d dimensions, exponentially many near-orthogonal directions: why superposition is inevitable in neural nets
livgorton · x · 2026-10-16
livgorton argues in a thread on an interpretability essay that superposition isn't a "radical" phenomenon: a d-dimensional space has only d orthogonal directions but exponentially many nearly orthogonal ones. Given how sparse neural network representations are, she'd be surprised if networks didn't exploit this capacity.
She adds that the definition has stayed consistent since Zoom In (2020), which described packing "more features into the limited number of neurons," relying on features rarely co-occurring; semantic unrelatedness provides good examples but isn't a requirement.
More from Research
- SpliceAI2 benchmarks show major gains across nine splicing-variant evaluations — anshulkundaje · 2026-10-16
- GRPO post-training collapses model distributions, clashing with long-horizon agents — zsakib_ · 2026-10-16
- RFdiffusion3 update in Science shows major gains in protease and metallohydrolase design — anshulkundaje · 2026-10-16
- ORL pushes diffusion LMs to a new speed-intelligence Pareto frontier with ~6.9x throughput gains — james_y_zou · 2026-10-16
- Why CoT is the key: classic paper shows transformers need it for serial problems — willcb · 2026-10-16
- Circuit view may dissolve much of deep learning's mystery, argues researcher thread — willcb · 2026-10-16