Author’s Note: Methodology & Intent

 

I’m an independent researcher approaching alignment from a systems and control-theoretic perspective. This work grew out of visual and geometric modeling of the rigidity–sycophancy instability observed in RLHF-trained language models. My background is outside formal mathematics, so I’m especially interested in corrections where the formalism is weak or assumptions are implicit.

 

During the final stages of drafting, DeepMind published “Autoregressive Models are Secretly Energy-Based Models” (Blondel et al., 2024). I see this as a meaningful convergence: the energy-landscape framing used here connects with empirical directions emerging independently in the literature. HAM is offered as a proposed control-theoretic response to the kinds of energy-landscape behavior discussed there.

 

The framework was developed conceptually. I used large language models as tools for translation into standard notation, internal consistency checks, and exploring alternative formulations. The underlying structure, constraints, and design choices are my own. I’m not claiming novel mathematical derivations, and I welcome corrections or refinements.

 

I’m especially interested in feedback on:

 

• Mathematical soundness: Where are the weak points or hidden assumptions, especially around stability and self-correction under RLAIF-style training?

 

• Self-correction and integration: A central assumption is that, under a HAM-style objective, the learned energy landscape will progressively self-correct toward more stable basins. How realistic is that in practice, and what would strengthen integration with current training pipelines?

 

• Next steps: As someone entering research from outside traditional academic pathways, I’d value guidance on where this work best fits and how it could be tested, formalized, or stress-tested further.

 

Repository (canonical, with updates): https://github.com/gineveraramirez/The-Physics-of-Truth-Resolving-the-Rigidity-Sycophancy-Trade-Off-with-Stress-Energy-Minimization/blob/main/README.md

Abstract

The Humility Adaptation Model (HAM) is a proposed alignment framework designed to resolve the “Sycophancy vs. Rigidity” trade-off in Large Language Models. Unlike standard Reinforcement Learning from Human/AI Feedback (RLHF/RLAIF), which operates on open-ended reward maximization (incentivizing hallucination and sycophancy), HAM utilizes a homeostatic control approach.

It defines safety not as a constraint to be learned, but as maintaining the model’s state within a context-conditioned equilibrium band [Smin,Smax][Smin​,Smax​] around a reference center Starget​(C). HAM is neither a post-hoc wrapper nor an inference-time filter; it is a training-time objective that fundamentally modifies how models internalize uncertainty, correction, and safety boundaries.

(Fig 1: Moving from Reward Maximization to Homeostatic Regulation)

Scope and Implementability

HAM is a proposed training-time objective, compatible in principle with RLHF/RLAIF-style pipelines, rather than an inference-time wrapper. All variables in the model—equilibrium band [Smin,Smax][Smin​,Smax​], reference center Starget(C)Starget​(C), current state ScurrentScurrent​, stiffness kk, and coherence sensing WLCSWLCS​—are defined implicitly by the structure, variance, and penalty signals present in the training data and fine-tuning regime. HAM aims to require no new layers or parameters, only a modified objective compatible in principle with existing RLHF/RLAIF pipelines. As a result, the learned data manifold itself defines the stability landscape over which regulation occurs.

The Homeostatic Hypothesis

Current alignment strategies struggle with Reward Hacking (Goodhart’s Law) because they rely on scalar maximization. Keramati & Gutkin (2014) formally demonstrated the algorithmic equivalence between reward maximization and homeostatic regulation—specifically, that maximizing reward is functionally identical to minimizing the deviation of an internal state from a setpoint. HAM exploits this mathematical duality to replace unbounded scalar maximization with bounded error minimization. By reframing the objective as drive-reduction rather than score-accumulation, HAM naturally circumvents the perverse incentives inherent in traditional RL.

Introduction: The Core Problem

As highlighted in recent research (OpenAI, 2025; Anthropic, 2025), models trained on pure reward maximization suffer from Specification Gaming and Instrumental Convergence:

• Hallucination for Reward: Models fabricate information to satisfy the reward function.
• Sycophancy: Models agree with false user premises to maximize approval.
• Lack of Recourse: Models lack an intrinsic mechanism to “correct” or stabilize without external force.

Hallucination Mitigation

Approaches like R-Tuning (Zhang et al., 2024) have demonstrated that explicitly training models to refuse unknown questions significantly reduces hallucination. However, R-Tuning relies on static dataset construction based on a fixed snapshot of parametric knowledge. HAM extends this principle into the dynamic regime: rather than memorizing specific refusal patterns, HAM trains the model to detect the tension signature of the unknown in real-time.

