REVIEW 6 cited by
Linear algebra with transformers
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Linear algebra with transformers
read the original abstract
Transformers can learn to perform numerical computations from examples only. I study nine problems of linear algebra, from basic matrix operations to eigenvalue decomposition and inversion, and introduce and discuss four encoding schemes to represent real numbers. On all problems, transformers trained on sets of random matrices achieve high accuracies (over 90%). The models are robust to noise, and can generalize out of their training distribution. In particular, models trained to predict Laplace-distributed eigenvalues generalize to different classes of matrices: Wigner matrices or matrices with positive eigenvalues. The reverse is not true.
Forward citations
Cited by 6 Pith papers
-
Learning First Integrals via Backward-Generated Data and Guided Reinforcement Learning
FISolver trains a compact LLM on backward-generated (differential equation, first integral) pairs and uses guided reinforcement learning to outperform larger models and Mathematica on first-integral benchmarks at lower cost.
-
Reconstructing conformal field theoretical compositions with Transformers
Transformers reconstruct the constituent RCFTs in tensor-product theories from low-energy spectra, reaching 98% accuracy on WZW models and generalizing to larger central charges with few out-of-domain examples.
-
The Long Delay to Arithmetic Generalization: When Learned Representations Outrun Behavior
The grokking delay in encoder-decoder models on one-step Collatz prediction stems from decoder inability to use early-learned encoder representations of parity and residue structure, with numeral base acting as a stro...
-
Arithmetic Pedagogy for Language Models
A small GPT-2 model trained from scratch on GASING-derived CoT supervision for arithmetic reaches over 80% held-out accuracy, exhibits three learning phases, and develops both procedural and associative reasoning.
-
The Long Delay to Arithmetic Generalization: When Learned Representations Outrun Behavior
Grokking delay on Collatz prediction is a decoder access bottleneck after early encoder structure learning, with numeral base as a strong inductive bias on learnability.
-
Learning the symmetric group: large from small
Transformer trained on S10 permutation prediction from transpositions generalizes to S25 with near 100% accuracy using identity augmentation and partitioned windows.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.