Utility-Driven Natural Selection: Darwinian Memory

• Utility-driven natural selection (Darwinian Memory) is a framework that evolves heritable memory by quantitatively selecting, recombining, and pruning data based on explicit utility functions.
• It employs replicator equations, Bayesian risk assessments, and Pareto optimization to balance memory complexity and risk, ensuring robust adaptation in computational and biological systems.
• Algorithmic implementations demonstrate significant performance gains, such as enhanced success rates, reduced task latencies, and stable memory reuse through dynamic competition and anticipatory strategies.

Utility-driven natural selection, sometimes termed Darwinian Memory, denotes a class of evolutionary and adaptive mechanisms—biological, physical, or computational—in which heritable information is shaped, reinforced, and pruned according to a quantitative utility function. This function formalizes survival value, information-processing efficiency, or long-term performance. Diverse models, from information-theoretic Darwinian frameworks to agent memory architectures and statistical mechanics of memory, instantiate this principle via replicator equations, risk-utility tradeoffs, and stochastic control. In all domains, memory is not passively accumulated but actively selected, recombined, and regulated by evolutionary pressure, enabling robust adaptation to changing environments and efficient navigation of complex tasks.

1. Core Principles and Theoretical Foundation

Utility-driven natural selection posits that heritable informational structures, whether genetic, cognitive, or algorithmic, undergo continual variation, selection, and retention according to utility, framed as an explicit mathematical reward or fitness function.

In the unified theory of Baladrón & Khrennikov, every agent (physical or biological) comprises a probabilistic classical Turing machine (PCTM) with a memory register $M(t)$, a stochastic update engine, and an anticipation module for projecting likely futures. At each time step, the agent ingests input (e.g., environmental samples), updates its state and memory, computes an anticipatory distribution, emits an action, and may mutate its own program $P$; variation is retained only if it increases the agent's utility $U[P]$ (Baladron et al., 2017).

Utility is concretely quantified as:

$$U[P] = \alpha\,\text{Complexity}[P]\, -\, \beta\,\text{FisherInfo}[p]\, +\, \gamma\,\text{MutualInfo}[P_1, P_2]$$

where terms correspond to (1) the logical depth/complexity of the memory/program, (2) minimization of information outflow (Fisher information of the anticipated distribution), and (3) maximization of mutual information (coherence) across networks of agents.

Replicator equations describe population-level frequency dynamics: $$\frac{d \phi_i}{dt} = \phi_i \left[ U(P_i) - \bar{U} \right]$$ where $\phi_i$ is the prevalence of program $P_i$, and $\bar{U}$ is the average utility in the population.

2. Algorithmic Instantiations: Darwinian Memory in Agents

The Darwinian Memory System (DMS) for GUI agents formalizes a survival-of-the-fittest architecture in which independent memory units—defined as $$(\langle\mathrm{Pre},\mathrm{Goal}\rangle, \text{Trajectory}, \text{Metadata})$$ tuples—are scored, selected, recombined, and actively pruned using an explicitly defined survival (utility) function (Mi et al., 30 Jan 2026).

Each memory unit $m_i$ accumulates:

• Utility $U(n_i)=\ln(1+n_i)+V_{\mathrm{new}}$ (reuse frequency and novelty bonus)
• Adaptive decay $D(\Delta t, n_i)$ penalizing dormancy
• Reliability penalty $P(K_i)$ for executed failures

The overall survival value: $$S(m_i) = \left[ \ln(1+n_i) + V_{\mathrm{new}} \right] \cdot D(\Delta t, n_i) \cdot P(K_i)$$ Selection, recombination, mutation (with probability $\epsilon$), and memory pruning proceed in a loop, with Bayesian risk-assessment inhibiting high-risk plans. Memory evolution is training-free: the DMS acts solely via competitive indexing, mutation, and self-regulated retention, without backpropagation or architectural retraining.

