Technical Summary: Forgetting Our Way to Shared Meaning

Problem Statement

The emergence and evolution of shared meaning in language rely on agents learning and agreeing upon conceptual categories. While existing models of conceptual semantics often utilize coordination games, they predominantly assume a "partnership" setting where players share identical payoffs. This assumption fails to capture the nuances of real-world linguistic communities, where agents possess asymmetric information and distinct cognitive architectures. Furthermore, current Large Language Models (LLMs) face theoretical challenges regarding the "symbol grounding problem" and the informational inefficiency of their training compared to human learning.

This paper addresses the gap in understanding how specific characteristics of semantic memory—specifically rates of forgetting, levels of entrenchment, and plasticity—affect the quality, stability, and speed of shared agreements. The authors investigate how memory adaptivity influences both the actual convergence of conceptual regions and the perceived convergence (the agents' belief that they have aligned), particularly in non-partnership settings where payoffs are not strictly shared.

Methodology

The authors propose a novel non-partnership coordination game to model conceptual alignment. The framework utilizes agent-based modeling with the following core components:

• Conceptual Representation: Following Gärdenfors (2014), meaning is represented as "conceptual regions" within a Euclidean space ($R^n$). These regions are convex subspaces formed by Voronoi tessellations around conceptual prototypes (centroids).
• Game Mechanics:
  • Two agents ($p_1, p_2$) start with randomly generated memories consisting of sets of prototypes.
  • In each round, an object (a vector in $R^n$) is presented.
  • Agents classify the object by announcing the signal corresponding to the closest prototype.
  • Payoff Structure: Unlike partnership games, payoffs are not shared. If signals match, agents receive a high payoff. If signals mismatch, an agent's payoff is determined by the distance between the object and the boundary of the concept signaled by the other player within their own memory space.
• Memory Update Strategies:
  • Adaptive Players: Update their prototypes by moving them a fixed percentage ($a$) toward the object whenever a mismatch occurs.
  • Non-Adaptive Players: Possess a degradation parameter ($d$). Their adaptiveness level decreases over time ($a' = a \times (1-d)$), simulating memory degradation or reduced plasticity.
• Convergence Metrics:
  • Actual Convergence: Measured by the average Euclidean distance between corresponding prototypes of the two agents falling below a tolerance threshold ($\delta$).
  • Perceived Convergence: Measured by the agents producing matching signals for a consecutive number of rounds ($\alpha$), independent of the actual distance between their prototypes.

Simulations were run with varying numbers of prototypes (3, 5, 10), adaptiveness levels (1%, 5%, 10%), and degradation rates for non-adaptive agents.

Key Contributions

1. Non-Partnership Game Model: The paper introduces a game-theoretic framework where agents do not share payoffs, allowing for a more realistic representation of epistemic access and the divergence between actual and perceived alignment.
2. Distinction Between Actual and Perceived Convergence: The study explicitly separates the objective state of conceptual alignment from the subjective belief of alignment, demonstrating that these two metrics can diverge significantly based on memory strategies.
3. Memory Adaptivity Analysis: The authors model the trade-offs between high adaptivity (rapid updating) and non-adaptivity (stability with degradation), providing a theoretical basis for how memory features influence language evolution without relying on complex meta-information sharing.

Results

Counterfactual simulations yielded the following findings:

• Adaptive Players:
  • Achieved actual convergence faster than non-adaptive players.
  • Ended with closer final conceptual regions (lower mean distance between prototypes).
  • Underestimated their alignment; they were less likely to perceive convergence early, often mistaking the instability of their own updating process for a lack of alignment with their partner.
• Non-Adaptive Players:
  • Achieved actual convergence later and with greater final distance between prototypes compared to adaptive agents.
  • Overestimated their alignment; they were more likely to perceive convergence earlier.
  • Their individual learning strategies were more stable, leading them to interpret signal matching as successful alignment even when actual conceptual distances remained larger.
• Impact of Adaptiveness Level: Higher adaptiveness (e.g., 10%) resulted in tighter final conceptual regions compared to lower adaptiveness (e.g., 1%).
• Impact of Degradation: In non-adaptive agents, the rate of memory degradation had a negligible effect on the timing of convergence but influenced the final distance between prototypes. Lower degradation allowed for slightly better final alignment, but once adaptation became negligible, agents could no longer effectively adjust to their partner's position.

Significance and Claims

The paper claims that the adaptivity of semantic memory is a critical factor in the emergence and evolution of shared meaning. The authors argue that:

• Cognitive Roots of Misalignment: Differences in meaning and the perception of these differences in linguistic communities may stem from cognitive features (memory adaptivity) rather than solely social or structural factors.
• Implications for LLMs: The findings suggest that training strategies for LLMs that treat new information with the same weight as old information (non-adaptive aggregation) may produce increasingly non-adaptive models. This contrasts with human learning, which shows a preference for new information. The paper posits that the choice between adaptive and non-adaptive memory update strategies has significant consequences for the stability and alignment of artificial agents.
• Perception vs. Reality: The study highlights a paradox where agents who are objectively better aligned (adaptive) may feel less confident in their shared meaning, while agents who are objectively less aligned (non-adaptive) may feel more confident due to the stability of their internal strategies.

The authors conclude that understanding these memory dynamics is essential for modeling how humans learn meaning and for addressing societal issues such as polarization and misinformation, where the interplay between memory adaptation and social connectivity determines the speed and quality of shared understanding.