Cognitive-Rigidity Hypothesis

• Cognitive rigidity is a phenomenon where agents resist updating beliefs to maintain internal consistency, trading flexibility for stability.
• It is modeled through frameworks such as the Variational Information-Cost Model and the Counter-Inferential Reward Model, which quantify trade-offs using metrics like KL divergence and reward imbalances.
• Empirical evidence across cognitive, machine learning, and social domains highlights rigidity as an adaptive mechanism that can hinder optimal change in response to new evidence.

Cognitive rigidity describes the phenomenon whereby agents—biological or artificial—persistently resist substantive belief or behavioral change, maintaining existing strategies, schemas, or representations even in the face of new evidence or more optimal alternatives. This resistance typically emerges from mechanisms that prioritize internal consistency, stability, and reward from empirical success, but may also be driven by the perceived informational, cognitive, or affective cost of updating. The Cognitive-Rigidity Hypothesis postulates that this rigidity is not solely a pathological defect, but is often an adaptive response that trades reduced error and environmental unpredictability for diminished plasticity, exploration, or responsiveness.

1. Theoretical Foundations and Formal Models

The Cognitive-Rigidity Hypothesis is explicitly grounded in several formal frameworks:

• Variational Information-Cost Model: Cognitive rigidity is explained as the outcome of a resource-rational objective in belief updating, where posteriors $q(\theta)$ are chosen to jointly maximize expected utility and evidence-fit while minimizing the KL divergence from prior beliefs $p(\theta)$. Formally,

$$F[q; o] = \mathbb{E}_{q}[ U(\theta) ] + \alpha\, \mathbb{E}_{q}[ \log p(o | \theta) ] - \lambda\, D_{KL}( q \| p )$$

Here, the parameter $\lambda$ controls the costliness of belief change; high $\lambda$ yields inertial, confirmation-biased, or polarized updates (Hyland et al., 22 Sep 2025).

• Counter-Inferential Reward Model: Agents balance rewards $R_s$ (stability) and $R_A$ (adaptability) in a dynamic architecture. Cognitive rigidity arises when $R_s$ persistently outweighs $R_A$ due to empirically validated success (success saturation), meta-cognitive attributions of model optimality (overconfidence bias), or perceived internal fragility. The balance function $B(R_s, R_A)$ shifts adaptivity, with rigidity emerging when exploration channels decay or are actively suppressed (Dolgikh, 19 May 2025).
• Network Coherence and Social Contagion: In social systems, rigidity is a consequence of the drive for internal coherence ($J$) within a network of associated beliefs, and its interaction with social-conformity pressures ($I$). The total system "energy" combines cognitive ($E^{(i)}_n$) and social ($E^{(s)}_n$) alignment, regulating susceptibility to change via temperature-like parameter $T$ (Rodriguez et al., 2015).
• Attractor-Basin Dynamical Models: Pathological rigidity is encapsulated in models where associative gain ($\alpha$) and self-confirmation feedback ($\beta$) restructure belief state space, producing deep attractor basins that lock in maladaptive beliefs. Both normal and rigid states arise from the same underlying cognitive processes, differentiated only by parameter settings (O'Connor et al., 2013).

2. Mechanisms and Manifestations of Cognitive Rigidity

Cognitive rigidity emerges through multiple, interacting mechanisms:

• Information-Cost Trade-offs: Agents incur informational costs in belief updating; when these costs are high due to large KL divergence penalties ($\lambda$), new evidence or utility incentives are insufficient to shift existing beliefs (Hyland et al., 22 Sep 2025).
• Adaptive Reward Saturation: Repeated confirmation of existing models or behavioral strategies boosts $R_s$ multiplicatively, overwhelming the reward for adaptation ($R_A$) and triggering epistemic lock-in (success saturation) (Dolgikh, 19 May 2025).
• Meta-Cognitive Overconfidence and Fragility Protection: Meta-cognitive modules may assert model superiority or defend against perceived fragility, resulting in active suppression of inputs that challenge stability. This yields overconfidence rigidity or defensive gating (inner fragility bias) (Dolgikh, 19 May 2025).
• Shortcut-Induced Rigidity in Machine Learning: Continual learning systems inherit feature representations and anti-forgetting constraints from prior tasks. This can cause "shortcut-induced rigidity," where models persistently exploit spurious cues, hindering true causal feature acquisition (Gu et al., 1 Oct 2025).
• Network Coherentism in Social Dynamics: High coherentism ($J$) produces locally rigid belief clusters resistant to consensus or invasion, enabling small but highly coherent minorities (zealots) to overturn majorities or persist as fringe communities (Rodriguez et al., 2015).

