Intrinsic Forgetting in Learning Systems

• Intrinsic Forgetting is the process by which information degrades internally due to limitations in capacity, interference, and decay mechanisms.
• It is observed in biological synaptic depotentiation and in deep network models where representational constraints and stochastic updates lead to performance decay.
• This phenomenon serves as both a challenge and a benefit, enabling noise suppression, enhancing memory efficiency, and protecting privacy in adaptive learning systems.

Intrinsic forgetting denotes the inevitable, algorithm- or system-internal process by which previously stored information is attenuated, revised, or rendered irretrievable even in the absence of external task or data distributional shift. Unlike catastrophic forgetting, which is driven by explicit shifts in task, data, or context, intrinsic forgetting arises from the interplay of representational constraints (capacity, interference), learning dynamics (optimization, stochasticity), and architectural or mechanistic properties (plasticity, decay, competition). Intrinsic forgetting is evident across biological and artificial systems, from synaptic depotentiation in neural circuits to information loss in deep networks and LLMs, and is increasingly recognized as both a challenge and a functional mechanism underpinning stability, adaptivity, and memory efficiency.

1. Formal Definitions and Foundational Frameworks

Intrinsic forgetting can be formalized from several perspectives:

• Predictive Self-Consistency Violation: A learning system exhibits intrinsic forgetting if its predictive distribution over future outcomes is not projectively self-consistent after updating on data sampled from its own generative model. Let $q(H^{t+k:\infty}|Z_{t-1},H_{0:t-1})$ denote the predicted future distribution and $u$ the update operator; then, the forgetting divergence is

$$\Gamma_k(t) = D\left(q(H^{t+k:\infty} | Z_{t-1},H_{0:t-1}) \ \|\ q_k^*(H^{t+k:\infty}|Z_{t-1},H_{0:t-1})\right)$$

where divergence $D$ quantifies the informational difference before and after an internally consistent update on own-expected targets. Any $\Gamma_k(t) > 0$ signals predictive information loss intrinsic to the learner’s update rule (Sanati et al., 6 Nov 2025).

• Capacity-Induced Lower Bound: For parameterized models, intrinsic forgetting is the irreducible increase in loss on old data (distribution $D_\mathrm{old}$) even under perfect rehearsal, arising solely when model capacity $C$ is saturated:

$$\Delta_\text{forg} = L_\text{old}(\theta_\text{new}) - L_\text{old}(\theta_\text{old}) > 0$$

cannot be eliminated by any regularization or replay if $C$ is exhausted (Marek et al., 25 May 2026).

• Within-Task Example Forgetting: For stationary data, individual examples are “forgotten” when their predicted label transitions from correct to incorrect over the training trajectory. Counting such events yields a per-example forgetting profile (Toneva et al., 2018).
• Geometry of Retrieval: Forgetting arises from similarity-based retrieval in finite- or low-dimensional embedding spaces subject to noise and interference, yielding a probability of correct recall that decays as a power-law with the number of competitors, independent of explicit decay (Barman et al., 27 Mar 2026).

2. Mechanistic Substrates and Mathematical Models

A wide variety of mechanistic substrates instantiate intrinsic forgetting:

• Synaptic Transience: Short-term potentiation windows (e.g., the $A_{\tau}(\sigma, t)$ indicator with window $u$0) induce forgetting by ensuring that only co-firings in the recent past are encoded; longer persistence induces topological pollution, while shorter leads to information loss. Optimal $u$1 balances stability and denoising (Chowdhury et al., 2017).
• Bounded Weights and Palimpsest Memory: In Hopfield (and related) networks, strictly bounded (clipped) synapses cause the basin of attraction of stored patterns to decay exponentially with temporal “age”:

$u$2

effectively implementing palimpsest memory with a hard tradeoff between recency and fidelity, controlled by the clipping threshold (Marinari, 2018).

• Sparse and Competitive Codes: Mechanisms such as plug-and-play forgetting layers (with inhibitory neural gates and cooperative/lateral inhibition) introduce active regulation of plasticity, selectively extinguishing less salient features and continually reallocating capacity (Peng et al., 2021).
• Curvature-Based Consolidation: Synapse-specific local estimates of energy landscape curvature $u$3 (e.g., $u$4) attenuate update magnitude, stabilizing “important” weights against interference and prolonging retention of salient patterns (Deistler et al., 2018).
• Adaptive Hierarchical Decay: Agent memory architectures (e.g., FadeMem) implement multi-layer (e.g., short/long-term) decay governed by context-sensitive importance scores:

$u$5

with $u$6 adapted via relevance, usage frequency, and recency, and discrete transitions between decay layers (Wei et al., 26 Jan 2026).

