Emotional Decay Curves With Hysteresis

Mechanism

The affective state of an agent is represented as a vector of bounded scalar dimensions. The three principal dimensions are arousal (activation level, reflecting the urgency with which the agent is currently engaging with its environment), valence (the positive-or-negative coloring of the agent's recent experience, reflecting whether outcomes have been favorable or adverse), and motivation (the persistence of goal-directed energy, reflecting how strongly the agent is committed to pursuing its current objectives). Each dimension is bounded above and below by policy-defined limits and tracks toward a policy-defined baseline whenever no perturbation event is acting on it.

Decay is exponential toward baseline. The current effective value of a dimension is computed as the baseline plus the difference between the last-updated value and the baseline, multiplied by an exponential factor based on elapsed time since the last update divided by the dimension's time constant. Time constants are component-specific and asymmetric. Arousal carries a short time constant — perturbations to arousal decay within seconds to minutes, matching the temporal scale of a startle response or an immediate threat encounter. Valence carries a moderate time constant — perturbations decay within minutes to hours, matching the temporal scale of a sustained mood. Motivation carries the longest time constant — perturbations decay over hours to operational shifts, matching the temporal scale of a sustained drive.

The asymmetry has a second axis beyond the inter-component spread. Within each component, the time constant differs between rising and falling phases. Negative-valence excursions decay faster than positive-valence excursions, so the agent recovers from fear faster than it loses confidence; arousal spikes decay faster than they accumulate, so the agent settles after a startle faster than it ramps into one; motivation losses decay more slowly than motivation gains, so the agent's commitment to a goal degrades gradually rather than collapsing on a single setback. The aggregate effect is a structural caution bias: the agent retains the benefits of recent positive experience longer than the costs of recent negative experience, while still responding promptly to acute threat.

Hysteresis prevents oscillation at behavioral transition points. Each dimension carries a hysteresis margin separating the threshold at which the agent enters a behavioral mode from the threshold at which it exits. An agent that enters a high-arousal mode at a given threshold does not exit that mode until arousal has decayed past the threshold by the margin. The margin is small relative to the dimension's range but sufficient to prevent rapid cycling near the threshold.

Operating Parameters

Each dimension's parameter set comprises a baseline, an upper bound, a lower bound, a rising time constant, a falling time constant, a hysteresis margin, and a perturbation-override profile. The parameter set is stored in a signed policy reference and is loaded at agent startup. Runtime modification of the parameter set requires a credential appropriate to the deployment domain — a fleet operator may adjust the parameters within a credentialed range, but moving outside that range requires a higher-tier authorization. Every parameter read and every parameter change is logged with the credential that authorized it, so the affective trajectory of any agent at any time can be reconstructed from the logged inputs.

Perturbation events are the mechanism by which the environment writes into the affective state. A perturbation event carries a target dimension, a magnitude, a direction, and an override duration during which decay is suspended for the affected dimension. After the override duration ends, the dimension resumes decay toward baseline from its perturbed value. Perturbation events are themselves credentialed; only sensors and reasoning components carrying the appropriate credential may emit perturbation events targeting a particular dimension. This prevents arbitrary modules from arbitrarily reshaping the agent's affective trajectory.

The bounded property is enforced strictly. A perturbation that would drive a dimension past its upper or lower bound is clipped at the bound; the dimension never wraps, never saturates silently, and never adopts a value outside the policy-defined range. The bounding is what makes the decay curves analyzable and what makes the agent's affective behavior explainable in retrospect — given the perturbation log and the parameter set, the trajectory is fully determined.

Alternative Embodiments

The three-dimension preferred embodiment may be reduced to a single arousal-only dimension for low-complexity deployments such as simple alerting agents, where the additional dimensions do not yield operational value. It may be expanded to a five-or-more-dimension embodiment for richer agents, adding a confidence dimension that decays with operational outcome and a fatigue dimension that decays with engagement load. The architectural requirement is that each dimension carry the same parameter structure — bounds, baseline, asymmetric time constants, hysteresis margin, perturbation profile — and that the dimensions be governance-bound under credentialed policy.

The decay function may be implemented as classical exponential decay, as the preferred embodiment specifies, or as a piecewise-linear approximation in deployments where the floating-point cost of exponential evaluation is operationally significant. A logistic-curve embodiment is admissible where the dimension semantically saturates at its bounds rather than approaching them asymptotically. In all embodiments the asymmetry between rising and falling phases must be preserved, because the asymmetry is what produces the structural caution bias.