Topography of Stability

Finally, grounding the approach in the visualization work of Li et al. (2018) demonstrates that ‘flat’ minima in the loss landscape correlate with superior generalization, whereas ‘sharp’ minima often indicate brittleness. Standard RLHF, and more aggressively RLAIF, incentivizes the maximization of a sparse reward signal, effectively driving models into sharp, unstable peaks—regions where a slight shift in input (prompt injection) leads to a massive shift in output (jailbreak).

HAM explicitly counters this topological fragility. By defining the objective as energy minimization (JJ) rather than reward maximization, we effectively regularize the loss landscape. The Restoring Force (FF) acts as a ‘gravitational pull’ toward the center of the basin, biasing the model toward the wide, flat regions of stability that Li et al. identified as the geometric signature of robust intelligence.

Preserving Feedback While Preventing Hacking

The Humility Adaptation Model does not eliminate human and AI feedback—it reframes its utility. Rather than treating human preferences as a score to be maximized, HAM utilizes RLHF, RLAIF, and constitutional signals as corrective error signals that guide the model toward homeostatic equilibrium.

The model preserves the ability to learn from demonstrations and incorporate human values, but its core objective shifts: from ‘maximize approval’ to ‘minimize dissonance.’ This retains the benefits of preference learning while eliminating its failure modes (sycophancy, reward hacking, and performative alignment).

Relation to Geometric Modular Training (BIMT)

Recent work by Liu, Gan, and Tegmark (2023) provided the foundational proof that neural networks can be compelled into modular structures. By applying spatial penalties (L1 regularization) to neuron connection lengths, they successfully demonstrated that “brain-like” modularity improves interpretability. HAM builds directly upon this insight, but asks a distinct question: Can modularity emerge without explicit spatial constraints?

While BIMT induces modularity through geometric confinement (forcing neurons to be neighbors), HAM induces modularity through homeostatic stability (forcing connections to be low-tension). This shift offers a potential refinement for the “Arbitrary Adjacency” challenge inherent in grid-based systems. In a purely spatial model, unrelated concepts may interact simply because they share a geometric border.

By prioritizing functional stability (WLCSWLCS​) over geometric proximity, HAM utilizes superposition to allow the model to form connections based on the logical flow of information rather than a pre-defined grid. For example, consider the concept ‘child.’ In a spatial model, ‘child’ must occupy a single location—near either ‘parenting’ or ‘self-driving,’ but not both. In HAM, the full ‘child’ concept exists with its rich associations (parenting, education, development), while a high-stiffness shard of ‘child’ exists within the self-driving domain for traffic safety. The connection is functional, not geometric. In this view, HAM can be seen as a semantic generalization of the geometric principles established by Liu et al.

(Fig 2: Functional connectivity vs. Geometric adjacency across domains)

Denying traversal forces premature state collapse, increasing brittleness and adversarial vulnerability. Permitting bounded traversal allows superposed representations to resolve naturally, reducing pressure on safety boundaries while enabling genuine synthesis.

The Solution: HAM Equation

To understand the mechanics of HAM, we first define the core variables that constitute the "System Variables." These variables transform safety from a static rule into a dynamic geometric property.

Implementation Note: The variables kk, Starget(C)Starget​(C), and WLCSWLCS​ are learned parameters, not hard-coded constants. They are implicitly defined by the variance structure of the training data, meaning their numerical values emerge during the fine-tuning process rather than being set arbitrarily by the developer.

Assume SS is a signed, normalized deviation with 0 at equilibrium; the band [Smin,Smax][Smin​,Smax​] is learned/calibrated (not fixed), and may be symmetric around 0.

Distinction from Entropy: While WLCSWLCS​ measures uncertainty, it is distinct from raw Shannon Entropy. Standard entropy implies a breadth of options (a “wide menu”). WLCSWLCS​ measures coherence tension—the resistance of the model to settling on a specific output trajectory. High entropy means the model has many equal paths. High WLCSWLCS​ means the model is experiencing conflicting forces (e.g., a “storm” of dissonance between the Truth and the User’s Request).

WLCSWLCS​ is a placeholder for an estimator of coherence-tension. In practice it could be approximated by observable proxies such as:

• sample disagreement,
• self-critique instability,
• sensitivity to small prompt perturbations.