• Bayesian Discount and Exponential Recency: In LLMs, intrinsic forgetting is mathematically modeled as a per-step exponential discount, such that context evidence is weighted by

$u$7

and entire in-context inference may be framed as a discounted Bayesian filter with discount $u$8 (where $u$9) (Tran et al., 28 Dec 2025).

3. Empirical Measurement, Quantitative Dynamics, and Architectural Factors

Intrinsic forgetting admits empirical scrutiny via multiple methodologies:

• Per-Sample Retention Tracing: For each example, record its correct vs. incorrect status at each epoch, fitting exponential decay models:

$$\Gamma_k(t) = D\left(q(H^{t+k:\infty} | Z_{t-1},H_{0:t-1}) \ \|\ q_k^*(H^{t+k:\infty}|Z_{t-1},H_{0:t-1})\right)$$0

Estimating $$\Gamma_k(t) = D\left(q(H^{t+k:\infty} | Z_{t-1},H_{0:t-1}) \ \|\ q_k^*(H^{t+k:\infty}|Z_{t-1},H_{0:t-1})\right)$$1 allows fine-grained quantification of forgetting and comparison across architectures (e.g., ViT vs. CNN) or seeds; findings indicate architecture- and seed-dependence at the instance level, but stability at class-aggregate scales (Daga et al., 13 Apr 2026).

• Privacy Leakage Decay: The detectability of memorized examples (using membership inference or canary attacks) falls precipitously as training proceeds on fresh data. In practical settings, measured membership inference precision or canary exposure decays to baseline on the order of 10–50k steps, conferring natural privacy to pretrain-stage examples (Jagielski et al., 2022). Deterministic training or non-convexity may prevent such decay.
• Forgetting Curves and Task Interference: In multi-task regimes (RL, continual learning), per-task value or reward retention $$\Gamma_k(t) = D\left(q(H^{t+k:\infty} | Z_{t-1},H_{0:t-1}) \ \|\ q_k^*(H^{t+k:\infty}|Z_{t-1},H_{0:t-1})\right)$$2 decays exponentially or as a power law with time elapsed on other tasks; cross-task interference parameters $$\Gamma_k(t) = D\left(q(H^{t+k:\infty} | Z_{t-1},H_{0:t-1}) \ \|\ q_k^*(H^{t+k:\infty}|Z_{t-1},H_{0:t-1})\right)$$3 critically shape global forgetting dynamics (Speckmann et al., 3 Mar 2025).
• Self-Generated and Real Replay: For capacity-limited LMs, even perfect replay (from stored or self-sampled prior data) cannot prevent forgetting above the intrinsic lower bound imposed by saturated models. Optimization hyperparameters (learning rates, batch sizes) modulate the realized rate, with self-generated replay enabling high learning rates while minimizing forgetting (Marek et al., 25 May 2026).
• Geometry and Dimensionality: Embedding models with low effective dimension ($$\Gamma_k(t) = D\left(q(H^{t+k:\infty} | Z_{t-1},H_{0:t-1}) \ \|\ q_k^*(H^{t+k:\infty}|Z_{t-1},H_{0:t-1})\right)$$4) exhibit strong interference effects; the probability of correct recall after $$\Gamma_k(t) = D\left(q(H^{t+k:\infty} | Z_{t-1},H_{0:t-1}) \ \|\ q_k^*(H^{t+k:\infty}|Z_{t-1},H_{0:t-1})\right)$$5 items decays as $$\Gamma_k(t) = D\left(q(H^{t+k:\infty} | Z_{t-1},H_{0:t-1}) \ \|\ q_k^*(H^{t+k:\infty}|Z_{t-1},H_{0:t-1})\right)$$6, with $$\Gamma_k(t) = D\left(q(H^{t+k:\infty} | Z_{t-1},H_{0:t-1}) \ \|\ q_k^*(H^{t+k:\infty}|Z_{t-1},H_{0:t-1})\right)$$7 (empirically matching the Ebbinghaus human forgetting exponent) (Barman et al., 27 Mar 2026).

