Reputation Decay Function

Defines the time interval after which a trust signal's weight is reduced to exactly 50% of its original value. This parameter, often denoted as λ (lambda) or t₁/₂, provides an intuitive knob for domain experts to tune decay aggressiveness without manipulating raw mathematical coefficients.

• A 30-day half-life means a signal from 30 days ago is worth half of a signal from today
• Shorter half-lives create highly reactive systems sensitive to recent behavior
• Longer half-lives preserve institutional memory and resist manipulation bursts
• Common in radioactive decay analogies and exponential trust models

The most widely adopted decay function where the weight of a signal decreases by a constant fraction per unit of time, following the formula w(t) = w₀ × e^(-λt). This produces a smooth, memoryless curve where the rate of decay at any moment is proportional to the current value.

• Memoryless property: the decay rate doesn't depend on signal age, only current weight
• Produces a long theoretical tail where signals never quite reach zero
• Computationally efficient to implement with simple multiplication per time step
• Natural fit for systems where trust erosion is continuous and proportional

A hard cutoff approach where signals are assigned full weight within a defined window and abruptly drop to zero beyond it. Unlike gradual decay functions, this creates a binary distinction between relevant and irrelevant historical data.

• Implemented as a step function: weight = 1.0 if age < T, else 0.0
• Eliminates computational overhead of tracking infinitely decaying signals
• Risk of boundary effects where signals just inside/outside the window are treated radically differently
• Common in streaming architectures with finite storage retention policies

Decay functions where weight decreases according to a polynomial relationship with time, such as w(t) = w₀ / (1 + t)^k or w(t) = w₀ × t^(-α). These produce heavier tails than exponential decay, meaning older signals retain more relative influence over longer periods.

• The exponent k or α controls decay aggressiveness
• Power-law decay is scale-free, exhibiting similar behavior across different timescales
• Observed in natural phenomena like citation decay in academic literature
• Useful when long-term reputation should decay more slowly than short-term activity signals

Rather than decaying purely by clock time, this approach ties weight reduction to discrete events or state transitions. A trust signal may persist at full strength until a specific invalidation event occurs, such as a credential revocation, a failed audit, or a detected anomaly.

• Decouples trust decay from arbitrary time constants
• Models real-world scenarios where trust is state-dependent, not time-dependent
• Requires an event detection pipeline to trigger weight recalculations
• Often combined with time-based decay as a hybrid model for defense-in-depth

An advanced approach where the decay rate λ is not a static constant but dynamically adjusted based on contextual signals. During periods of high volatility or detected manipulation attempts, the system automatically accelerates decay to prioritize fresh evidence.

• Feedback loops from anomaly detection systems can increase decay rates
• Entity-specific decay rates may reflect individual behavioral volatility
• Requires careful calibration to avoid oscillation or overfitting to noise
• Represents the frontier of context-aware trust scoring architectures

The most common mathematical implementation where a signal's weight decreases by a constant factor over equal time intervals. Formula: W(t) = W₀ * e^(-λt), where λ (lambda) is the decay constant.

• Half-life parameter defines how long it takes for a signal to lose 50% of its weight
• Produces a smooth, continuous degradation curve
• Ideal for modeling natural forgetting in dynamic trust systems
• Example: A citation from 30 days ago might retain only 37% of its original weight with a half-life of 22 days

A simpler alternative where signal weight decreases at a constant rate per unit of time until it reaches zero. Formula: W(t) = max(0, W₀ - k*t).

• Predictable and transparent degradation pattern
• Easier to explain to non-technical stakeholders
• Risk of abrupt cliff effects when weight hits zero
• Suitable for systems with fixed expiration windows, such as security certificates or compliance audits
• Example: A trust endorsement loses 10% of its value per month, expiring completely after 10 months

The critical parameter that determines the rate of obsolescence in exponential decay systems. A shorter half-life creates a more responsive, recency-biased trust score.

• Short half-life (days): Prioritizes fresh interactions; high volatility
• Long half-life (months/years): Preserves historical reputation; slower to react to behavior changes
• Domain-specific tuning is essential—financial fraud signals may require half-lives of hours, while academic citations might use years
• Often implemented as a configurable policy rather than a hard-coded constant

The mechanism by which decay functions are applied during graph traversal in reputation graphs. As trust propagates from a seed node through multiple hops, both distance and time attenuate the signal.

• Hop-based decay: Each edge traversal reduces weight by a discount factor
• Time-based decay: Edge weights themselves degrade with age
• Combined models apply both simultaneously: W(edge) = W₀ * γ^hops * e^(-λt)
• Prevents stale endorsement chains from indefinitely influencing current trust scores
• Critical for Trust Rank and Bayesian Trust Network implementations

An alternative to continuous time-based decay where signal weight reduction is triggered by discrete events rather than clock time.

• Examples of triggers: New model release, policy change, detected anomaly, credential rotation
• Useful when the relevance of a signal is tied to versioning or state changes, not calendar time
• Often combined with time decay as a hybrid model: baseline temporal decay plus instant devaluation on trigger events
• Prevents outdated certifications or deprecated protocols from persisting in trust calculations after a breaking change

Choosing the appropriate decay function requires balancing mathematical properties against domain requirements.

• Exponential: Memoryless property; constant half-life; never reaches absolute zero
• Linear: Finite lifespan; predictable depletion; abrupt cutoff
• Logistic/Sigmoid: Slow initial decay, rapid mid-life drop, gradual tail; models 'shelf life' with a grace period
• Step function: Binary validity windows; simplest to implement but least granular
• Gaussian: Bell-shaped relevance curve peaking at a specific age; models 'peak relevance' for time-delayed impact signals
• Selection should be validated against empirical data on how signal predictiveness actually degrades over time