Note: EfficientNet — Compound Scaling

The problem, from first principles

If a CNN isn't accurate enough, the classic fix is to make it bigger — but "bigger" has three independent knobs: more layers (depth), more channels per layer (width), and larger input images (resolution). Scaling only one of these hits diminishing returns quickly: an extremely deep but narrow, low-resolution network wastes its depth on features too coarse to matter, and an extremely wide but shallow network can't build up the hierarchical features depth provides. EfficientNet's insight was that these three axes interact, so they should be scaled together, in a fixed, empirically-tuned ratio, controlled by a single number.

From theory to code

Theory says: pick base per-step multipliers for depth, width, and resolution (alpha, beta, gamma), and scale all three simultaneously by raising each to the power of a single "compound coefficient" phi that the user chooses based on how much extra compute budget is available.

Implement compound_scale(phi, alpha=1.2, beta=1.1, gamma=1.15) against that reasoning.

Constraints

• phi: a non-negative integer (phi=0 means "the unscaled base model").
• alpha, beta, gamma: positive floats, each the base multiplier applied once per unit increase in phi.
• Returns a 3-tuple of floats: (depth_mult, width_mult, resolution_mult).
• phi=0 always returns (1.0, 1.0, 1.0) regardless of alpha/beta/gamma, since raising anything to the power 0 is 1.

Hints

Open one at a time. Each gives away a little more than the last.