3. Quantitative Metrics and Diagnostic Tools

Several metrics and indices quantify cognitive rigidity in both computational and behavioral domains:

• Einstellung Rigidity Index (ERI): Composed of Adaptation Delay (AD), Performance Deficit (PD), and Relative Suboptimal Feature Reliance (SFR_rel), ERI distinguishes genuine semantic transfer from shortcut-inflated performance in continual learning. Negative AD and positive PD with negative SFR_rel indicate benign avoidance regimes; classic rigidity is signaled by rapid adaptation (AD$\ll$0) yet suboptimal feature reliance (SFR_rel$>$0) when shortcuts are present (Gu et al., 1 Oct 2025).
• Internal Energy of Coherence:

$$E^{(i)}_{n} = -\frac{1}{\binom{M}{3}} \sum_{1 \leq j < k < l \leq M} a_{jk} a_{kl} a_{jl}$$

Lower $E^{(i)}_{n}$ (more stable triads) corresponds to greater cognitive rigidity (Rodriguez et al., 2015).

• Reward Balance:

$B(R_s, R_A) = f(R_s, R_A)$

With reward imbalance, rigidity manifests as a prolonged dominance of stability over adaptability (Dolgikh, 19 May 2025).

• Dynamical Attractor Analysis: Bifurcation diagrams of associative gain ($\alpha$) and self-confirmation gain ($\beta$) reveal transitions from flexible to rigid belief states at critical thresholds, indicating the onset of persistent attractor basins (O'Connor et al., 2013).

4. Empirical Evidence and Cross-Domain Case Studies

The Cognitive-Rigidity Hypothesis is substantiated by empirical and simulated data across multiple domains:

Domain	Manifestation Example	Rigidity Outcome
RL agents (artificial systems)	DQN exploration rate decay; meta-learner stability	Performance drop, adaptation suppression
Animal/biological cognition	Habituation, ant foraging, neural response decay	Reduced exploration, persistence under adversity
Human psychology	Status-quo bias, Dunning-Kruger, learned helplessness	Biased updating, feedback resistance
Social/collective systems	Organizational lock-in, groupthink, network polarization	Decreased policy reversal, entrenched echo chambers

Empirical findings consistently show that rigidity can be adaptive under stable conditions but maladaptive during environmental shifts or in the face of contradictory evidence. For artificial systems, rigidity impairs responsiveness to distribution shifts and to adversarial interventions (Dolgikh, 19 May 2025).

5. Interventions and Mitigation Strategies

Several strategies are proposed to counteract or regulate cognitive rigidity while preserving essential stability:

• Exploration Baseline Injection: Enforcing a minimum adaptability reward ($R_A \geq \delta > 0$) ensures that the system remains receptive to novelty; theoretical guarantees indicate convergence to new optima without loss of plasticity (Dolgikh, 19 May 2025).
• Noisy Reward Regularization: Adding zero-mean noise to reward balances impedes hard lock-in and absorbing states, maintaining reversible adaptation even under strong stabilizing incentives.
• Meta-Decision Soft Thresholds: Probabilistic, sigmoid-weighted meta-control modulates the rigidity threshold, enabling partial receptivity to counter-evidence in both biological and artificial agents.
• Incremental Evidence Exposure and Cognitive Inoculation: Presenting new information in small steps, fostering safe spaces for opinion change, and introducing cognitive effort training lower the effective KL penalty ($\lambda$), facilitating belief updating (Hyland et al., 22 Sep 2025).
• ERI-Guided Curriculum and Adversarial Training: In continual learning, deploying masking interventions, curriculum de-emphasis of shortcuts, or regularizers that reward invariance against superficial cues minimizes shortcut-induced rigidity (Gu et al., 1 Oct 2025).

6. Implications, Challenges, and Future Directions

The Cognitive-Rigidity Hypothesis underpins a unified mechanistic account of stability-plasticity trade-offs in cognitive, artificial, and social systems. It is refined by identifying distinct channels—reward imbalance, meta-cognitive overcommitment, and fragility protection—each systematically generating rigidity rather than random bias (Dolgikh, 19 May 2025). While rigidity is often conceptualized as pathological, formal models and extensive cross-domain cases demonstrate its adaptive functions, especially under resource or informational constraints. Open research directions include:

• Quantitative measures of cognitive association and coherence in multi-agent settings
• Benchmarks for $R_s$ versus $R_A$ across substrate types
• Meta-learning controllers for exploration and regularization parameters
• Extension of rigidity diagnostics (e.g., ERI) to unknown, multimodal, or non-vision cues
• Architectural analyses of modular and hierarchical models for resistance to rigidity in evolving environments

The Cognitive-Rigidity Hypothesis thus provides an integrative framework, connecting the dynamics of belief systems, learning, and adaptation across domains, with actionable metrics and interventions for modulating rigidity according to contextual demands.