How Do Transformers Learn Variable Binding in Symbolic Programs?
Background
Experiment Overview
Learn about the background and motivation for the project, experimental design, main results, and how to use this website.
Watch Video Abstract
Watch a short video abstract presenting the key findings of our ICML 2025 paper with animated plots.
Glossary
A reference guide for key technical terms relevant to the background and design of the experiment.
Program Graph Visualizer
Visualize variable assignment programs as interactive directed graphs.
Basic Analysis
Program Analysis
Interactive heatmap showing model predictions across checkpoints and test programs. Click cells to copy programs for detailed analysis.
Training Trajectory
Track the model's performance across 105,400 training steps, revealing three distinct learning phases.
Checkpoint Analysis
Analyze the predictions of individual training checkpoints across different attributes with interactive bar charts or Sankey diagrams.
Checkpoint Stats
Generate a report for each model checkpoint showing different metrics including accuracy by feature, prediction distributions, confusion matrices, and feature importance.
Advanced Analysis
Checkpoint Comparison
Compare multiple training checkpoints to visualize differences in accuracy, prediction patterns, and feature-based performance across training stages.
Logit Analysis
Visualize how the model's internal logit values evolve across layers and training steps. Compare logits for correct answers vs first line constants.
Attention Heads Patching
Visualize the results of causal intervention experiments on attention heads to understand how different heads affect the model's ability to process variable chains.
Subspace Visualization
Visualize how variable names and numerical constants organize into distinct clusters in the model's representation space during training.