Dual-Evolving Memory (EvoMem) Systems

• Dual-Evolving Memory (EvoMem) is a memory architecture that decouples fast, adaptive storage from slow, stable memory to tackle non-stationary patterns.
• It leverages dual-memory modules inspired by biological systems and hardware designs to balance rapid adaptation with long-term retention.
• EvoMem is applied in computational neuroscience, incremental machine learning, and multi-agent systems to optimize stability-plasticity tradeoffs and improve dynamic performance.

Dual-Evolving Memory (EvoMem) is a class of memory architectures and learning principles that encode and retrieve information across two or more evolving timescales or memory modules. Originally emerging from theoretical analyses of memory for dynamic patterns in biological and artificial systems, EvoMem has developed into a central motif across computational neuroscience, large-scale machine learning, hardware design, multi-agent systems, distributed optimization, and trust-oriented LLM agent frameworks. The core property underpinning EvoMem is its capability to simultaneously preserve long-term invariants and adapt swiftly to recent, potentially non-stationary changes, often by explicitly separating fast and slow-evolving storage, or by hierarchical or compartmental memory structures.

1. Theoretical Foundations of Dual-Evolving Memory

The canonical EvoMem formalism was introduced in the context of generalizing Hopfield-type energy-based networks to handle both static and evolving patterns, motivated by the dichotomy of distributed memory in the olfactory cortex and specialized, rapidly-adapting memory in the adaptive immune system (Schnaack et al., 2021). Given patterns $\sigma=(\sigma_1,\dots,\sigma_L)$, memory is encoded as minima of a generalized Hopfield energy function: $$E_J(\sigma) = -\frac{1}{2L} \sum_{i\neq j} J_{ij}\, \sigma_i\, \sigma_j = -\frac{1}{2}\langle \sigma | J | \sigma \rangle.$$ A discrete-time, Hebbian-type rule governs synaptic updates upon presentation of evolving (mutated) exemplars: $$J_{ij}(t\!+\!1) = (1-\lambda)J_{ij}(t) + \lambda\, \sigma_i^\alpha(t)\, \sigma_j^\alpha(t).$$ The optimal adaptation to dynamic stimuli requires the learning rate $\lambda^*\simeq\sqrt{8\mu/(N-1)}$, where $\mu$ is the per-step mutation rate and $N$ the number of classes. While increased $\lambda$ enables tracking of rapidly evolving patterns, it also induces shallow energy minima with “mountain-pass” connections, increasing the likelihood of misclassification—a degeneracy not present for static patterns.

To address this, EvoMem introduces explicit network compartmentalization: the system is divided into $C$ disjoint subnetworks, each responsible for a fraction of the memory classes. Distributed encoding dominates for static stimuli, whereas for highly evolving patterns, the unique optimum is maximal specialization, $C=N$, with each compartment tuned for rapid plasticity ($\lambda_c\to 1$) (Schnaack et al., 2021).

A related analytical framework optimizes the tradeoff between utility (average affinity to evolving targets) and risk (variance/loss due to forgetting), encoding memory as an exponentially decaying mixture of patterns. The optimal learning rate can be derived as $$E_J(\sigma) = -\frac{1}{2L} \sum_{i\neq j} J_{ij}\, \sigma_i\, \sigma_j = -\frac{1}{2}\langle \sigma | J | \sigma \rangle.$$0, with $$E_J(\sigma) = -\frac{1}{2L} \sum_{i\neq j} J_{ij}\, \sigma_i\, \sigma_j = -\frac{1}{2}\langle \sigma | J | \sigma \rangle.$$1 quantifying risk tolerance and $$E_J(\sigma) = -\frac{1}{2L} \sum_{i\neq j} J_{ij}\, \sigma_i\, \sigma_j = -\frac{1}{2}\langle \sigma | J | \sigma \rangle.$$2 controlling affinity nonlinearity (Schnaack et al., 2021).

2. Biologically Inspired and Hardware Realizations

The EvoMem paradigm is tightly linked to neuroscientific and biophysical observations. In biological synapses and memristive (metal–oxide) devices, memory traces naturally bifurcate into a fast, volatile (“short-term memory,” STM) component and a slow, nonvolatile (“long-term memory,” LTM) residue (Giotis et al., 2021). The total resistance of a memristive synapse $$E_J(\sigma) = -\frac{1}{2L} \sum_{i\neq j} J_{ij}\, \sigma_i\, \sigma_j = -\frac{1}{2}\langle \sigma | J | \sigma \rangle.$$3 splits into $$E_J(\sigma) = -\frac{1}{2L} \sum_{i\neq j} J_{ij}\, \sigma_i\, \sigma_j = -\frac{1}{2}\langle \sigma | J | \sigma \rangle.$$4 (STM, rapid, large-amplitude, fast decay $$E_J(\sigma) = -\frac{1}{2L} \sum_{i\neq j} J_{ij}\, \sigma_i\, \sigma_j = -\frac{1}{2}\langle \sigma | J | \sigma \rangle.$$5) and $$E_J(\sigma) = -\frac{1}{2L} \sum_{i\neq j} J_{ij}\, \sigma_i\, \sigma_j = -\frac{1}{2}\langle \sigma | J | \sigma \rangle.$$6 (LTM, incremental, persistent).

