Hill Space: Neural nets that do perfect arithmetic (to 10⁻¹⁶ precision)
10 months ago
- #neural networks
- #mathematical operations
- #optimization
- Neural networks often struggle with basic arithmetic and discrete selection tasks.
- The constraint W = tanh(��) �� σ(M��) enables systematic reliability in discrete selection by allowing optimal weights to be calculated rather than learned.
- Specific weight configurations can produce machine-precision mathematical operations, including matrix multiplication, exponential primitives, and trigonometric operations.
- Hill Space, created by the constraint, maps unbounded learned weights to the [-1,1] range, guiding optimization toward discrete selections.
- The paper explores Hill Space learning dynamics, a framework for new primitives, experiments, and implementation details.