Dynamic Memory Update Mechanisms

• Dynamic Memory Update (DMU) is a family of mechanisms that systematically updates memory representations using explicit mathematical rules for fusion, pruning, and compression.
• DMU techniques enhance system adaptability and resource efficiency by dynamically managing memory content in response to new data and environmental changes.
• Applications of DMU span robotics, LLM personalization, federated learning, and high-performance computing, yielding measurable performance improvements in diverse domains.

Dynamic Memory Update (DMU) encompasses a family of mechanisms aimed at maintaining, evolving, and compressing memory representations in intelligent systems, machine learning agents, optimization algorithms, robotic systems, high-performance computing, and low-level memory management. DMU involves rules and algorithms for modifying memory content in response to new observations, evidence, or environmental changes, often with the goals of enhancing adaptability, stability, and resource efficiency. Across domains, the distinctiveness of DMU lies in its explicit, often mathematically principled, update policies that enable continuous memory adaptation rather than static or ad hoc memory overwriting.

1. Formal Definition and General Principles

DMU refers to systematically updating the contents of a memory structure—be it a high-level database, neural memory, vector store, key–value map, or physical memory allocation—in response to new inputs or events. The update mechanism is typically governed by:

• Explicit mathematical rules for fusion (add), staleness-tracking or deletion (remove), and compression (merge/prune).
• Learning-based or controller-based policies for deciding when, how, and what to update.
• Optimization objectives involving metrics such as entropy, redundancy, staleness, or accuracy on downstream tasks.

Within the DMU paradigm, memory is not static but a dynamic data structure reflecting the evolving state of the environment, agent, or computation.

2. Representative Architectures and Mathematical Update Rules

DMU instantiations differ by domain, but share several canonical formulations:

2.1. Spatio-Semantic Memory in Robotics

In "DynaMem" (Liu et al., 2024), the DMU mechanism maintains a 3D spatio-semantic map $M$ as a sparse voxel grid indexed by quantized coordinates. For each voxel $v_k$, its state is:

$$\text{Voxel record:}\; (x_k, y_k, z_k),\; C_k,\; f_k,\; t_k,\; I_k$$

where $C_k$ is the count, $f_k$ the pooled vision-LLM (VLM) feature, $t_k$ last-seen time, and $I_k$ is the image ID.

• Add (Fusion):
  • When a new point $p_j$ with feature $f_j$ is mapped to voxel $k$:

  $$\text{If}\; k \in M:\ \begin{cases} C_k \leftarrow C_k + 1 \ f_k \leftarrow \frac{(C_k-1) f_k + f_j}{C_k} \ t_k \leftarrow T \ I_k \leftarrow \text{Current image ID} \end{cases}\ \text{else}\; M[k] \leftarrow (C_k=1,\ f_k=f_j,\ t_k=T,\ I_k)$$

• Remove (Ray-casting deletion):

  • For existing $v_k$, delete if projected depth $d_k$ satisfies:

  $0 < d_k < \min(d_\text{max},\ D[h, w] + \epsilon)$

  where $D[h,w]$ is current depth at projected pixel, $d_\text{max}$ is a sensor-dependent maximum, and $\epsilon$ absorbs noise.

2.2. Bayesian-Inspired Memory Update for LLM Agents

In affective LLM agents (Lu et al., 31 Oct 2025), each memory unit $m_i$ has a sentiment profile $P_i=[p_+,p_-,p_0]$ and total cumulative evidence $W_i$.

• Bayesian Fusion:

$$P_i^{(t+1)} = \frac{W_i^{(t)} \cdot P_i^{(t)} + S_\text{new} \cdot P_\text{new}}{W_i^{(t)} + S_\text{new}}, \quad W_i^{(t+1)} = W_i^{(t)} + S_\text{new}$$

Here, $S_\text{new}$ is the "strength" of the incoming evidence, promoting evidence-weighted blending.

• Entropy-driven pruning:
  • Compute unit entropy $H(m_i) = -\sum_k p_k \log_2 p_k$ (over sentiment categories).
  • Drop units if $H(m_i) > H_\text{high}$ or $W_i \ll \text{thres}$.

2.3. Dynamic Memory in Federated Learning

FedDyMem (Chen et al., 28 Feb 2025) uses a local memory generator on each client, periodically updating a compacted memory bank $\mathcal{M}^{n, t}$ using a weighted average of per-sample embeddings, with round-based exponential moving average:

$$\mathcal{M}^{n,t}_\text{reduce} = \alpha_t\,\bar{\mathcal{M}}^{n,t}_\text{reduce} + (1 - \alpha_t)\,\mathcal{M}'^{n,t-1}, \quad \alpha_t = \frac{1}{t+1}$$

After aggregation at the server via $k$-means, global memory is broadcast back to all clients.

2.4. Adaptive Optimization (RLLC)

In adaptive optimizers (Szegedy et al., 2024), $k$ memory units are updated via linear propagators, with an evolving "learning law" $L_t$:

$$M_t = U(M_{t-1}, g_t) = M_{t-1} B + g_t a^T \ L_t = L_{t-1} + c_2 M_{t-1}^+ g_t \ \theta_t = \theta_{t-1} - c_1 (M_t L_t)$$

$M_{t-1}^+$ denotes the Moore–Penrose inverse, and $B, a$ encode momentum or higher-order recurrence.

3. DMU in System and Memory Management

Low-level DMU mechanisms handle the allocation and reclamation of physical or virtual memory in constrained environments.

