Online Learning Algorithms

Online Learning Algorithms#

Study the approximation carried by each algorithm before treating its output as a gradient estimate. The examples deliberately use different model structures: a matched task would be easier to compare visually, but it would not exercise the structural assumptions that distinguish these estimators.

Note

Read Core Concepts first. The chapters assume that you understand ETP selection and the role of hidden-state recurrences.

Choose an algorithm#

D-RTRL

Follow diagonal recurrent traces across a sequence and examine when the approximation can differ from BPTT.

D-RTRL: parameter-dimensional online traces
pp-prop

Follow input/output-factorized traces and the contraction that turns those factors into parameter gradients.

pp-prop: input/output-factorized online traces
e-prop

Separate local eligibility traces from symmetric or random-feedback learning signals in a recurrent spiking network.

e-prop: local eligibility and learning signals
OSTL

Compare the with-H recurrent rule with the without-H feedforward rule.

OSTL: with-H and without-H regimes
SnAp

Widen a trace over an explicitly sparse recurrent dependency graph.

SnAp: sparse n-step recurrent influence

Select by retained structure#

Chapter

Trace structure

Appropriate regime

Important boundary

D-RTRL

Parameter-shaped trace with a diagonal hidden-Jacobian approximation

General recurrent ETP models

Cross-position recurrence is approximated

pp-prop

Separate input and output factors

Linear-memory recurrent SNN training

Factorization error is model dependent

e-prop

Local trace times a broadcast learning signal

Recurrent LIF/ALIF networks

Random feedback is not symmetric feedback

OSTL

With-H or without-H temporal factor

Recurrent or feedforward SNNs, respectively

The two regimes are not interchangeable

SnAp

Sparse n-step recurrent neighborhood

Structurally sparse recurrence

Dense recurrence saturates too early to be informative

For a first pass, read D-RTRL before pp-prop, then choose the SNN-specific or sparsity-specific chapter that matches the model. No chapter establishes universal equality with BPTT; each states the regime and checks appropriate to its approximation.