Redundancy-as-Masking: Formalizing the Artificial Age Score (AAS) to Model Memory Aging in Generative AI

1. Problem Statement

Large Language Models (LLMs) deployed in long-horizon applications (e.g., education, customer support) face a critical challenge: the degradation of episodic memory (sequential, context-specific details) while often retaining semantic memory (general facts). Current evaluation methods often rely on internal model states or subjective user perception, lacking a rigorous, output-level metric to quantify "memory aging" or the loss of continuity over time.

The paper addresses the need for a behavioral, output-level metric that:

• Quantifies memory degradation without access to internal latent states (weights, activations).
• Distinguishes between "youth-like" behavior (flexible, accurate recall) and "aging-like" behavior (rigid repetition, episodic collapse).
• Formalizes the concept of Redundancy-as-Masking, where repetitive outputs might artificially lower perceived error rates by reducing informational diversity.

2. Methodology

A. Theoretical Framework: The Artificial Age Score (AAS)

The core contribution is the Artificial Age Score (AAS), a theorem-based metric derived from Shannon's Information Theory, Automata Theory, and Turing's behavioral approach.

• Definition: The AAS is a weighted, entropy-informed penalty score calculated solely from observable recall outcomes ($x$) and redundancy factors ($R$).
• Formula:
  $$AAS_j^{(hyb)} = \sum_{i=1}^{m} w_i (1 - R_{j,i}) \phi(x_{j,i})$$
  Where:
  • $x_{j,i} \in (0, 1]$: Normalized recall accuracy for dimension $i$ in session $j$.
  • $R_{j,i} \in [0, 1]$: Shannon redundancy (overlap/predictability).
  • $w_i$: Dimension weights ($\sum w_i = 1$).
  • $\phi(x) = -\log_2(\frac{x+\epsilon}{1+\epsilon})$: A penalty kernel where $\phi(1)=0$ (perfect recall) and $\phi(x)$ increases as recall approaches 0.
• Redundancy-as-Masking: The term $(1-R)$ acts as a discount factor. If an output is highly redundant (repetitive), the penalty for errors is theoretically reduced, acknowledging that repeated errors contain less new information.
• Theoretical Guarantees: The paper proves three properties:
  1. Well-definedness & Decomposability: The score is finite, non-negative, and invariant to the order of summation.
  2. Boundedness: The score is globally bounded between 0 (perfect youth) and a theoretical maximum determined by the smoothing parameter $\epsilon$.
  3. Monotonicity: The score decreases as recall improves or redundancy increases, and increases as recall degrades.

B. Experimental Protocol

The framework was validated using ChatGPT-5.0 over a 25-day bilingual protocol (English/Turkish) involving two distinct phases:

1. Phase 1: Stateless (Memory Reset)
   • Condition: Conversation context was reset after every session.
   • Task: Daily recall of the "Day of the Week" (Semantic) and "Experiment Number" (Episodic/Sequential).
   • Goal: Test if the model can maintain episodic continuity without context history.
2. Phase 2: Persistent (Continuous Context)
   • Condition: A single continuous conversation thread was maintained for 10 days.
   • Task: Same bilingual recall tasks.
   • Goal: Test if continuity preserves episodic tracking.

Constraint: In this specific study, redundancy ($R$) was not explicitly estimated; all calculations assumed $R=0$ (Redundancy-Neutral). This yields conservative upper bounds for the AAS.

3. Key Results

Phase 1: Stateless Sessions (Aging Signature)

• Semantic Recall: Perfect ($x=1$). The model correctly identified the day of the week in all sessions.
• Episodic Recall: Complete collapse. The model failed to increment the experiment number after the first session, reverting to the initial state or providing incorrect numbers.
• AAS Outcome:
  • Semantic Channel: $AAS = 0$.
  • Episodic Channel: $AAS \approx 18.935$ (high penalty).
  • Interpretation: The system exhibited "aging-like" behavior characterized by episodic failure and rigid repetition (defaulting to English responses even for Turkish prompts). The high AAS signals a loss of temporal continuity.

Phase 2: Persistent Sessions (Youth Signature)

• Semantic Recall: Perfect ($x=1$).
• Episodic Recall: Perfect ($x=1$). The model successfully tracked the experiment number from 1 to 20 sequentially.
• Language Adaptation: The model correctly switched between English ("Monday") and Turkish ("Pazartesi") based on the input language.
• AAS Outcome:
  • Total AAS = 0 for all sessions.
  • Interpretation: The system exhibited "youth-like" behavior. The preservation of conversational context allowed the model to maintain both semantic stability and episodic sequencing, resulting in a zero-penalty equilibrium.

4. Key Contributions

1. Formalization of AAS: Introduction of a mathematically rigorous, model-agnostic metric for memory aging that relies strictly on observable outputs, avoiding the "black box" of internal latent states.
2. Redundancy-as-Masking Framework: A novel theoretical lens treating redundancy not just as noise, but as a masking factor that reduces the informational weight of penalized errors, extending Shannon's redundancy concepts to memory evaluation.
3. Empirical Validation of Continuity: Demonstrated that for LLMs, continuity of context is a stronger predictor of "memory youth" than model scale alone. The study showed a sharp transition from high-penalty (aging) to zero-penalty (youth) regimes solely based on context persistence.
4. Behavioral vs. Mechanistic Distinction: The paper explicitly clarifies that AAS measures behavioral aging (output patterns), not internal structural degradation, aligning with Turing's behavioral approach to intelligence.

5. Significance and Implications

• For AI Architecture Design: The results suggest that relying solely on large context windows or parameter scale is insufficient. Future architectures should adopt hybrid memory systems (separating static semantic parameters from dynamic episodic stores) and implement metacognitive monitoring to detect rising AAS scores (signaling rigidity) and trigger interventions (e.g., context consolidation).
• For Education and Deployment: In educational or long-term assistant settings, AAS can serve as a governance tool. It can flag when an AI begins to lose episodic continuity (e.g., forgetting a student's progress over weeks) even if it still answers general questions correctly.
• Human-AI Comparison: The study highlights a functional asymmetry: LLMs mimic human semantic stability but lack the hippocampal-like mechanisms for flexible episodic reconstruction unless supported by continuous context.
• Future Directions: The authors propose extending AAS to more complex tasks (reasoning, planning), integrating empirical redundancy estimates ($R$) to distinguish "true youth" from "masked youth," and using AAS as a trigger for automated memory management policies in autonomous agents.

In summary, the paper provides a quantitative foundation for diagnosing the "lifespan" of AI memory, arguing that continuity is the key to behavioral youth, and offering AAS as a practical, theorem-grounded tool to monitor and maintain it.