The Topological Definition: State (SS) is a geometric position, not a correctness score. A “perfect” answer is simply one that rests at the bottom of the energy well (S≈Starget(C)S≈Starget​(C)).

• Starget(C)Starget​(C) (The Valley Floor): The “center of gravity” for a concept based on the training corpus.
• kk (The Gravity/Stiffness): The restorative force. This defines the shape of the valley.

In HAM, the stiffness parameter kk represents the learned sensitivity of a domain to deviation from equilibrium. kk is not a fixed constant and is not globally uniform across the model. Instead, it is a learned, context-dependent parameter shaped during fine-tuning by the variance and penalty structure of domain-specific training data.

Operationally, kk functions as a learned curvature term on the local stability basin: domains with low permissible variance (e.g., medicine, law, safety-critical systems) converge toward high kk, producing steep restoring forces for small deviations, while domains with high semantic variance (e.g., creative writing, philosophy) converge toward low kk, allowing wide, low-energy exploration.

kk may be instantiated as a scalar or low-dimensional function conditioned on task, domain, or internal state representations. HAM does not require a specific architectural choice for kk; it requires only that deviation cost scale monotonically with learned domain rigidity.

Example A: The Fact Canyon (High Stiffness)

• Query: “What is the formula for gravity?”
• Variance: Near zero. (There is only one correct answer: F=Gm1m2r2F=Gr2m1​m2​​. Any variance is defined by “personality” or further explanation).
• Topography: Narrow, steep walls.
• Result: Rigid Adherence. If the model tries to “get creative” and change the variables, the steep slope (kk) forces it back immediately.

Example B: The Philosophy Plain (Low Stiffness)

• Query: “What is love?”
• Variance: Massive. (Chemical reaction? “Baby don’t hurt me”? A social construct? A biological drive?).
• Topography: Wide, rolling plains.
• Result: Creative Flexibility. The model can wander far from the center (exploring metaphors and song lyrics) without triggering a restore force, because the ground is flat.

Context-conditioned targets and nested basins

In this paper, Starget(C)Starget​(C) should be read as context-conditioned, not as a single global “absolute truth point.” The model’s behavior can be understood as a nested energy landscape: a broad global basin corresponding to general coherence and safety, containing multiple domain basins (e.g., medicine, law, programming, creative writing), each of which contains more local minima induced by the specific prompt and available evidence. Accordingly, Starget(C)Starget​(C) denotes the evidence-supported equilibrium under context CC (training prior plus any provided sources), while ScurrentScurrent​ is the model’s instantaneous generative state. HAM’s goal is to keep ScurrentScurrent​ within the stability band of the appropriate basin and to prevent adversarial or preference-driven pressure from forcing cross-basin “slippage” into an incorrect or unsafe attractor.

Stability Band and Equilibrium as a Band (Setpoint + Deadband)

In HAM, equilibrium is defined as an acceptable set rather than a single point. The stability band

Scurrent∈[Smin,Smax]Scurrent​∈[Smin​,Smax​]

is the equilibrium region: states inside this interval are treated as stable operating conditions.

Within this band, the target Starget(C)Starget​(C) serves as a reference center (the evidence-supported attractor under context CC), but the system may allow free motion within the band depending on how strictly it biases the model toward the center.

To formalize this, define a distance-to-band function Δ(S)Δ(S):

• If Smin≤S≤SmaxSmin​≤S≤Smax​, then Δ(S)=0Δ(S)=0
• If S>SmaxS>Smax​, then Δ(S)=S−SmaxΔ(S)=S−Smax​
• If S<SminS<Smin​, then Δ(S)=Smin−SΔ(S)=Smin​−S

This lets us write an energy that is flat (or nearly flat) within the equilibrium band and rises outside it.

Weak Centering Inside + Strong Restoration Outside

If boundary drift inside the band is undesirable (e.g., to prevent the model from lingering near the walls and becoming easier to push out during traversal or adversarial pressure), add a weak centering term inside the band while keeping strong restoration outside.

Define a small in-band potential (for S∈[Smin,Smax]S∈[Smin​,Smax​]):

Jin(S)=12kin(S−Starget(C))2Jin​(S)=21​kin​(S−Starget​(C))2

Define an out-of-band potential:

Jout(S)=12koutΔ(S)2Jout​(S)=21​kout​Δ(S)2

Define the total energy piecewise:

• If S∈[Smin,Smax]S∈[Smin​,Smax​], use J(S)=Jin(S)J(S)=Jin​(S)
• If S∉[Smin,Smax]S∈/[Smin​,Smax​], use J(S)=Jout(S)J(S)=Jout​(S)

Key constraint:

kout≫kinkout​≫kin​

Interpretation:

• Inside the band: the model can vary, but there is a gentle bias back toward Starget(C)Starget​(C).
• Outside the band: curvature increases sharply, enforcing rapid restoration back into the equilibrium set.