Plasticity events (write pulses) affect both components, but STM is transient and can be overwritten, whereas LTM persists, supporting “palimpsest” operation. Mathematical models show that, with suitable device engineering, the nonvolatile component can survive hundreds of overwrites, effectively doubling memory capacity compared to single-timescale devices. Experimental systems demonstrate robust familiarity detection, automatic denoising, and resilience even after destructive overwrites, all without special control logic (Giotis et al., 2021).

3. EvoMem in Machine Learning and Incremental Clustering

Dual-evolving memory structures address the stability–plasticity dilemma in continual, multi-view, or streaming learning settings. For instance, MemEvo (Kong et al., 18 Sep 2025) employs a neuroscience-inspired architecture comprising:

• A hippocampal (“fast plastic”) module that encodes new data via a view alignment operator,
• A cognitive forgetting mechanism based on power-law decay, reweighting historical information,
• A prefrontal (“slow consolidation”) module that aggregates old and new representations in a third-order tensor and applies nonconvex low-rank regularization.

The combined incremental optimization objective balances rapid adaptation to new views (plasticity) with gradual knowledge integration and resistance to forgetting (stability). Empirical evaluations on diverse multi-view clustering tasks show that the introduction of dual-evolving memory modules yields significant improvements over both static and prior incremental methods, maintaining bounded resource requirements and fast convergence (Kong et al., 18 Sep 2025).

Analogously, in infinite-horizon autoregressive video generation, MemRoPE (Kim et al., 12 Mar 2026) compresses streaming context into two memory tokens using exponential moving averages with distinct decay rates: a long-term token preserving identity and a short-term token following recent dynamics. This allows constant-cost, unbounded context aggregation, overcoming the limitations of sliding window and static anchor approaches.

4. EvoMem Architectures in Agent Planning and Multi-Agent Systems

The EvoMem principle underpins advanced agentic reasoning frameworks, especially in multi-agent and planning scenarios:

• In multi-agent planning (Fan et al., 1 Nov 2025), EvoMem defines two complementary evolving memory modules: Constraint Memory (CMem), which holds persistent, session-spanning task constraints, and Query-feedback Memory (QMem), an intra-session scratchpad of past attempts and error feedback. This division echoes the phonological loop and visuospatial sketchpad in the cognitive psychology of working memory. The combination enables iterative, self-correcting LLM-based planning that is robust to constraint drift and redundant errors.
• Test-time “self-evolving” memory systems for LLM agents (Wei et al., 25 Nov 2025) universally structure memory as a four-tuple (F, R, C, U): frozen LLM, retrieval operator, context-constructor, and memory update rule. EvoMem frameworks here contrast static “history” modules with dynamic dual-memory designs, supporting streaming benchmarks and action-reasoning-refine cycles.

In distributed AI, EvoMem is implemented as a paired long-term memory $$E_J(\sigma) = -\frac{1}{2L} \sum_{i\neq j} J_{ij}\, \sigma_i\, \sigma_j = -\frac{1}{2}\langle \sigma | J | \sigma \rangle.$$7 (tracking stable, optimal configurations) and short-term memory $$E_J(\sigma) = -\frac{1}{2L} \sum_{i\neq j} J_{ij}\, \sigma_i\, \sigma_j = -\frac{1}{2}\langle \sigma | J | \sigma \rangle.$$8 (tracking recent transient workload statistics), with formal mechanisms for mutual update and absorption, optimizing computation, communication, and deployment jointly (Li et al., 9 Jan 2026).

5. Meta-Evolution and Memory Architecture Optimization

EvoMem is also the basis for bilevel evolutionary design of memory systems (Zhang et al., 21 Dec 2025). In MemEvolve, not only the episodic contents $$E_J(\sigma) = -\frac{1}{2L} \sum_{i\neq j} J_{ij}\, \sigma_i\, \sigma_j = -\frac{1}{2}\langle \sigma | J | \sigma \rangle.$$9 but also the architecture $$J_{ij}(t\!+\!1) = (1-\lambda)J_{ij}(t) + \lambda\, \sigma_i^\alpha(t)\, \sigma_j^\alpha(t).$$0—encode, store, retrieve, manage modules—are subject to meta-evolutionary search loops. Outer loop diagnosis and recombination of memory architectures enable agents to progressively refine their own memory strategies across environments and backbones, resulting in robust, transferable memory abstractions and up to 17% gains on challenging benchmarks.

