories, but its engagement strength was modulated by the training trajectory.
Methodological Rigor: The paper emphasizes that without measuring relaxation (the "hold" phase), transient differences could be misinterpreted as persistent circuit branches. The matched-loop design provides a compact method to control for age and exposure while testing for history dependence.

The author notes limitations regarding external validity (small synthetic models) and the inability to fully separate optimizer state memory from parameter memory, cautioning against generalizing these findings to frontier language models without further testing across rates, optimizers, and naturalistic tasks.