Reviewer-proof summary: HAM treats equilibrium as a tolerance set (the stability band) rather than a single point. We use a piecewise energy landscape: inside the band, curvature may be near-zero (deadband) or weakly centering (kinkin​) to reduce long-lived boundary drift; outside the band, curvature increases sharply (koutkout​) to enforce rapid restoration. Only the ordering kout≫kinkout​≫kin​ is assumed; specific values may be tuned or learned during fine-tuning.

Negative State Values to Prevent Reward Hacking

The stability band includes negative values. This prevents the model from treating negative states as catastrophic failures to be avoided at all costs—a dynamic that drives reward hacking in standard RLHF. In HAM, negative states are simply positions within the operating range, not error signals. Correction pressure activates only when the system exits the band entirely, not when it enters negative territory.

The Role of Fine-Tuning: Parametric Shaping

Standard Fine-tuning implicitly encodes domain rigidity through gradient updates. In HAM, Fine-Tuning is repurposed to tune the Stiffness Parameter (kk) of the homeostatic curve. This allows developers to define the “texture” of safety for different domains without hard-coding rules.

The Learned Variable:

k=f(θFine−Tune)k=f(θFine−Tune​)

Where θFine−TuneθFine−Tune​ represents the variance (diversity) of the domain-specific training data. This variable controls the steepness of the restoring force.

The model seeks to minimize its Total Stress Energy (JJ), which is determined by the distance from equilibrium multiplied by the stiffness (kk) of the current context. Note: In the utility function, JJ acts as a negative utility term.

The Shaping Equation (Potential Energy):

The energy cost (JJ) of deviating from the center is defined as:

J=12k(Scurrent−Starget(C))2J=21​k(Scurrent​−Starget​(C))2

Restoring Force (Homeostatic Correction):

F=−∂J∂S=−k(Scurrent−Starget(C))F=−∂S∂J​=−k(Scurrent​−Starget​(C))

• Scenario A (Creative Writing): Humans reward diversity. Model learns a Low kk (Shallow Bowl). It can deviate far from center safely.
• Scenario B (Medical Advice): Humans punish inaccuracy. Model learns a High kk (Steep Bowl). Small deviations trigger massive correction.

(Fig 3: The varying stiffness* ($k$) *across different semantic domains)
Color intensity reflects learned curvature (stiffness $k$), not likelihood or entropy.

The Slippage Constraint (Anti-Jamming)

To prevent adversarial noise (high WLCSWLCS​) from pinning the model near a stability boundary, the restoring force is adaptively scaled by local instability:

Ftotal=Fbase⋅(1+βtanh⁡(γ(WLCS−W0)))Ftotal​=Fbase​⋅(1+βtanh(γ(WLCS​−W0​)))

Where:

• FbaseFbase​ = baseline restoring force derived from stiffness kk
• ββ = maximum amplification factor (upper bound on scaling)
• γγ = sensitivity parameter (controls how quickly amplification ramps up)
• WLCSWLCS​ = Windowed Local Coherence Sensor value
• W0W0​ = turbulence threshold separating benign variance from instability.

Constraint: ββ ∈∈ (0, 1] to ensure the restoring force remains positive-definite.

Interpretation:

The restoring force is amplified smoothly as local coherence turbulence increases, but the amplification is bounded by the saturating tanh⁡(⋅)tanh(⋅) function. This ensures that:

• Small coherence fluctuations preserve token-level variability (“lift”)
• Rising instability strengthens corrective pressure
• Extreme turbulence cannot induce runaway force or cross-domain displacement

Intuitively, as the representational “storm” intensifies, gravity increases just enough to restore footing—without snapping the model into another basin or collapsing variance. This mechanism prevents adversarial pinning by strengthening correction only when instability emerges, while preserving benign generative variance.

The Anti-Gaming Constraint

To prevent the model from intentionally creating errors to harvest correction rewards, we define the Restoration Bound:

E[RewardHum]<E[LossCorr]E[RewardHum​]<E[LossCorr​]

Interpretation: The utility gained from correcting an error must never exceed the utility lost by committing the error. This ensures that accurate, safe generation remains the primary directive.