6. Trust, Safety, and Dual-Memory Filtering in LLM Agents

A salient direction is the application of EvoMem to trustworthy learning and mitigation of agent memory misevolution (Cheng et al., 3 Feb 2026). TAME (Trustworthy Agent Memory Evolution) deploys two separate memory banks: Executor Memory for utility-maximizing strategies, and Evaluator Memory for assessing and filtering based on multi-dimensional trust metrics (safety, robustness, truthfulness, privacy, fairness). All candidate plans are filtered against Evaluator Memory's constraints prior to execution, ensuring that learning does not degrade trustworthiness during benign evolution. On the Trust-Memevo benchmark, TAME achieves simultaneous improvements in both performance and aggregate trust, outperforming non-evolving and single-memory baselines.

7. Comparative Summary of Dual-Evolving Memory Paradigms

Domain/Architecture	Evolving Components	Fast/Short-Term	Slow/Long-Term	Key advantage	Reference
Energy-based Hopfield EvoMem	$$J_{ij}(t\!+\!1) = (1-\lambda)J_{ij}(t) + \lambda\, \sigma_i^\alpha(t)\, \sigma_j^\alpha(t).$$1, network partition $$J_{ij}(t\!+\!1) = (1-\lambda)J_{ij}(t) + \lambda\, \sigma_i^\alpha(t)\, \sigma_j^\alpha(t).$$2	Follow pattern drift	Maintain deep attractors	Optimal for evolving/static patterns	(Schnaack et al., 2021)
Memristive palimpsest	$$J_{ij}(t\!+\!1) = (1-\lambda)J_{ij}(t) + \lambda\, \sigma_i^\alpha(t)\, \sigma_j^\alpha(t).$$3, $$J_{ij}(t\!+\!1) = (1-\lambda)J_{ij}(t) + \lambda\, \sigma_i^\alpha(t)\, \sigma_j^\alpha(t).$$4	Volatile STM update	Slow LTM consolidation	Hardware dual-memory, doubled capacity	(Giotis et al., 2021)
Incremental clustering	Zₜ (VAM), Z_hist	View alignment	Aggregated, ARMR-consolidated tensor	Balances plasticity-stability in streaming data	(Kong et al., 18 Sep 2025)
Video generation (MemRoPE)	$$J_{ij}(t\!+\!1) = (1-\lambda)J_{ij}(t) + \lambda\, \sigma_i^\alpha(t)\, \sigma_j^\alpha(t).$$5, $$J_{ij}(t\!+\!1) = (1-\lambda)J_{ij}(t) + \lambda\, \sigma_i^\alpha(t)\, \sigma_j^\alpha(t).$$6	Recent dynamics	Global identity anchor	Unbounded, constant-cost streaming memory	(Kim et al., 12 Mar 2026)
Multi-agent planning	QMem, CMem	Feedback iteration	Fixed session constraints	Iterative, constraint-aware LLM planning	(Fan et al., 1 Nov 2025)
Meta-evolved agent memory	$$J_{ij}(t\!+\!1) = (1-\lambda)J_{ij}(t) + \lambda\, \sigma_i^\alpha(t)\, \sigma_j^\alpha(t).$$7, $$J_{ij}(t\!+\!1) = (1-\lambda)J_{ij}(t) + \lambda\, \sigma_i^\alpha(t)\, \sigma_j^\alpha(t).$$8	Episodic contents	Architecture-level evolution	Robust, transferable, optimized systems	(Zhang et al., 21 Dec 2025)
Trustworthy LLM agents	Executor/Evaluator	Performance strategies	Trust evaluation/constraints	Joint safety-utility, mitigates misevolution	(Cheng et al., 3 Feb 2026)

These architectures, while various in implementation, share the central EvoMem tenet: decoupling rapid plastic adaptation from slow, stable memory evolution, and leveraging the interface or filtering between these timescales or modules to achieve optimality, robustness, or safety in dynamic, multi-faceted environments.

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References:

• Learning and organization of memory for evolving patterns (Schnaack et al., 2021)
• Risk-utility tradeoff shapes memory strategies for evolving patterns (Schnaack et al., 2021)
• Palimpsest Memories Stored in Memristive Synapses (Giotis et al., 2021)
• MemEvo: Memory-Evolving Incremental Multi-view Clustering (Kong et al., 18 Sep 2025)
• MemRoPE: Training-Free Infinite Video Generation via Evolving Memory Tokens (Kim et al., 12 Mar 2026)
• MemEvolve: Meta-Evolution of Agent Memory Systems (Zhang et al., 21 Dec 2025)
• EvoMem: Improving Multi-Agent Planning with Dual-Evolving Memory (Fan et al., 1 Nov 2025)
• Evo-Memory: Benchmarking LLM Agent Test-time Learning with Self-Evolving Memory (Wei et al., 25 Nov 2025)
• Self-Evolving Distributed Memory Architecture for Scalable AI Systems (Li et al., 9 Jan 2026)
• TAME: A Trustworthy Test-Time Evolution of Agent Memory with Systematic Benchmarking (Cheng et al., 3 Feb 2026)