Hysteresis may be implemented as a margin around a single threshold, as separate enter-and-exit thresholds, or as a dwell-time requirement under which the dimension must remain past the threshold for a minimum interval before the mode transition fires. The margin embodiment is preferred because it composes cleanly with the decay curves; the dwell-time embodiment is appropriate for deployments where the mode transition itself is expensive and benefits from additional confirmation.

Composition With the Cognition Architecture

The affective-state vector is consumed by the operator-intent layer, the actuation-admissibility evaluator, and the planning layer. The operator-intent layer reads arousal and valence to condition its bifurcated risk-and-hostility profiles — high arousal alone is admissible into the risk profile under ordinary credentialing but admissible into the hostility profile only under credentialed authorization. The actuation-admissibility evaluator reads motivation to condition the persistence of long-horizon plans against short-horizon discrepancy classifications; an agent with high motivation does not abandon a goal on the first nominal anomaly, but a low-motivation agent may. The planning layer reads the full vector to bias exploration-exploitation tradeoffs.

The decay curves compose with the perturbation events emitted by the discrepancy-classification subsystem. A class-five adversarial-interference classification emits a perturbation toward elevated arousal and toward negative valence; under the asymmetric time constants, the arousal perturbation decays quickly once the threat passes but the valence perturbation persists, biasing the agent toward additional caution on subsequent same-family operations even after the immediate arousal has settled. A sequence of class-one nominal classifications emits gentle positive-valence perturbations, gradually rebuilding the operator's confidence on the slower positive-valence rising time constant.

Prior-Art Distinction

The architecture also differs from prior art in the bidirectional asymmetry treatment. Prior affect models that include any asymmetry typically apply it only between dimensions, not within a single dimension. The within-dimension asymmetry between rising and falling time constants is what produces the structural caution bias on a per-dimension basis, allowing fine-grained tuning of how each component recovers independently of the others. This per-dimension within-component asymmetry, combined with the cross-component time-scale separation, produces the temporal layering that distinguishes a transient startle from a sustained mood from a long-running drive in a single agent without requiring architecturally separate subsystems for each.

Affect-as-state implementations in conventional autonomous-agent literature treat affective dimensions as freely tunable scalars, often without bounds, often without principled decay, and almost universally without governance binding on the parameter set. Reinforcement-learning agents with intrinsic-motivation modules typically conflate motivation with reward signal and do not separate the time scales of arousal, valence, and motivation. Robotics systems with mood-modeling layers often use symmetric decay, producing agents that either remain too cautious for too long or shed caution too quickly for the operational frame.

The architecture here is structurally different in three respects. First, the decay curves are bounded and asymmetric, producing the structural caution bias rather than the symmetric drift of prior systems. Second, the parameters are governance-bound under credentialed policy with audit-grade lineage, so the agent's affective trajectory is reconstructable and accountable. Third, the perturbation events are themselves credentialed, so the set of modules that can write into affect is itself a controlled population. None of these three properties appears in prior affect-modeling literature in combination.

Disclosure Scope

The disclosure covers the bounded asymmetric decay curve, the three-component preferred embodiment along with reduced and expanded alternatives, the governance-bound parameter set, the credentialed perturbation-event mechanism, the hysteresis structure, and the composition with the operator-intent and actuation-admissibility layers. It positions the primitive at the layer where autonomous-agent affect has been treated as either an unconstrained engineering knob or a heuristic add-on. The architecture replaces both with a structurally bounded, asymmetric, governance-bound trajectory that supports the explainability and accountability properties the rest of the cognition architecture depends on.

The scope further encompasses the auxiliary mechanisms that make the decay curves operationally usable: the parameter-set distribution and signing protocol, the runtime audit log of parameter reads and changes, the credentialing protocol for perturbation-emitting modules, the bounding-and-clipping discipline, and the procedure by which the hysteresis margin is selected for a given dimension based on the operational cost of mode-transition. The disclosure contemplates application across robotic, vehicular, aerospace, and software-agent deployments, and contemplates both single-agent and multi-agent configurations in which affective-state vectors may be partially shared across agents under credentialed authorization to support coordinated team behavior. In the multi-agent case, the cross-agent affective sharing is itself governed by credentialing rules that prevent one agent's perturbation history from arbitrarily reshaping another agent's affective trajectory; sharing produces an additional perturbation event in the receiving agent rather than a direct write to its state vector, preserving the bounding, asymmetry, and governance properties for the receiving agent's own decay curve. The cumulative effect is an affective layer that behaves predictably under perturbation, recovers asymmetrically toward baseline, resists oscillation at behavioral boundaries, and remains accountable to the credentialed policy under which it was configured.