methods/api.md

---
family: hybrid
components: [optimization, architecture]
introduced-in: "[[liang2023-api]]"
stores: [layer input-subspace bases (via DualGPM), per-task expanded channel parameters]
requires-boundaries: "yes"
requires-task-id: "train+test"
memory-growth: sublinear
tags: [method]
---

# API (Adaptive Plasticity Improvement)

## What it does

A from-scratch continual learner that couples orthogonal-projection stability
with measured, demand-driven expansion. Old tasks are protected by projecting
each new-task gradient onto the complement of the accumulated old-task subspace
(maintained by DualGPM). Because that projection steadily consumes the space
left for new tasks, API measures how much of the raw new-task gradient survives
the projection — a per-layer gradient-retention ratio (GRR) it shows correlates
with new-task accuracy — and, before training each task, expands only the layers
whose retention has fallen below a target, adding input channels in proportion
to the deficit. So stability comes from the projection and plasticity is
restored exactly where the projection has depleted it.

## Aspects

- **Stores**: the DualGPM old-task subspace bases (see [[dualgpm]]) plus the
  per-task expanded channel parameters Bₗ,ₜ. No raw samples, no stored
  gradients. Expanded parameters (API-Param) grow monotonically but stay small
  relative to the basis store (Split CIFAR100: total 2.0M, capacity 105%).
- **Update rule**: for each new task t, (1) compute per-layer GRR(l,t) =
  E‖ĝₗ,ₜ‖/‖gₗ,ₜ‖ (surviving projected-gradient norm over raw), (2) set added
  input dimension dₗ ← dₗ + max(⌊K(ρ − GRR(l,t)) + 0.5⌋, 0) so low-retention
  layers grow and layers with GRR ≥ ρ do not, (3) train the (now wider) network
  with DualGPM-projected SGD; the newly added channels' transform Bₗ,ₜ is
  trained for the current task while the portions of Bₗ,ₜ belonging to previous
  tasks are frozen. K=10, ρ=0.5 across all experiments.
- **Requires**: task boundaries at training; task identity at *both* train and
  test — inference selects the task-specific expanded weight Wₗ,ₜ by task id
  (multi-head task-IL). From-scratch; per-layer ε_th matched to GPM; K, ρ tuned
  for the memory/accuracy trade-off.
- **Costs**: memory sublinear in tasks (DualGPM store rises then falls;
  expanded params grow slowly). Compute: one GRR estimation pass + DualGPM SVDs
  per task; training projects every mini-batch gradient. Inference is a single
  forward pass through the task-selected weights.

## Documented behavior

- [[liang2023-api]] (introduces): task-IL from-scratch, 20-task streams — best
  ACC on all four benchmarks (Split CIFAR100 81.4 / BWT −0.8; Split
  Mini-Imagenet 65.9 / −0.3; 5-Datasets 91.1 / −0.5; CIFAR100-sup 60.2) above
  GPM (78.9 / 61.2), TRGP (80.5 / 62.5) and expansion baselines, at lower memory
  than GPM and lower capacity (105%) than DEN/RCL/APD (130–191%). Ablations: the
  GRR-driven expansion beats a fixed-per-task "Equal" channel budget at matched
  accuracy; DualGPM-vs-GPM backing changes memory not accuracy; API's gain over
  GPM widens with task index as GPM's plasticity falls. Authors flag the method
  is confined to the task-IL setting (task id at test) and leave class-IL /
  task-free extension open.

## Links

combines:: [[dualgpm]] (supplies the old-task gradient subspace and the orthogonal projection that provides stability; API adds the measured expansion on top)
uses:: [[orthogonal-update-projection]] (new-task gradients projected onto the old-task subspace complement each step — DualGPM's constraint, providing the stability half)
uses:: [[retention-gated-channel-expansion]] (per-layer input channels added before each task in proportion to the gradient-retention deficit ⌊K(ρ − GRR(l,t))+0.5⌋, so only projection-choked layers grow — GRR read directly off the projection as a data-free plasticity gauge)

## Papers engaging this method

```dataview
LIST FROM [[]] AND ("papers" OR "influences")
```