Elapsed-Time Memory Decay¶

A recurrent-model update that uses elapsed time to contract carried state or stale input toward a target before incorporating the next observation.

Version: v1 · 2026-10-03 · History
Domain-specific #: 13181

Core Idea¶

Elapsed-time memory decay is a recurrent-model operation: measure the interval since an observation or event, use that interval to move carried state or stale input toward a target, and incorporate the next observation through the adjusted value. GRU-D and Neural Hawkes implement this with different states, targets and timing conventions. “Decay” means shrinking departure from the target; the raw state or output need not fall, and no universal real-world forgetting law is asserted.[^{ref-70eceaacc153][}ref-781f45938d9a]

Scope of Application¶

GRU-D uses per-variable observation gaps to move missing values toward empirical means and damp a previous hidden state before a new GRU update. Neural Hawkes evolves continuous-time LSTM cells exponentially toward learned steady states between typed events, then updates them when the next event arrives. Missingness masks and event intensities belong to those respective architectures, not to every instance of the shared operation.[^{ref-70eceaacc153][}ref-781f45938d9a]

Clarity¶

Name the retained quantity, time gap, target, decay law and next update. A model that only appends timestamps to input may be time-aware without explicitly changing memory. A Neural Hawkes cell can rise toward its target while its deviation contracts, so a universal claim that the raw state fades is false.[^{ref-70eceaacc153][}ref-781f45938d9a]

Manages Complexity¶

Irregular sequences need not treat equally many observed steps as equally much elapsed time. The time-to-state map summarizes staleness in one recurrent update; rates may be learned per variable or cell. It supplies a modeling bias rather than proof that every older measurement is less useful, and it must be tested on the relevant data.[^{ref-70eceaacc153][}ref-781f45938d9a]

Abstract Reasoning¶

Hold observed values and event order fixed, then vary the elapsed gap. If the retained state or stale input changes toward a specified target before the next update, the mechanism is present. If only an appended time feature changes, it is a related but different architecture. Compare learned rates and targets against held-out evidence before interpreting them as real temporal behavior.[^{ref-70eceaacc153][}ref-781f45938d9a]

Knowledge Transfer¶

The operation transfers literally from irregular clinical measurements to continuous event streams, but GRU-D's masks and mean target do not transfer to Neural Hawkes's intensity model. Live prime Temporal Dynamics is the staged necessary skeleton because duration changes the update; physical Temporal Decay and Degradation is not the identity of an engineered recurrent memory transition.[^{ref-70eceaacc153][}ref-781f45938d9a]

[^ref-70eceaacc153]: Zhengping Che, Sanjay Purushotham, Kyunghyun Cho, David Sontag and Yan Liu, “Recurrent Neural Networks for Multivariate Time Series with Missing Values”, Scientific Reports 8, 6085 (2018), Methods §§“Notations” and “GRU-D: model with trainable decays,” equations 10–16 and Fig. 3. [^ref-781f45938d9a]: Hongyuan Mei and Jason Eisner, “The Neural Hawkes Process: A Neurally Self-Modulating Multivariate Point Process”, author-hosted original paper (2017), §3.2.2, PDF pp. 3–4, equations 4–5 and the between-event \(c(t)\) expression.

Relationships to Other Abstractions¶

Current abstraction Elapsed-Time Memory Decay Domain-specific

Parents (1) — more general patterns this builds on

Elapsed-Time Memory Decay presupposes Temporal Dynamics Prime

The elapsed interval must change the carried model state or stale input before its next update.

Hierarchy path (1) — routes to 1 parentless root

Elapsed-Time Memory Decay → Temporal Dynamics → Time

Neighborhood in Abstraction Space¶

Elapsed-Time Memory Decay sits in a sparse region of the domain-specific corpus (60^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Program Execution & Runtime Concepts (27 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08