Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
A reported stochastic Nesterov experiment is empirical evidence
Example
Sutskever, Martens, Dahl, and Hinton report experiments on the Curves, MNIST, and Faces deep-autoencoder tasks using sigmoid networks, their sparse initialization, 750,000 parameter updates per trial, minibatches of size 200, and no regularization. They used a slowly increasing momentum schedule capped by and selected the best training learning rate for each schedule from . In Table 1, the Curves training squared error is for their Nesterov variant with and for the zero-momentum SGD baseline. The paper reports training errors only; this setup-specific empirical comparison supplies no general stochastic convergence rate or test-risk guarantee.
Example references
Nesterov accelerated gradient algorithm The deterministic algorithm evaluates the gradient at the look-ahead point; the reported experiment replaces the full gradient by a minibatch gradient.
Bottou, Curtis, and Nocedal, Optimization Methods for Large-Scale Machine Learning
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
4 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Ilya Sutskever, James Martens, George Dahl, and Geoffrey Hinton, On the Importance of Initialization and Momentum in Deep Learning (standard reference, not scraped)
- Léon Bottou, Frank E. Curtis, and Jorge Nocedal, Optimization Methods for Large-Scale Machine Learning (standard reference, not scraped)