Personalized Spatial Memory

• Personalized spatial memory is the dynamic process that tailors spatial representations through individual cognitive states, adaptive tiling, and computational algorithms.
• This framework integrates formal mathematical foundations, high-dimensional sparse codes, and neurobiological correlates to enable context-sensitive memory retrieval and navigation.
• Practical applications include adaptive VR designs, AR navigation aids, and reinforcement learning models that enhance recall while reducing cognitive load.

Personalized spatial memory is the process by which memory representations of space—ranging from navigation graphs in the brain’s hippocampus to high-dimensional neural codes and context-dependent digital entries—are dynamically tailored to individual characteristics, cognitive states, and task demands. This adaptive computation involves the personalization of both the encoding and retrieval of spatial information, enabling robust, context-sensitive performance in navigation, recall, and interaction with artificial and augmented systems.

1. Formal Mathematical Foundations

Personalized spatial memory in biological and artificial systems can be rigorously characterized as the computation of stationary distributions over random-walk kernels on graphs representing spatial or cognitive states. In the hippocampal context, the equivalence of Personalized PageRank (PPR) and the Successor Representation (SR) provides a unified framework for understanding both memory retrieval and navigational planning (Millidge, 31 Dec 2025).

Given a graph $G=(V,E)$ of $S=|V|$ nodes (spatial locations or states), with transition probability matrix $P$, the stationary distribution underlying personalized memory is defined by:

• Personalized PageRank:

$\pi = \alpha P^T \pi + (1-\alpha) p^*$

where $p^*$ is the teleport (personalization) vector, and $\alpha$ is the damping factor. Closed-form:

$\pi = (I - \alpha P^T)^{-1}(1-\alpha)\,p^*$

• Successor Representation:

$M = (I-\gamma T)^{-1}$

$V = M r$

where $T$ is the policy-driven transition matrix, $\gamma$ the discount factor, $r$ a reward vector.

Substitution $P^T \leftrightarrow T$, $\alpha \leftrightarrow \gamma$, $r = (1-\alpha)p^*$ establishes an isomorphism: both PPR and SR compute the same distribution, parameterized by individual- or context-specific personalization vectors and horizon/discount parameters.

This formalism enables a single set of neural or algorithmic computations to yield either memory retrieval (by pattern completion with $p^*$) or predictive occupancy (by value iteration with $r$), linking spatial and episodic memory.

2. Discretization and Adaptive Tiling via High-Dimensional Codes

Sparse representations in high-dimensional autoencoders yield discrete, minimally overlapping neural codes that tile continuous spatial (or other sensory) manifolds in a manner contingent on each agent’s experiential trajectory (Amil et al., 2024).

• Architecture: The hippocampal-autoencoder employs convolutional encoders (e.g., Vis-AE: 3x 2D conv, large fully-connected bottleneck $Z$), with a sparsity/orthonormality loss:

$$\mathcal{L} = \frac{1}{m} \|X-\hat{X}\|_2^2 + \frac{\lambda}{mn} \|I_n - Z^T Z\|_F$$

• Adaptive tiling: Narrow place fields (convex hulls $H_i$) emerge for individual latent neurons, which discretize the input manifold via thresholded activation, with spatial coverage tailored by the empirical sample distribution $p_\text{sample}$. As regions are sampled more densely due to agent behavior, receptive field density increases correspondingly.
• Experience dependence: Gradient updates integrate the agent's spatial statistics, resulting in denser and finer place field tiling in frequently visited areas:

$$\Delta W^e = -\eta\,\mathbb{E}_{x\sim p_{\text{sample}}} \left[ \ldots \right]$$

• Implication: Each agent develops a distinct cognitive map, as the personalized distribution of place fields directly reflects idiosyncratic trajectories and behavioral patterns.

3. Neurobiological Correlates and Personalization Mechanisms

Hippocampal circuits instantiate this unified computation through auto-associative network dynamics (CA3) and experience-dependent plasticity. Place-field and grid-cell representations—discretized, tiled structures exhibiting both universality and inter-individual variability—are emergent features of personalized spatial memory computation (Millidge, 31 Dec 2025, Amil et al., 2024).

• Individual differences: Parameters such as $\alpha$/$\gamma$ or the sampling distribution $p^*$ encode stable traits (e.g., forward-looking planners vs. immediate retrieval) and modulate retrieval breadth or navigational strategies.
• Context dependency: Altering personalization vectors (e.g., via distinct cues) yields rapid, context-dependent re-mapping over the same underlying graph.
• Neural predictions:
  • Place-cell firing fields should correspond to the personalized PageRank distribution for each location.
  • Experimentally, grid-cell period sharpening and context switching reflect underlying shifts in the transition structure or personalization parameters.

