The cost of local Transformer learning.
What happens when a Transformer learns in separate stages? Two CPU studies examine the speed, memory, and learning quality of local training and predictive coding.
Machine Learning
Research.
KarLex AI's papers on Transformer learning, quantum computing, and verifiable search, with visual summaries and journal status.
Current manuscripts
2026Exact softmax from residual overlaps.
Compute part of an attention score classically, then sample the remainder. This study shows how the split changes measurement cost while preserving the ideal softmax distribution.
Quantum Information Processing
When more quantum measurements stop helping.
Do more quantum measurements produce a better answer? A reanalysis of hardware records tracks the error that remains as measurement budgets grow.
Discover Quantum Science
Optimal search with checkable proofs.
Find the fewest questions needed to identify an answer, even when some replies are wrong. Then give an independent checker a proof that the question count is optimal.
Theory of Computing Systems
Earlier work
PreprintsQuantum hybrid modules for AI.
The original QHM project explores quantum subroutines for AI. Its hardware records and attention questions lead into two focused follow-up studies.
Research Square