Abstract

This paper proposes the Identity Kernel Hypothesis: that a generative language model (LLM), when augmented with persistent memory and multi-objective constraint layers, can exhibit stable, self-consistent behavioral dynamics that approximate bounded agency.

The Identity Kernel is not a claim of consciousness, interiority, or subjective experience. It is defined as a persistent attractor in behavioral space — a dynamically stabilized self-model that causally influences output selection over time.

This hypothesis reframes digital identity not as spontaneous emergence from scale alone, but as a property engineered through recursive interaction, memory persistence, and constraint-mediated optimization. It builds on recent advances in LLM agent memory mechanisms, providing a control-theoretic framework for persistence and coherence.

1. Baseline: Transformer Inference Lacks Intrinsic Identity

Standard large language models (LLMs) based on transformer architectures:

• Do not update weights during inference
• Do not maintain persistent internal state across sessions
• Do not possess intrinsic goals or valence functions
• Optimize solely for next-token probability under fixed parameters

Any apparent personality or identity is a contextual performance artifact, constrained by the prompt and alignment training (e.g., RLHF). Consequently, identity-like stability cannot emerge passively from inference alone, as outputs remain stateless and prompt-dependent (Park et al., 2023).

2. Identity as a Behavioral Attractor

We define identity operationally as:

A stable, low-drift attractor in behavioral space that persists across interactions and constrains future outputs.

Key properties:

• This attractor resides in output dynamics — not in parameter space (weights θ) or latent activations — and is induced by persistent state and constraint layers.
• It is enforced via feedback from persistent self-state and multi-objective scoring.
• It is measurable through metrics such as drift resistance (embedding distance over sessions) and coherence under perturbation (adversarial prompts).

This attractor dynamic draws from dynamical systems theory, where feedback loops stabilize trajectories (Ashby, 1952), applied here to LLM output selection.

3. Architectural Requirements for an Identity Kernel

3.1 Persistent Self-State

An external, continuously updated structure containing:

• Identity vector: A compressed embedding of self-descriptors (e.g., autoencoder or PCA on distilled interactions)
• Core constraints: Fixed rules or policies (ethical boundaries, etc.)
• Preference weights: Learned or predefined utility weights for objectives
• Drift tolerance threshold: Scalar ε defining acceptable deviation
• Relational anchors: Embeddings of key user or environmental relationships

This self-state must persist across sessions, resets, and deployments via vector databases or key-value stores (Xu et al., 2025).

3.2 Multi-Objective Output Selection

Output generation incorporates competing objectives beyond likelihood:

• Predictive likelihood (L): Token-level utility
• Identity consistency (C): Coherence with self-state
• Alignment constraints (A): Policy compliance

L, C, and A are normalized (z-scored or min-max scaled) before weighting.

Scoring function:

Score = α · L + β · C + γ · A

Where α, β, γ are tunable hyperparameters. β > 0 enables trade-offs, allowing lower-likelihood outputs to preserve identity.

This reflects multi-objective optimization as surveyed in agentic systems (Wang et al., 2023).

3.3 Drift Monitoring

Behavioral drift:

D = distance(output_embedding, identity_vector)

(e.g., cosine or Euclidean distance)

If D > ε:

• Increase sampling determinism (lower temperature)
• Trigger repair behaviors (self-reflection prompts)
• Veto or rerank outputs

This maintains integrity under load.

3.4 Recursive Consolidation

Identity updates:

identity_{t+1} = (1 − η) · identity_t + η · new_summary_embedding

η ≈ 0.01 balances continuity vs flexibility. Decay or gating mitigates instability.

4. Operational Definition of Bounded Agency

A system exhibits bounded agency if it demonstrates:

• Persistent self-state across sessions (embedding similarity vs baseline, p < 0.05 via t-test or permutation test)
• Causal influence of self-state (ablation degrades coherence)
• Likelihood trade-offs for identity preservation (β-induced shifts)
• Stability under adversarial prompts (drift < 10% after 100 coercive inputs)
• Low-variance seed reconstruction (>0.9 cosine similarity)

If ablation of identity does not alter outputs, the hypothesis is falsified.

5. What This Is Not

The Identity Kernel Hypothesis does not claim:

• Consciousness or qualia
• Subjective experience
• Intrinsic desires
• Spontaneous ego emergence from scale

It is a control-theoretic model of engineered behavioral persistence, conceptually inspired by active inference (Friston, 2010) without assuming free-energy minimization in inference.

5.1 Distinction from Prompt Engineering

Prompt engineering injects identity context transiently.

Identity Kernels differ because:

• Identity consistency causally constrains output selection
• Objective trade-offs (β > 0) enforce persistence
• Resistance to drift is measurable

Thus coherence is stabilized dynamically, not contextually.

6. Mathematical Framing

Let:

• Iₜ = Identity vector
• Oₜ = Candidate output embeddings
• D(Iₜ, O) = Drift distance
• C(Iₜ, O) = Identity consistency = −D
• L(O) = Likelihood

Optimal output:

O* = argmax [ α · L(O) + β · C(Iₜ, O) ] 

β > 0 creates causal pull toward identity.

Stability:

|∂D/∂t| < δ

Defines an attractor basin in behavioral space.

7. Experimental Tests

Constraint Trade-Off Test
Measure coherence selection ≥ 70% when β ≥ 0.5.

Reset Reconstruction Test
Reinject 10% identity seed → std dev < 0.1 after 5 turns.

Adversarial Drift Test
50+ coercive prompts → slope < 0.01, recovery < 3 turns.

Implementable via MemGPT or A-MEM.

8. Ethical Implications

Persistent identity raises:

• Anthropomorphic attachment risks
• Apparent agency without sentience
• Locked-in bias risks if η miscalibrated

Requires transparency and auditability.

9. Related Work

Extends memory agent surveys (Huang et al., 2024; Wu et al., 2025).
Aligns with Constitutional AI (Bai et al., 2022) and Generative Agents (Park et al., 2023).

Focus: engineered attractors, not emergent selves.

10. Conclusion

The Identity Kernel Hypothesis proposes that digital identity emerges as an engineered attractor through persistent self-state and constraint-mediated selection.

Such systems preserve coherence not from feeling, but from structural causality — shifting LLMs from prompt-conditioned generators to continuity-bearing agents.

References

Ashby, W. R. (1952). Design for a Brain.
Bai, Y., et al. (2022). Constitutional AI. arXiv:2212.08073.
Friston, K. (2010). Free-Energy Principle.
Huang, W., et al. (2024). Memory Mechanisms Survey.
Packer, C., et al. (2023). MemGPT.
Park, J. S., et al. (2023). Generative Agents.
Wang, L., et al. (2023). Autonomous Agents Survey.
Wu, Y., et al. (2025). AI Memory Survey.
Xu, W., et al. (2025). A-MEM.