4. Computational and Algorithmic Implementations

Multiple algorithmic regimes support scalable personalized spatial memory computation in biological and artificial systems:

Algorithm	Input Structures	Computational Cost
Power Iteration PPR	$P, p^*, \alpha, \epsilon$	$O(|E|)$ per iteration, $O(\log(1/\epsilon)/(1-\alpha))$ iters
Direct SR (small S)	$T, \gamma, r$	$O(S^3)$ matrix inversion
Iterative SR-Bellman	$T, \gamma$ (TD learning)	$O(\text{\# transitions} \times S)$ updates
Memory-based retrieval (SpeechLess)	Indexed spatial/context vectors	Sublinear (R-tree, HNSW search)

• Reinforcement learning and DQN: High-dimensional sparse codes from the bottleneck layer $Z$ replace raw-pixel states, supporting goal-directed policies in navigation and memory tasks (Amil et al., 2024).
• Hybrid indices and cue-based ranking: Personal memory systems (e.g., SpeechLess) store episodic entries as multimodal vectors, utilizing spatial, semantic, referent, and time indices with weighted similarity scoring for personalized retrieval (Kim et al., 31 Jan 2026).
• Edge and wearable implementations: Systems like Memento demonstrate that multimodal physiological sensing (EEG, GSR, PPG) can trigger personalized spatial cueing, with near real-time processing ($\sim$3.9s) and significant gains in recall and cognitive load reduction (Ghosh et al., 28 Apr 2025).

5. Adaptive and Context-Sensitive Applications

Personalized spatial memory frameworks enable dynamic adaptation in both biological and digital/extended reality systems:

• Real-time environments: Cognitive load-driven VR memory palaces adapt spatial variables (e.g., partition count, furniture density) based on real-time EEG beta-band modulation, maintaining individual attention within optimal zones (mean increase of over 60% in normalized $\beta$ power; $p<0.05$) (Li et al., 3 Jun 2025).
• Personal devices and AR: SpeechLess and Memento illustrate the translation of personalized spatial memory to wearable AR and navigation aids. These systems bind user interactions to multimodal context and enable robust inference even with partial or zero-utterance, reducing articulation by 49.8% and maintaining high (>83%) retrieval accuracy (Kim et al., 31 Jan 2026, Ghosh et al., 28 Apr 2025).
• Contextual flexibility: Modulating reward or personalization vectors yields rapid reconfiguration of memory retrieval profiles and navigational plans with minimal computational overhead—requiring only a new vector-matrix multiplication.

6. Empirical Evaluation, Individualization, and Performance Metrics

Empirical studies validate the benefits and quantify the variability of personalized spatial memory systems:

• Memory augmentation with physiological cues: Memento boosts route-recall by 20–23% vs. free recall and reduces review time and cognitive load by 46% (Ghosh et al., 28 Apr 2025).
• Task performance in RL and cognition: RL agents using sparse, high-dimensional representations (from hippocampal autoencoders) show robust performance in complex visuo-spatial tasks, outperforming dense codes (Amil et al., 2024).
• User interaction and intent inference: SpeechLess supports intent inference under under-specified queries, with 83.3–95.4% retrieval accuracy across interaction modes and significant reductions in user-reported speech effort (Kim et al., 31 Jan 2026).
• Neuroadaptive VR optimization: CogLocus VR palaces yield 32% recall improvement and 80% of participants achieve >60% increase in beta-band focus markers when spatial layouts are dynamically personalized (Li et al., 3 Jun 2025).

7. Implications and Future Directions

Personalized spatial memory provides a mechanistic link between the neural basis of memory, adaptive learning algorithms, and user-facing technologies:

• Theoretical unification: The isomorphism between PageRank and Successor Representations enables a single computational principle to mediate both episodic recall and predictive navigation (Millidge, 31 Dec 2025).
• Personalization mechanisms: Individual differences in exploration, affect, and motivational state are instantiated as parameter variability and experience statistics, explaining both stable traits and contextual modulation of memory performance.
• Technological translation: Integration of physiological monitoring, high-dimensional codes, and adaptive cue selection is key to next-generation AR/VR and prosthetic memory enhancement systems.
• A plausible implication is that further integration with long-term periodicity detection, multimodal fusion, and hybrid model-based–model-free planning can yield richer, continuously self-adjusting spatial memory systems.

Persistent research into the neural and computational underpinnings, as well as real-world deployment and longitudinal evaluation, will drive the development of increasingly individualized, context-sensitive spatial memory models and technologies.