Exterior-Memory

Code and data for "When Does Skew-Symmetric Wedge Memory Help? Mapping the Boundary Between Global Aggregation and Associative Recall."

Tensor Cache (arXiv:2605.22884) found that writing a skew-symmetric (wedge-product) memory instead of a plain outer-product one hurts associative recall, and traced this to a crosstalk term in the read. That ablation was run in a causal, streaming setting. This repo tests whether the same failure shows up in a non-causal, global-aggregation setting, or whether it's specific to recall.

Short version of the result: skew-symmetric memory loses to the symmetric baseline on every recall configuration tested (60/60), but wins or ties on most aggregation configurations (22/30). The paper has the full writeup.

• experiment.py — trains all four models (MeanMLP, Attention, Symmetric Memory, Exterior Memory) on both tasks, across two capacity settings, five seeds, and a size sweep. Writes results_full.csv. Supports a --quick flag for a fast smoke-test run (see below).
• results_full.csv — raw output from the sweep, one row per run. This is what every table and figure in the paper is computed from.
• make_figures.py — regenerates the three paper figures from the CSV.
• Exterior-Memory.tex / Exterior-Memory.pdf — the paper.

pip install -r requirements.txt
python experiment.py
python make_figures.py

The sweep is 384 short training runs (15k steps each, small models). It splits across however many CUDA devices are visible; on a single GPU it just runs sequentially. On two T4s it took a few hours.

For a fast sanity check before committing to the full sweep, run python experiment.py --quick, which cuts training to a couple hundred steps on a single seed over a reduced size sweep. Run python experiment.py --help to see all options (steps, seeds, output path).

results_full.csv already has everything. make_figures.py reads it directly, so you can check the figures/tables against the paper without running the sweep again.

@article{shabani2026exterior,
  title={When Does Skew-Symmetric Wedge Memory Help? Mapping the Boundary
         Between Global Aggregation and Associative Recall},
  author={Shabani, Laerti},
  journal={arXiv preprint},
  year={2026}
}

MIT, see LICENSE.