3.1. GPU Allocators

"Ouroboros-SYCL" (Standish, 25 Apr 2025) uses lock-free, bin-wise queues (segregated by allocation size) to update free lists in-place. Updates are performed by atomic push/pop on the relevant bin, with chunk refills amortizing costs across multiple allocations.

Key cost formula:

$$T_\text{alloc} = \tau_\text{pop} + p_\text{miss} \cdot [\tau_\text{chunkpop} + C \tau_\text{push}]$$

Fragmentation is measured as the average over $$(\text{bin-rounded size} - \text{request size})/\text{bin-rounded size}$$.

3.2. Feedback-Based Dynamic Storage in HPC

"DynIMS" (Xuan et al., 2016) employs a proportional feedback controller to update in-memory storage allocation:

$U_{k+1} = U_k - \lambda M (r_k - r_0)$

where $r_k$ is observed utilization, $r_0$ the safety threshold, $M$ total RAM, and $\lambda$ a controller gain. This ensures rapid shrinkage during bursts and smooth expansion when demand recedes.

4. Memory Management, Compression, and Pruning Strategies

DMU systems must balance adaptability with resource constraints.

• Pruning via explicit deletion: Old or invalid memory units are periodically removed based on age, staleness, or entropy thresholds (e.g., voxel deletion in DynaMem (Liu et al., 2024), keyframe/image pruning).
• Compression/merge: Similar units are merged (e.g., via clustering, Bayesian fusion, weighted averaging, or $k$-means aggregation in FedDyMem (Chen et al., 28 Feb 2025)).
• Memory bloat mitigation: Entropy-guided drop of redundant or confusing units is employed in personalized LLM agents (Lu et al., 31 Oct 2025), halving memory size without degrading performance.
• FIFO or queue-based retention: Persistent memories (e.g., global geometric encodings in Mem4D (Cai et al., 11 Aug 2025)) use FIFO buffers, temporal downsampling, and never evict anchor entries.

5. Applications and Empirical Impact

DMU has yielded significant improvements across modalities and tasks:

• Open-vocabulary robotic manipulation: DMU in DynaMem (Liu et al., 2024) achieved 70% pick-and-drop success on non-stationary objects, over 2× higher than static memory baselines.
• Personalization and coherence in LLM agents: DMU reduced long-term memory footprint by 63.7–70.6%, improving personalization, coherence, and accuracy (Lu et al., 31 Oct 2025).
• Federated anomaly detection: Communication-efficient DMU enabled feature-aligned federated learning with stabilized accuracy and reduced bandwidth (Chen et al., 28 Feb 2025).
• Dynamic scene reconstruction: Decoupled DMU for static/dynamic components (Mem4D (Cai et al., 11 Aug 2025)) resolved the “Memory Demand Dilemma,” preserving fidelity and drift-free global structure.
• Optimization: Adaptive DMU optimizers with 2–4 memory units and RLLC outperformed classical methods (SGD, Adam, momentum) by 1–2 pp on vision benchmarks (Szegedy et al., 2024).
• System efficiency: DMU controllers such as DynIMS (Xuan et al., 2016) delivered up to 5× improvements in mixed HPC+Spark workloads via dynamic cache adjustments.

6. Broader Theoretical Context and Extensions

DMU mechanisms are closely related to:

• Bayesian sequential updating: Many DMUs fuse beliefs or evidence according to precision-weighted updates.
• Control theory: Feedback-driven DMU (e.g., DynIMS) mirrors classic proportional-integral-derivative (PID) schemes to stabilize resource usage.
• Reinforcement learning and meta-learning: Recent frameworks (e.g., AtomMem's policy-learned CRUD operations (Huo et al., 13 Jan 2026)) formulate DMU as a learned decision process, with explicit rewards for efficient, task-aligned memory behaviors.
• Hierarchical and multi-modal memory: Extensions include clustering memory units into higher-order structures and updating joint embeddings across text, image, and audio.
• Asynchronous and background consolidation: To avoid latency spikes, background threads may handle DMU's merge and prune phases.

7. Implementation Patterns and Best Practices

• Mathematically explicit update rules enable tractable analysis and allow modular swapping (e.g., varying fusion/decay policies).
• Atomicity and concurrency: In low-level allocators (SYCL, CUDA), lock-free atomic operations are mandatory for correct in-kernel DMU.
• Parameter tuning: Controller gains, entropy thresholds, and pruning aggressiveness require empirical tuning for stability and effectiveness.
• Metric smoothing and batching: Moving averages, low-pass filters, or batch EMAs help avoid overreaction to noisy observations.
• Benchmarking against baselines: State-of-the-art DMU designs consistently demonstrate large gains over static or naive baselines across robotics (Liu et al., 2024), language agents (Lu et al., 31 Oct 2025), optimization (Szegedy et al., 2024), and system workloads (Xuan et al., 2016).
• Scalability: Modern DMU systems architect for $O(1)$ or $O(d)$ per-update cost, with regular background compaction for $O(M^2)$ merges amortized.

The DMU frameworks referenced here include "DynaMem" (Liu et al., 2024), "Dynamic Affective Memory Management for Personalized LLM Agents" (Lu et al., 31 Oct 2025), "FedDyMem" (Chen et al., 28 Feb 2025), "Mem4D" (Cai et al., 11 Aug 2025), "Dynamic Memory Management on GPUs with SYCL" (Standish, 25 Apr 2025), "AtomMem" (Huo et al., 13 Jan 2026), "DynIMS" (Xuan et al., 2016), and the RLLC optimization work (Szegedy et al., 2024). These works collectively provide the core experimental, mathematical, and empirical basis for the technical understanding of Dynamic Memory Update in contemporary research.