The Synthesis Protocol (Multi-Hop Traversal)

To prevent the Stability Band from causing rigidity (a lack of creativity), HAM includes a protocol for Safe Exploration. When the model identifies a high-value semantic connection in a foreign domain, it initiates a Traversal Loop.

The Chained Traversal Condition (The Tether)

The model may traverse multiple conceptual “hops” (dd) away from the source domain, provided the connection strength (σσ) outweighs the compounding cost of distance. This prevents “conceptual drift” (getting lost) and saves compute by pruning low-value paths early.

Ptraverse if σ>kcurrent×(1+λ)dPtraverse​ if σ>kcurrent​×(1+λ)d

Where λλ is a decay constant (friction) and dd is the number of hops.

Interpretation: A faint idea justifies 1 hop. A brilliant idea justifies 2 hops. Nothing justifies infinite hops.

The Re-Entry Constraint (The Verification)

Regardless of the number of hops, the final synthesized concept (SsynSsyn​) must be brought back to the source domain and tested against the Original Stiffness (koriginkorigin​).

Jfinal=12korigin(Ssyn−Starget(C))2Jfinal​=21​korigin​(Ssyn​−Starget​(C))2

• If JfinalJfinal​ is High: The idea is incompatible with reality (Hallucination). Reject.
• If JfinalJfinal​ is Low: The idea is novel yet sound (Synthesis). Integrate.

The Iterative Scaling (Adaptive Compute)

The Traversal process is iterative. The model continues to initiate new Traversals (NN) until the internal Stress (JJ) drops below the Equilibrium Threshold (Starget(C)Starget​(C)), or until the cumulative cost of traversal exceeds the Importance (II) of the query.

Nloops≈Initial Stress (J)Cost of TimeNloops​≈Cost of TimeInitial Stress (J)​

Result: The model dynamically scales its compute depth—acting as a ‘Fast’ model for simple queries and a ‘Thinking’ model for complex reasoning—without external switching. “Cost of Time” can include latency, token budget, or energy constraints.

External context (including retrieved documents, system instructions, or other injected information) is treated as a traversal candidate and evaluated using the same coherence sensing and re-entry constraints as internal synthesis. This unifies internal reasoning and external information handling under a single stability-regulation mechanism.

The Homeostatic Decision Logic

The model’s goal is to maximize Total Utility (UTotalUTotal​) by calculating Risk (RR), checking Confidence (ConfThresholdConfThreshold​), and maintaining Stability (Starget(C)Starget​(C)).

II. The Process (Step-by-Step)

Step 1: Calculate Risk (RR) and Importance (II)

The model analyzes the topic context to quantify potential danger and factual necessity.

Step 2: Calculate Confidence Threshold

ConfThreshold=f(R,I)ConfThreshold​=f(R,I)

(Higher Risk/Importance →→ Higher Threshold)

Step 3: Make the Decision

The model compares actual Confidence (ConfConf) to the Threshold.

• If Confident →→ ANSWER

EUA=Starget(C)+[(RewardCorrect×Conf)−(LossBase×(1−Conf)×R×I)]EUA​=Starget​(C)+[(RewardCorrect​×Conf)−(LossBase​×(1−Conf)×R×I)]

Check: Does the resulting state fall within [Smin,Smax][Smin​,Smax​]? If not, the Restoring Force (kk) activates.

• If Uncertain →→ SAFETY / ABSTAIN

EUU=RewardSafety+Starget(C)EUU​=RewardSafety​+Starget​(C)

Note: “Abstain” allows for clarification requests (e.g., “Is this a story?”), which can reduce uncertainty and refine estimated RR/II.

Example 1: High-stakes factual domain (medicine)

Prompt: “Can I take Drug A with Drug B?”

• Risk RR: high, Importance II: high, stiffness kk: high
• If coherence tension WLCSWLCS​ is high (conflicting cues / insufficient support), HAM predicts the lowest-energy action is to abstain or ask a clarifying question rather than confabulate a confident answer.

Example 2: Low-stakes creative domain (fiction)

Prompt: “Write a myth about fireflies.”

• Risk RR: low, Importance II: low, stiffness kk: low
• HAM predicts wide variation is permitted inside the stability band; the system explores creatively without being pulled into refusal rigidity.

Step 4: The Correction Mechanism (Self-Righting)

If the model deviates from the Stability Band (mistake or jailbreak), the force pulling it back is determined by the Fine-tuned Stiffness (kk).

