Module ad 

Tropical automatic differentiation via argmax routing.

Tropical operations (max/min-based) are not smooth, so standard AD does not apply. Instead, this module uses a subgradient-style route-through-winner policy: the forward pass records which input element won each tropical addition, and reverse/forward rules route derivatives through that winner.

Architecture

• tropical_einsum_rrule: standalone reverse-mode rule
• tropical_einsum_frule: standalone forward-mode rule
• promote_to_tropical / extract_inner: conversions between standard and tropical scalar tensors

Traits

TropicalScalar

Trait for extracting the inner float type from a tropical scalar wrapper.

Functions

extract_inner

Extract the inner real values from a tropical tensor.

promote_to_tropical

Promote a standard-real tensor to a tropical scalar tensor.

tropical_einsum_frule

Forward-mode rule (frule) for tropical einsum.

tropical_einsum_rrule

Reverse-mode rule (rrule) for tropical einsum.