4. Functional Consequences and Theoretical Implications

Intrinsic forgetting is not solely a limitation; several findings demonstrate its computational utility:

• Noise Suppression and Denoising: Finite-memory (forgetting) windows optimally suppress spurious feature coincidences and denoise place-cell co-firing data, clarifying topological signatures of the environment (Chowdhury et al., 2017).
• Resource Efficiency and Stability–Plasticity Trade-Off: Intermediate forgetting rates—neither minimal nor maximal—optimize the balance between stable retention and rapid adaptation, as shown by U-shaped total error curves in LLM temporal reasoning and memory benchmarks (Tran et al., 28 Dec 2025).
• Data Pruning and Support Discrimination: Intrinsic example forgetting rates identify data “support vectors,” permitting aggressive data reduction (up to 80% removal in MNIST, 30% in CIFAR-10) without loss of generalization (Toneva et al., 2018).
• Continual Memory Management: Adaptive decay (e.g., FadeMem) with LLM-guided fusion and conflict resolution can shrink storage requirements by 45% while improving multi-hop reasoning and retrieval, directly leveraging controlled forgetting for artificial agent memory management (Wei et al., 26 Jan 2026).
• Curricula and Retention Optimization: Spaced repetition and item-level scheduling based on forgetting rates may not outperform random sampling due to seed- and architecture-induced stochasticity at the instance level, but class-level forgetting remains stable and actionable (Daga et al., 13 Apr 2026).
• Privacy Amplification: The natural decay of memorization in large-scale model training offers defense against extraction attacks, implicitly protecting early-seen examples (Jagielski et al., 2022).

5. Connections to Biological and Cognitive Theories

Intrinsic forgetting in artificial systems mirrors key principles found in biological and cognitive settings:

• Cognitive Decay Kernels: Human-like power-law and exponential forgetting curves emerge from combinatorics of memory retrieval under interference and bounded resource constraints, not from explicit decay at the trace level (Barman et al., 27 Mar 2026).
• Hierarchical and Differential Decay: Fuzzy Trace Theory’s distinction between gist (semantic, slowly forgotten) and verbatim (lexical, rapidly forgotten) memory traces, and ACT-R’s power-law recency weighting, are mirrored in time-dependent multi-layer models in tagging and artificial episodic memory (Kowald et al., 2014, Wei et al., 26 Jan 2026).
• Biological Plausibility and Local Learning: Local, curvature-aware consolidation rules provide biologically accessible mechanisms for stability, negating the need for global information or replay buffers and aligning with synapse-level imaging data on stability and turnover (Deistler et al., 2018).
• Fragmentation and Recall in RL: The composition of task-specific curiosity modules, fragmentation according to state heterogeneity, and content-based recall matches observed partitioning and module-reuse in animal navigation and exploration (Hwang et al., 2023).

6. Limitations, Open Questions, and Emerging Directions

The theory and measurement of intrinsic forgetting remains an active area, with several unresolved issues:

• Measurement Boundaries: Practical empirical studies rely on state-of-the-art privacy or inference methods, which may underestimate residual traces, especially in non-convex or deterministic settings (Jagielski et al., 2022).
• Instance vs. Aggregate Stability: While class-level forgetting is interpretable, instance-level forgetting is dominated by stochasticity. This challenges pruning, curriculum, and scheduling methods premised on stable per-example difficulty (Daga et al., 13 Apr 2026).
• Replay, Self-Consistency, and Bayesian Limits: Intrinsic forgetting is zero for exact Bayesian learners with self-consistent update trajectories, but approximate learners exhibit unavoidable divergence in their predictive distribution across steps. Studying the structure of this divergence and its ramifications for learning efficiency and retention is an open line (Sanati et al., 6 Nov 2025).
• Interference vs. Decay: Geometric analyses posit that interference—rather than temporal decay—drives real-world forgetting curves; whether this holds across other learning or memory architectures, and how systems can best modulate effective dimensionality, remains unresolved (Barman et al., 27 Mar 2026).
• Optimal Policy for Memory Management: The design of schedules or memory architectures that best exploit class-level forgetting statistics despite instance-instability is ongoing, as is the integration of adaptive, content-aware consolidation within artificial systems (Wei et al., 26 Jan 2026, Deistler et al., 2018).
• Functional Role in Reasoning and Adaptation: Evidence is mounting that forgetting is a key driver of flexible, adaptive computation—enabling agents and models to prevent overfitting, prioritize relevant features, and align resource usage with environmental volatility (Chowdhury et al., 2017, Tran et al., 28 Dec 2025).

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Intrinsic forgetting, therefore, is not simply a consequence of imperfection or limited resource; it is a defining property of dynamical learning systems operating under real-world resource constraints, interference, and adaptation pressures, and is now understood as both a challenge to, and enabler of, robust, flexible, and efficient computation.