“Challenge: Hand coding weights for efficient sequence memorisation” by Linda Linsefors, Lucius Bushnaq

We hand coded weights for one layer MLPs that memorises labels for input token sequences of length two. The number of facts our hand-coded models can memorise with 90% accuracy[1]scales roughly linearly with the models' parameter count[2], just like trained models for the same architecture. However, our hand-coded models' scaling prefactor still falls short of trained models' by a factor of . A hybrid solution in which we handcode the MLP input weights and learn the MLP output weights, which amounts to a linear classification problem[3], falls short by a factor of .

Figure 0: Max number of facts each model can learn when requiring 90% accuracy on evaluation. The fitted lines are best fit for solving for .

We pose a challenge to the community: Find better constructions than ours that can memorise more facts in the same number of weights and close the gap to the trained solution further.[4]

Background: Why sequence memorization, and why an MLP?

The goal of this research is to get a clearer understanding of how look-ups are encoded in LLMs.

We expect that a lot of the information stored in the weights of an LLM is memorized facts, rather than general circuits. [...]

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Outline:

(01:11) Background: Why sequence memorization, and why an MLP?

(03:54) Outline

(06:21) Training data

(07:26) Testing Various Model Architectures

(08:46) Model variations

(08:50) Mixing

(09:51) MLP

(10:21) Norms

(10:46) Results

(14:43) Scaling

(15:55) Challenge: Benchmark for understanding

(16:53) Rules

(17:48) Model architecture

(19:11) Evaluation Criteria

(20:13) How this challenge relates to known constructions

(22:08) Our attempt

(23:10) Algorithm: Summary

(25:23) Algorithm: More details

(26:15) Assigning neurons to labels

(27:45) Embedding weights

(28:44) Unembedding weights

(29:11) Hybrid model: Half hand-coded, half learned

(29:23) Hyperparameter search over S and top_fraction

(29:53) Results

(31:36) Takeaways

(32:39) Do the matrices look similar?

(34:25) Contributions and acknowledgements

(34:52) Appendix A: Near-optimal construction for

(37:18) Appendix B: More on what parts of the model matter

(41:10) MLP + Norms + No Residual around MLP + No Bias + ReLU

(42:13) Triple or pairwise comparisons

(42:32) Mixing

(45:03) MLP

(46:42) Norms

(48:52) Residual Connection around the MLP

(50:12) MLP Bias

(51:37) Activation Function

(52:28) Appendix C: More on Scaling

(53:17) Appendix D: Best S (number of neurons per label) for the hand-coded and hybrid models

(56:07) Appendix E: Best "top_fraction" for the hand-coded and hybrid models

The original text contained 30 footnotes which were omitted from this narration.

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First published:
July 23rd, 2026

Source:
https://www.lesswrong.com/posts/KWtchKwwnJkd4bwCi/challenge-hand-coding-weights-for-efficient-sequence-1

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Narrated by TYPE III AUDIO.

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