Dynamic Memory: Adaptive & Evolving Storage

• Dynamic memory is a system that continuously updates stored information through real-time additions, deletions, and modifications to adapt to changing environments.
• It employs diverse architectures, including dual-memory frameworks, energy-based dynamics, and RL-driven allocators, to manage and optimize memory retrieval and storage.
• Empirical studies demonstrate that dynamic memory improves performance in robotics, machine learning, and systems by maintaining accuracy and efficiency under nonstationary conditions.

Dynamic memory refers to a class of memory representations, algorithms, architectures, or physical mechanisms in which the memory changes over time through active addition, deletion, modification, or transformation of stored information. Unlike static memories, which assume an immutable or once-reconstructed store, dynamic memory systems are designed to remain consistent, relevant, and optimal as environments, access patterns, or neural/physical substrates evolve. Dynamic memory appears in diverse domains ranging from cognitive and neural modeling, machine learning, robotics, and computer systems to economics and VLSI architecture, with each field emphasizing distinct formalizations, performance metrics, and operational principles.

1. Distinction Between Static and Dynamic Memory

Static memory is a fixed data structure constructed once for a given environment or data distribution. For example, classic spatio-semantic world models in robotics or static associative networks in computational neuroscience never update or remove stale content. In contrast, dynamic memory continuously integrates new observations and removes or updates obsolete, redundant, or contradictory data to maintain fidelity to changing environments or tasks. This online adaptation ensures operational consistency under nonstationarity and enables robust performance where static methods collapse due to misalignment between representation and reality. Representative examples include DynaMem’s online spatio-semantic voxel structure for mobile robots (Liu et al., 7 Nov 2024), dynamic dual-memory for video scene reconstruction (Cai et al., 11 Aug 2025), and the Exponential Dynamic Energy Network (EDEN) where the energy surface itself evolves to support sequential retrieval (Karuvally et al., 28 Oct 2025).

2. Mathematical Representations and Update Mechanisms

Dynamic memory implementations are domain-specific but unified by their ongoing, real-time update logic. In high-capacity neural models, memory is parameterized as a high-dimensional dynamic energy surface or evolving associative map. In robotics, DynaMem maintains a sparse voxel grid, each voxel $v$ characterized by

• 3D position,
• observation count $C_v$,
• last-seen timestamp $t_v$,
• semantic feature vector $f_v$,
• source image index $I_v$.

On receipt of a new observation, DynaMem performs the following updates: $$\begin{aligned} &C_v \leftarrow C_v + 1\ &f_v \leftarrow \frac{C_v-1}{C_v}f_v + \frac{1}{C_v}f_i\ &t_v \leftarrow \text{current time}\ &I_v \leftarrow \text{current image ID} \end{aligned}$$ Removal is handled by ray-casting against current depth maps, deleting voxels inconsistent with new geometry. Such bidirectional flow (additions and removals) is the hallmark of a dynamic memory.

In computational neuroscience, EDEN introduces a time-dependent energy function $E(v,t)$ whose attractors evolve due to coupling with a slow modulatory variable $s(t)$, yielding a network where memory transitions are controlled by the ratio $r = \alpha_s / \alpha_c$ between self- and cross-memory strengths (Karuvally et al., 28 Oct 2025).

In computer systems, dynamic memory allocation and management involve heap or region-based allocators with rules for splitting, merging, and recycling blocks in response to allocation/free requests and changing process demands (Lim et al., 20 Oct 2024, Standish, 25 Apr 2025). In dynamic memory controllers (e.g., DynIMS), online feedback is used to infer usage and adapt storage sizes (Xuan et al., 2016).

3. Memory Retrieval, Query, and Disambiguation Strategies

Dynamic memory systems are characterized not only by their ability to evolve, but by their query mechanisms, which must remain efficient and accurate under continual change.

• In DynaMem (Liu et al., 7 Nov 2024), open-vocabulary object queries are handled using a hybrid combination of:
  • Vision-LLM feature search (cosine similarity between text query embedding $f_q$ and voxel feature $f_v$),
  • Multimodal LLM question-answering over recent image-context windows,
  • Cross-verification via open-vocabulary detectors to confirm retrieved locations.
  • The hybrid pipeline exploits large-scale retrieval and fine-grained disambiguation critical for handling open-world, dynamic environments.
• In dynamic neural architectures, memory is accessed and updated by query-dependent attention or energy-based dynamics, enabling context-dependent retrieval that adapts as the underlying memory shifts (Karuvally et al., 28 Oct 2025, Pham et al., 2018).
• In systems, dynamic memory allocators leverage RL or evolutionary policies to adapt placement and retrieval choices on the fly depending on observed usage and fragmentation patterns (Lim et al., 20 Oct 2024, Risco-Martín et al., 28 Jun 2024), often outperforming or matching static best-fit/worst-fit heuristics especially in adversarial settings.

