Located Memory Activation Mechanism

• Located Memory Activation Mechanism is a framework that localizes storage and retrieval to specific addresses or regions, ensuring rapid and selective memory recall.
• It integrates biological models, differentiable architectures, and hardware protocols to achieve simultaneous activation and efficient processing.
• By confining memory processes to contiguous, well-defined blocks, the mechanism reduces interference and enhances scalability in both computational and neural systems.

Located memory activation mechanisms comprise a family of architectures and principles in which the storage, retrieval, or triggering of memory is localizable by address, pattern, or network substructure, so that access is restricted or targeted to a well-defined region or set of units. These mechanisms span biological memory models (e.g., neurosome codes in cortical networks), neural and differentiable computing architectures (e.g., block-allocated Kanerva++ memories), and hardware-oriented distributed system protocols (e.g., Active Access for RDMA). Localized activation provides computational advantages in speed, reduced interference, and data-centric operation by permitting efficient recall, comparison, or triggering of memory contingent on precisely delimited cues or addresses.

1. Biophysical Substrate: 2D Neurosome Codes in Cortical Memory

In the model of Xu & Xu, each long-lived memory trace in the cortex is encoded as a two-dimensional (2D) code—an induced subgraph of $m$ neurosomes (neurons), geometrically forming a compact patch in the neuronal layer, with the defining feature that all pairs in the code are linked by strong, effectively delayless, electrical synapses (ES) with $w_{ij} \geq \theta_e$ ($\theta_e \approx 0.8\text{–}1.0$). This structure ensures that excitation of any single member results in near-simultaneous (~0.1 ms) excitation of the entire code due to the strength and connectivity of the ES network. The adjacency matrix $A_C$ for a code $C$ is the $m \times m$ all-ones matrix, guaranteeing strong connectivity (Xu et al., 2017).

Temporary memory is established via an echoing dynamic—bidirectional projections between adjacent cortical layers $L^1$ and $L^2$, implemented as discrete-time updates: $$x^{(1)}(t+\Delta t) = H(W^{21}x^{(2)}(t) - \theta_{mem}), \quad x^{(2)}(t+\Delta t) = H(W^{12}x^{(1)}(t) - \theta_{mem}),$$ where $H$ is the Heaviside function, $W^{12}, W^{21}$ are cross-layer weights, and $x$ encodes binary spike states. Each echoing pass reinforces intra-layer connections via a Hebbian rule,

$\Delta w_{ij} = \eta x_ix_j(1 - w_{ij}/w_{max}),$

eventually converting weaker chemical or mixed synapses to permanent ES bonds after sufficient rehearsal ($m \gtrsim M$). Code decay is governed by exponential relaxation: $dw_{ij}/dt = -\alpha(w_{ij} - w_0),$ with fast decay (large $\alpha$) for transient memory and slow decay for consolidated codes.

Code formation is statistically modeled: the formation probability after $m$ rehearsals is $P_{form}(m) \approx [1 - e^{-\eta m}]^{m(m-1)/2}$, reflecting the need for all code links to convert. Similarly, code persistence over time $t$ is $P_{decay}(t) = 1 - [1-e^{-\alpha t}]^{m(m-1)/2}$.

The overall storage capacity is bounded by the constraint that each neurosome participates in only one code to prevent overlap-induced interference. For $N \approx 10^{10}$ neurosomes and $m \approx 10$, the maximum number of non-overlapping codes is $K_{max} = N/m \approx 10^9$.

Recall is initiated by activating any subset of the code, rapidly triggering the entire clique due to saturating input $I_i = \sum_{j\in C} w_{ij} x_j(0) \geq \theta_e$; by setting the activation threshold $\theta_a < \theta_e$, all members fire synchronously. The activated code then projects vertically to analysis neurons, enabling symbolic comparison, e.g., code overlap yields a corresponding aggregate response in the analysis layer, facilitating similarity measurement (Xu et al., 2017).

2. Localized Memory Access in Differentiable Machine Architectures

Kanerva++, a modern extension of the Kanerva Machine, imposes a two-dimensional grid structure on the memory tensor $M \in \mathbb{R}^{C \times W \times H}$ and allocates memory locally using keys $y_{tk} \in \mathbb{R}^3$ (scale and translation) produced per observation. Each write is a deterministic feed-forward operation, encoding a block at a spatially contiguous region of $M$; no iterative optimization or global addressing is required at write time (Ramapuram et al., 2021).

During retrieval, the read operation maps keys to contiguous sub-blocks of $M$ using a differentiable spatial transformer $f_{ST}$: $m_{tk} = f_{ST}(M, y_{tk}),$ which crops an $a \times b$ window by affine transformation followed by bilinear sampling. Multiple blocks per sample (keys per observation) may be stacked for joint decoding. The read locality is crucial: only the addressed blocks contribute to the latent context used for subsequent prediction or reconstruction, and gradients during training propagate through these spatial positions only. This organization results in emergent local neighborhoods in memory, minimizes interference, and enables fast $O(K)$ read complexity, with $K$ blocks per access, independent of the total memory size.

This contiguous block allocation contrasts with slot-based memory systems (e.g., classic Kanerva or slot-attention mechanisms), which lack spatial contiguity. Empirical ablations indicate that block-structuring notably improves the conditional ELBO on sequential tasks and supports smooth interpolation in latent space. The mechanism conceptually parallels heap allocation in computing, where related information is placed in neighboring addresses for efficiency and modularity (Ramapuram et al., 2021).

