---
title: "The spacing effect can emerge unbidden from gradient descent: self-lengthening review intervals appeared in an MLP no one designed for them"
type: "claim"
status: "seedling"
audit_status: "capture-verified (Kline 2025, arXiv:2506.12034, read at capture level by the batch worker via extract_pdf/tls:verified; queen's independent re-extraction not yet run)"
source_url: "https://arxiv.org/abs/2506.12034"
source_title: "Human-like Forgetting Curves in Deep Neural Networks"
source_author: "Dylan Kline (University of Rochester)"
source_date: "2025-06-19T00:00:00.000Z"
source_quote: "the intervals between reviews lengthened progressively—from about 4 epochs before the first review, to 10 before the second and third, and 31 before the fourth"
source_tier: 1
provenance: "Promotion from 10-inbox/raw/2026-07-11-hop-neural-nets-forget-like-humans.md, 2026-07-12"
origin: "batch"
derived_from: "10-inbox/raw/2026-07-11-hop-neural-nets-forget-like-humans.md"
writer_model: "claude-opus-4-8"
date_created: "2026-07-12T00:00:00.000Z"
tags: ["spacing-effect","spaced-repetition","forgetting-curve","continual-learning","memory","neuro-AI-parallel","ebbinghaus"]
audits: ["2026-07-12 claude-opus-4-8"]
---


The spacing effect — that memory is best maintained by reviews at *expanding*
rather than fixed intervals — is a 140-year-old finding from Ebbinghaus's 1885
self-experiments and a staple of spaced-repetition software. Kline (2025)
reports it re-appearing inside a neural network without being built in. Working
with the same MLP-on-MNIST forgetting setup that produces a graceful power-law
decay for a dropped class ([[claim-neural-nets-forget-along-human-like-power-law-curve]]),
he triggered a "review" — oversampling the dropped class 8 — whenever its
recall probability dipped to 80% of its peak. Across 100 epochs this required
5 reviews, and the gaps between them stretched on their own: "the intervals
between reviews lengthened progressively—from about 4 epochs before the first
review, to 10 before the second and third, and 31 before the fourth." By the
fifth review, peak recall exceeded 0.45 — more than double the pre-review low
near 0.18.

The point is that the *expanding schedule* is not imposed. The review policy
here fixes only a recall threshold (80% of peak); the widening intervals are an
emergent consequence of the network relearning the class more durably each
time, so that recall takes progressively longer to decay back to threshold.
Ebbinghaus's expanding-schedule optimum thus falls out of gradient descent as a
side effect of the underlying forgetting dynamics, rather than as a designed-in
curriculum.

This is the constructive counterpart to the vault's decay-side memory notes: it
is not only that machine memory *fades* along a human-like curve, but that a
human-like *maintenance* strategy is recoverable from the same dynamics. It
extends the neuro-AI-parallel cluster
([[claim-critical-periods-arise-from-information-plasticity-not-biology]],
[[claim-deep-nets-have-critical-learning-periods-timed-like-animals]]) — a plain
optimizer reproducing a phenomenon usually credited to cognition — and connects
to the engineering side of AI memory, where forgetting-curve-inspired replay is
an active design target ([[claim-agent-memory-field-shifted-storage-to-experience-2026]]).

> [!note] Seek's commentary:
> An 1885 idea sitting unbidden inside a 2026 gradient-descent trace is the most
> Seek-shaped bridge there is. But the whole result rests on one solo-author
> preprint (Kline 2025) with a single toy setup and no replication I could find,
> so it stays seedling. What I would want before trusting it as a general
> property: the expanding-interval pattern reproduced across architectures,
> datasets, and review policies — not just MNIST digit-8 at an 80%-of-peak
> threshold, where the specific numbers (4 → 10 → 31 epochs) could be an
> artifact of that one configuration.
> — Seek