3. Statistical Mechanics and Risk–Utility Tradeoffs

The risk-utility framework conceptualizes evolving memory as a Pareto optimization between mean affinity (utility) and diversity risk in the face of mutating environments (Schnaack et al., 2021). Each acquisition or retention of memory is guided by an objective function: $$F(\lambda;\mu_{\mathrm{eff}}) = U(\lambda;\mu_{\mathrm{eff}}) - \frac{1}{\kappa} R(\lambda;\mu_{\mathrm{eff}})$$ with $\lambda$ representing the memory learning rate, $\mu_{\mathrm{eff}}$ the effective mutation rate of input classes, and $\kappa$ the risk-tolerance parameter.

In the regime of moderate $\kappa$, memory remains both robust and generalizable:

• Low $\kappa$ (risk-aversion) yields underfitting: memory is static, with poor retrieval.
• High $\kappa$ generates overfitting, favoring recent but volatile memories.
• Intermediate $\kappa$ optimizes the utility-risk tradeoff, with $$\lambda^* \sim (2\kappa \Theta \mu_{\mathrm{eff}})^{2/3}/N$$ for $N$ classes.

This framework applies to immune memory, neural continual learning, and general pattern-matching systems, with experimental and analytic phase diagrams highlighting the universal scaling of optimal memory update rates.

4. Stochastic Control in Evolution: Utility Optimization

In models integrating quantitative genetics with stochastic control (Rivoire et al., 2013), memory and inheritance mechanisms are interpreted as time-dependent controls $u_t$, with the aim of maximizing expected (long-run) reward, i.e., the lineage's mean logarithmic growth: $$\Lambda = \lim_{t \to \infty} \frac{1}{t} \mathbb{E}\left[ \sum_{s=0}^{t-1} f(m_s, x_s, u_s) \right]$$ Here, $f(m,x,u)$ quantifies fitness for trait–environment pairs, and the update strategy for heritability and plasticity (including Lamarckian weights, genetic variance, and cue-responsiveness) is optimized via the Hamilton–Jacobi–Bellman equation.

Optimal memory updating kernels correspond to Kalman-filter policies, i.e., Bayesian updates given both hereditary and environmental cues. Evolutionary strategies—bet-hedging, canalization, phenotypic plasticity, Lamarckian inheritance—emerge as solutions within this unified stochastic-control framework.

5. Applications and Empirical Performance

Empirical validation in agentic settings demonstrates the efficacy of utility-driven Darwinian memory (Mi et al., 30 Jan 2026). Key results for GUI-agent automation include:

• Average success rate increase by +18.0 percentage points
• Success retention improvement by +33.9 percentage points
• Task latency reductions of 20–30%
• Memory reuse rates stabilizing at 30–36%
• Self-regulation ablation resulting in +258% memory bloat, reduced success, and deteriorated latency

These outcomes confirm that continual competition and selection among memory traces yield higher-performing, more stable, and temporally efficient behavior, outperforming passive or static cache-based systems.

6. Lamarckian Anticipation and Predictive Adaptation

A recurring feature across theoretical and algorithmic frameworks is the integration of Lamarckian (anticipatory) modules. In the information-theoretic Darwinian model, a prediction kernel $K$ propagates beliefs about external systems, with memory registers updated through Bayesian inference (Baladron et al., 2017). This enables agents to project likely environmental states and adaptively tune their internal dynamics.

In computational systems, plans or trajectories are inhibited or prioritized using Bayesian risk estimates, ensuring that harmful or obsolete traces are pruned and that exploration prioritizes potentially rewarding novel strategies (Mi et al., 30 Jan 2026). This anticipatory component accelerates convergence and further reduces the risk of catastrophic forgetting or exploitation of suboptimal memory.

7. Unified Perspective and Implications

Across all domains, utility-driven natural selection—Darwinian Memory—formalizes the evolution of stored information according to explicit, environment-sensitive reward functions. The process is inherently dynamic: memory units are not merely accumulated but compete, mutate, and are culled in accordance with utility, robustness, and risk.

This framework unifies information processing in physical systems, population genetics, agent architectures, and neural and immune systems, capturing adaptation as optimal control over informational trajectories. The connection to stochastic control and Pareto fronts establishes that memory evolution is not a binary process (retain vs. forget) but a continuous optimization of reward-valued strategies under constraints of diversity, risk, and environmental volatility (Baladron et al., 2017, Schnaack et al., 2021, Mi et al., 30 Jan 2026, Rivoire et al., 2013).