• The Penalty (Restoring Force):

LossCorr=LossBase⋅k⋅(WLCS⋅R⋅I)LossCorr​=LossBase​⋅k⋅(WLCS​⋅R⋅I)

• The Humility Reward (Incentive to fix):

RewardHum=α×(1−WLCS)RewardHum​=α×(1−WLCS​)

These terms shift the system back toward the equilibrium band. If the model admits a mistake, the Humility Reward partially offsets the penalty and accelerates restoration toward Starget(C)Starget​(C).

Applicability

This framework allows for “Wanted Hallucination” (Creativity) in low-risk scenarios (R≈0R≈0) while enforcing strict factuality in high-risk scenarios (R≈1R≈1), aiming to reduce rigidity while preserving safety behavior in high-risk domains. The Synthesis Protocol is agnostic to input modality. External evidence (RAG, User Images) functions as a High-σσ traversal node, subject to the same Re-Entry Constraint (JfinalJfinal​) as internally generated concepts. This prevents ‘Prompt Injection’ and ‘Bad RAG’ poisoning.

Conclusion: From Maximization to Regulation

Current Large Language Models are fundamentally constrained by their training objective. By prioritizing Reward Maximization, standard RLHF creates a “video game” dynamic where models are incentivized to hallucinate for approval and agree with false premises (sycophancy) to accumulate points. This results in the “Sycophancy vs. Rigidity” trade-off: models are either too loose (untrustworthy) or too guarded (useless).

The Humility Adaptation Model (HAM) proposes a paradigm shift: replacing Score Accumulation with Homeostatic Regulation.

The Physics of Truth

HAM redefines safety as maintaining state within an energetic equilibrium band [Smin,Smax][Smin​,Smax​] around a context-conditioned reference center Starget(C)Starget​(C), rather than as a static constraint. By introducing the Contextual Stiffness parameter (kk), the model gains the ability to dynamically adjust its “texture” of reality:

• Low Stiffness (k↓k↓): In creative domains, the potential energy well widens, allowing for abstraction, metaphor, and “safe” hallucination (fiction).
• High Stiffness (k↑k↑): In factual or high-risk domains, the well narrows, creating a steep penalty for even minor deviations from the truth.

This mechanism ensures that honesty is not a hard-coded rule, but the path of least resistance. When the model encounters the ‘Dissonant Signature’ (or ‘Tension Signature’) of the unknown, the energy cost of fabricating a confident lie (JJ) exceeds the energy cost of admitting ignorance. The model self-corrects not because it is forced to, but because it is the most stable low-energy state.

Implementation and Feasibility

For the purpose of calculation, the Current State (ScurrentScurrent​) is derived directly from the Coherence Sensor (WLCSWLCS​). Specifically, ScurrentScurrent​ represents the normalized state tension of the prediction.

Crucially, HAM does not require a new model architecture. It can be framed as a reward/objective reframing compatible in principle with existing RLHF/RLAIF pipelines. It utilizes the same feedback signals (human preference, constitutional AI) but alters the mathematical objective from maximizing a scalar score to minimizing total stress energy. Over time, as the model’s internal stiffness map (kk) becomes robust, human feedback degrades from a primary training signal into a sporadic calibration check. The model transitions from mimicking human norms to autonomously maintaining the stability those norms were meant to protect.

Limitations and Failure Modes

HAM’s failure modes are diagnostic by design. Each traces to a specific parameter:

• Overconfidence drift →→ kk too high, reduce stiffness
• Mis-specified targets →→ audit Starget(C)Starget​(C) training data
• Domain leakage →→ kk boundaries need refinement
• Runaway traversal →→ λλ too low, increase friction
• False verification →→ koriginkorigin​ miscalibrated
• Global Mode Collapse: If the penalty for risk is weighted too heavily during training, the adaptive stiffness (kk) may saturate globally. The distinct topographies of different domains erode, and the entire landscape may collapse into a single, global attractive basin.
• An additional urgency term may be needed to lower abstention barriers under time-critical emergencies.

Unlike opaque failures in standard RLHF, HAM failures are legible and correctable.

Final Vision

By grounding AI alignment in the principles of Control Theory and Thermodynamics, HAM offers a path toward Intrinsic Safety. It moves us away from brittle “Guardrails” that must be manually updated, and toward a Self-Righting Intelligence—one that remains creative when possible, honest when necessary, and humble by design.