Training curves
Accuracy
Loss (log-x; slingshot events appear as spikes)
Cross-entropy loss on the same runs: train loss falls to near zero at memorization; test loss falls only at generalization. Sudden spikes are the slingshot instabilities.
Fourier structure
Embedding spectrum
Neuron frequency alignment
Attention patterns
Per-example attention (rows: query · columns: key · stronger colour = more weight)
Sampled held-out examples saved during analysis. The final row of each map is the “=” position — the one whose output becomes the answer.
Direct logit attribution
Mean direct contribution to the correct answer
Exact decomposition (no LayerNorm): component outputs at the “=” position, projected through the unembedding, sum to the model's centered logits. Near-zero bars for layer-0 components reflect indirect action, not unimportance — compare the ablation panel.
Ablation & activation patching
Mean-ablation: accuracy when each component is off
Sorted worst-first: the lower a bar, the more the model depends on that single component (necessity).
Patching: recovery (denoise) per component
How much of the clean answer margin returns when this one component's clean activity is copied into a corrupted run (sufficiency of its information).
Residual-stream patching (layer × position)
Recovery when a single residual-stream vector is patched clean into a corrupted run: the answer information sits at the operand positions entering block 0 and entirely at “=” after block 1.
Path-patching matrix
Sender → receiver edge effects
Fraction of the answer margin destroyed when only the sender→receiver path carries corrupted information (receiver input channel q/k/v resolved; blank cells are non-causal orderings).
Component ranking
Sorted by causal necessity (normalized performance lost under mean ablation). All four lenses shown for comparison.
Neuron-level refinement
Definitions
- Faithfulness
- Performance of the model with everything outside a component set mean-ablated, linearly normalized so 0 = everything ablated and 1 = intact model. The scale extrapolates beyond [0, 1].
- Mean ablation
- Replacing a component's activation with its average over the training set, computed separately per sequence position.
- Activation patching (denoise)
- Run a corrupted prompt, copy in one component's activation from the clean prompt, and measure how much of the clean answer margin returns (0 = corrupt baseline, 1 = fully clean).
- Path patching
- Corrupt only the direct connection from one sender component into one receiver input (q, k, v, or MLP input), everything else clean; report the fraction of the answer margin destroyed. Exact here because the residual stream is a linear sum of component outputs.
- Direct logit attribution (DLA)
- A component's output at the “=” position projected through the unembedding onto the correct answer (centered over answers). Direct path only.
- Embedding Fourier power
- Squared norm of the number-token embedding projected onto the orthonormal cos/sin basis over Z₉₇, summed per frequency (DC excluded).
- Rotation-formula R²
- Fraction of the centered logit tensor's variance explained by orthogonal projection onto cos/sin(2πk(a+b−c)/97) at the seed's key frequencies.
- Slingshot
- A transient optimizer instability: training accuracy collapses from ~100% and recovers within ~10³ epochs. Detected in the saved histories as train accuracy < 90% after having reached 99%.
- Architecture
Sources: per-seed metrics.json,
fourier.json, discovery.json,
ranking.csv, patching.json,
path_patching.json, dashboard_data.json under
results/production/, assembled by
visualization_site/build_data.py.