3. Hardware-Level Located Memory Activation: Active Access for RDMA

Active Access (AA) introduces a programming model and hardware facility for located memory activation in high-performance distributed compute systems, especially those utilizing RDMA (Remote Direct Memory Access). In AA, memory pages may be marked as "active" and associated with handler routines; upon a remote put or get referencing an active page, hardware in the Input/Output Memory Management Unit (IOMMU) intercepts the transaction, logs the access, and triggers the registered handler (Besta et al., 2019).

The AA mechanism involves the following components:

• Handler registration and active marking: Via $AA\_RegisterHandler$, programmers map a page and handler function, updating the IOMMU PTE (Page Table Entry) to encode handler identifier, activation bits (Write-Log, Read-Log, Write-Log-Data, Read-Log-Data), and user-domain id (IUID).
• Access interception pipeline: RDMA operations generate PCIe TLPs, which are routed through NIC to IOMMU; context selection and page translation identify the active page and associated handler.
• Access-log and notification: If the access matches activation bits, the IOMMU logs the event and, upon reaching a threshold, notifies a CPU thread to invoke the user handler.
• Performance model: Total activation latency per event is

$$T_{total} = T_{network} + T_{translation} + T_{dispatch}$$

where $$T_{translation} = T_{ctx} + (1-p_{miss})T_{tlb} + p_{miss}T_{walk}$$.

This localized activation enables "compute-at-memory" semantics: computation (e.g., resolving hash table collisions or logging) is performed synchronously as soon as a remote access arrives, reducing round-trips and resource contention. AA delivers 2–3× higher throughput in distributed hashtable benchmarks with collision rates 5–25%, up to 50–80% communication time reductions in parallel sorts, and empirically incurs <5% additional latency for fault tolerance. Memory access logging and incremental checkpointing are also accelerated since only touched/active pages are considered.

Key hardware elements include the extended IOMMU PTE format, content-addressable memory (CAM) for per-IUID access logs, tag buffers to reassemble split transactions, and (optionally) flushing buffers for consistent data flush. The use of located memory activation transforms ordinary memory pages into "activation portals," providing programmability and performance (Besta et al., 2019).

4. Memory-Induced Collective Activation in Networked Systems

Allahverdyan et al. introduced a memory-induced activation mechanism for sustaining self-sustained collective activity in networks, focusing on scenarios where structural loops are absent or sparse (e.g., tree-like social or neural structures). Each node $i$ maintains a potential ("memory") $w_i(t)$ and an active state $m_i(t)$ determined by thresholding $w_i(t)$: $m_i(t) = H[w_i(t) - u_i]$

$$w_i(t+1) = [1-m_i(t)]\left[(1-\kappa_i)w_i(t) + r_i + \sum_j q_{ij}m_j(t)\right]$$

where $\kappa_i$ controls forgetting, $r_i$ is intrinsic drive, and $q_{ij}$ captures edge coupling. Memory variables accumulate subthreshold input even when inactive, enabling individual nodes to collect and integrate network activity over multiple timesteps.

Persistence requires that $u > r/\kappa$ (no self-activation). The collective arises when coupling $q > (u-r)/K$; numerically, there exist sharp thresholds $Q^-, Q^+$ separating extinction, bistability, and self-sustained regimes. Memory in the nodes substitutes for topological loops: clusters of nodes can sequentially trigger each other by retaining partial input until the entire local group remains active indefinitely, even in loop-free topologies (Allahverdyan et al., 2017).

Additional mechanisms include weak threshold noise (e.g., Glauber-type or trichotomic) which can seed localized activity clusters below deterministic thresholds, as well as randomization of edge weights to redistribute attention and further reduce the minimal coupling needed for sustainment. Scaling results show percolation-like transitions and robust partial synchronization, modulated by memory and network structure.

5. Functional and Comparative Analysis

Located memory activation provides a consistent framework across diverse domains:

• Speed and efficiency: Local activation (as in neurosome codes or block memory) ensures all necessary units are triggered near-simultaneously, reducing propagation time and minimizing unnecessary activity outside the target region (Xu et al., 2017, Ramapuram et al., 2021).
• Reduced interference and improved recall: Non-overlapping allocation (one-code-per-cell, or block-aligned storage) avoids destructive interference common in slot-based or global addressing schemes, improving capacity and retrieval reliability (Xu et al., 2017, Ramapuram et al., 2021).
• Programmability and hardware acceleration: Mechanisms such as AA offer fine-grained programmability—operations are "attached" to physical regions in memory, yielding performance benefits for distributed data processing (Besta et al., 2019).
• Emergent collective behavior: In networked systems with node-level memory, collective activation and persistent patterns arise even in the absence of cycles or loops in network topology, with thresholds governed by memory decay and coupling (Allahverdyan et al., 2017).

Comparison Table:

Mechanism	Domain	Locality Principle
2D Neurosome Code	Biological	ES clique, geometric patch
Kanerva++ Block Memory	Differentiable	Contiguous 2D grid blocks
Active Access (AA)	Hardware/Dist	Virtual page and handler
Memory-Induced Network	Networked Dyn.	Local memory + input sum

Shared across these systems is the notion that memory access/activation need not be global but can (and often must) be localized to preserve specificity, exploit structural regularity, or harness parallelism.

6. Implications and Future Directions

Located memory activation mechanisms highlight the computational and representational benefits of spatial, structural, or address-based locality. Advances in differentiable memory models (such as Kanerva++) suggest increasing utility for locally-contiguous allocators in generative and sequential learning, while AA-type hardware extensions point toward future runtime systems where computation is more tightly coupled to memory events. In biological and dynamical systems, the emergence of robust patterns from local activation and memory underscores the generality of the paradigm for persistent collective computation.

A plausible implication is that further development in both hardware and algorithmic strategies will continue to exploit the structural alignment between memory location, activation, and task semantics, sharpening the efficiency and expressiveness of both artificial and natural memory systems.