Differential Memory Decay: A Continuous-Time Model of Forgetting and Semantic Drift
Authors: Priyam Ghosh, Krish Jaiswal, Sauhard Gupta
A continuous-time mathematical framework for differential memory decay — formalizing forgetting as a computational primitive through decay operators, graph-Laplacian diffusion, and replay-based stabilization.
Abstract
Forgetting is not a defect of memory systems but a prerequisite for long-term stability, generalization, and adaptive intelligence. Biological memory relies on multiple interacting mechanisms of decay, including synaptic weakening, semantic drift, and structural pruning, to prevent interference, regulate representational capacity, and maintain coherence over time.
In contrast, contemporary artificial memory systems used in large language models and agentic frameworks typically accumulate information indefinitely, lacking principled mathematical formulations for controlled forgetting. This discrepancy leads to semantic overload, unbounded memory growth, and instability in long-horizon reasoning.
Core Contributions
1. Continuous-Time Decay Framework
We develop a continuous-time mathematical framework for differential memory decay, grounded in both computational neuroscience and energy-based dynamics. We formalize several distinct classes of decay operators:
- Linear forgetting at multiple timescales
- Category-specific decay matrices for selective memory pruning
- Competition-driven normalization to prevent representational collapse
- Graph-Laplacian diffusion that induces semantic smoothing and drift
2. Replay as Anti-Decay
We further show that replay, modeled as energy descent in the absence of external input, acts as an anti-decay mechanism that selectively stabilizes long-term attractors while allowing transient information to fade.
The interaction between decay and replay creates a natural hierarchy:
High-frequency memories → Rapid decay (hours)
└── Unless reinforced by replay
Semantic associations → Slow drift (days–weeks)
└── Stabilized by graph structure
Core knowledge → Near-permanent (months+)
└── Deep energy minima resist decay
3. Stability & Coherence Results
Through analytical results and synthetic experiments, we demonstrate how the interaction between decay, diffusion, and replay yields memory representations that remain:
- Compact — bounded memory growth regardless of input volume
- Stable — robust to perturbation and noise
- Semantically coherent — related concepts stay clustered over time
Key Insight
Unlike prior work that focuses on storage or retrieval mechanisms, this paper isolates forgetting as an independent and valuable computational primitive. The framework presented here is architecture-agnostic and provides a theoretical foundation for integrating biologically motivated forgetting into future artificial memory systems.
Citation
@article{ghosh2026differential,
title={Differential Memory Decay: A Continuous-Time Model of Forgetting and Semantic Drift},
author={Ghosh, Priyam and Jaiswal, Krish and Gupta, Sauhard},
year={2026},
doi={10.13140/RG.2.2.19914.63689}
}