4. Memory Models: Hybrid and Multi-Timescale Architectures

The challenge of simultaneously capturing long-term stability and short-term plasticity has led to dual-memory or multi-timescale designs.

• The Mem4D framework (Cai et al., 11 Aug 2025) separates persistent structure memory (PSM, for long-lived, stable geometry) from transient dynamics memory (TDM, for recent high-frequency motion). The two are alternately read at every decoding stage, balancing drift-free consistency for static regions with high-fidelity dynamic reconstruction.
• In neural sequential memory, EDEN implements two populations (fast feature layer $v$, slow modulatory population $s$), producing a system that can act as either static associative memory ($r>1$) or a sequential memory with controlled "escape time" $\tau$ for transitions ($r<1$). This unifies classic Hopfield attractor behavior with robust sequence retrieval.
• In reinforcement learning for curiosity and exploration, dynamic neural memories are augmented with dual-learner or bootstrap mechanisms, consolidating novel state representations only when significant prediction gaps persist, blending plastic memory growth with consolidation (Gao et al., 2022).

5. Dynamic Memory in Systems and Infrastructure

Dynamic memory is a central concern in computer system design, where allocation patterns, fragmentation, workload diversity, and process isolation demand adaptive policies.

• On general-purpose CPUs/GPUs, dynamic memory allocators range from page- and chunk-based strategies (with lock-free queues, bitmaps, or virtual lists) to RL-guided and grammar-evolution optimizations for embedded contexts (Standish, 25 Apr 2025, Lim et al., 20 Oct 2024, Risco-Martín et al., 28 Jun 2024).
• For container-dense cloud/server environments, dynamic memory extension offloads cold pages from DRAM to flash based on per-context access prediction and memory pressure, enabling dramatically higher density without critical latency degradation (Rellermeyer et al., 2019).
• In HPC/data center settings, dynamic DRAM control orchestrates compute and storage allocation via feedback models to achieve both high utilization and rapid adaptation to workload peaks (Xuan et al., 2016). These approaches use proportional-integral control, watermarks, and online measurement to avoid static partitioning failure modes.

6. Dynamic Memory Beyond Engineering: Fractional Calculus, Economics, and Theory

Dynamic memory appears in formal models beyond engineering, notably in continuous-time economics via power-law fading kernels and fractional calculus (Tarasova et al., 2017, Tarasova et al., 2017). In these models, present output $Y(t)$ depends not only on instantaneous input but on a weighted integral over the entire past: $Y(t) = \int_0^t M(t, \tau) X(\tau)\,d\tau$ where $M(t,\tau)$ is a kernel satisfying fading, time-homogeneity, and recoverability principles. Replacing the derivative in macroeconomic growth equations by a Caputo or Riemann–Liouville fractional derivative yields models with explicit non-local memory, generating solutions expressed through Mittag-Leffler functions. The memory exponent $\alpha$ controls the response curve, interpolating between elastic and inertial dynamics.

Paging theory generalizes from static to dynamic memory capacity, with competitive-ratio analysis revealing that minimal capacity changes can drastically change the performance boundaries of online caching algorithms; still, classical algorithms like LRU remain robust under adversarial dynamic conditions (Peserico, 2013).

7. Empirical Outcomes, Performance, and Practical Implications

Across robotics, ML, RL, system libraries, and embedded hardware, empirical studies consistently establish the superiority or necessity of dynamic memory approaches in nonstationary, open-world, or adversarial settings.

• In DynaMem (Liu et al., 7 Nov 2024), real-robot pick-and-drop success on nonstationary objects is increased from 30% (static memory) to 70% (dynamic memory with feature/mLLM retrieval), more than doubling reliability.
• Mem4D’s dual-memory achieves state-of-the-art scene reconstruction metrics, with component ablations directly quantifying the loss in either stability or dynamic fidelity (Cai et al., 11 Aug 2025).
• RL-based allocation strategies stably exceed static heuristics on mixed/adversarial memory streams and scale, while evolutionary optimization produces DMMs with 86× speedup and 36% quality improvement over baselines in embedded contexts (Lim et al., 20 Oct 2024, Risco-Martín et al., 28 Jun 2024).
• Control-theoretic dynamic memory allocation in data centers admits up to a 5× performance gain versus static partitioning (Xuan et al., 2016), while page migration in flash-augmented servers allows over 2× higher container density than DRAM-only configurations (Rellermeyer et al., 2019).
• In fractional-growth economics, memory-modified solutions capture long-term persistence and delayed response, aligning better with empirical macroeconomic series (Tarasova et al., 2017).

Dynamic memory, as a formalism and as a system property, is recognized as crucial for robust, adaptive, and scalable performance across artificial and biological computation, engineered systems, and complex physical and socioeconomic domains. Its mathematical, algorithmic, and empirical foundations continue to inform the design and analysis of learning, inference, control, and memory-augmented architectures.