Addressable Semantic Space

• Addressable Semantic Space is a framework where semantic states are stored at stable, queryable addresses—such as coordinates, node identifiers, or content-derived hashes—enabling direct retrieval and comparison.
• It encompasses diverse realizations including conceptual spaces, LLM feature geometry, and persistent graphs, each with its own method of encoding and operationalizing semantic relationships.
• Empirical applications demonstrate its practicality in reducing computational overhead, improving traversal latency, and enabling robust navigation in semantic databases and memory systems.

Searching arXiv for recent and foundational papers on addressable semantic space and closely related formulations. Addressable Semantic Space is a class of semantic representation in which meanings are assigned stable, queryable addresses rather than being recoverable only through transient recomposition. In the literature, those addresses take several forms: coordinates in conceptual domains, projections onto named semantic axes, persistent graph nodes and neighborhoods, anchor-relative latent codes, instance identifiers in spatial maps, and content-derived hashes in higher-order knowledge stores. The common property is operational addressability: semantic states can be retrieved, compared, traversed, aligned, or updated by acting on their addresses directly, with similarity, locality, or identity given explicit mathematical form (Martin, 17 Feb 2026, Kozlowski et al., 29 Apr 2026, Wheeler et al., 2024, Li, 12 Apr 2026).

1. Conceptual scope and representational forms

The notion spans multiple technical traditions. In conceptual-space models, a domain is a Cartesian product of quality dimensions, points in that domain are semantic addresses, properties are convex regions, and prototypes function as canonical addresses for properties; semantic distortion is then measured geometrically, in the cited instantiations by Euclidean distance and Gaussian similarity transforms (Wheeler et al., 2024, Wheeler et al., 2023, Wheeler et al., 2022). In contextual and feature-space work, addressability arises because each axis is explicitly named and semantically interpretable, so a coordinate on “Biomotion,” “Human,” “measure,” or “unit” can be directly queried and compared across contexts (Chronis et al., 2023). In LLMs, semantic axes built from antonym contrasts make hidden-state geometry directly addressable by projection and steering (Kozlowski et al., 29 Apr 2026). In persistent memory systems, addressability is structural: nodes possess stable identifiers, traversal resolves through adjacency and direct references, and mutation is confined to bounded neighborhoods rather than global search (Martin, 17 Feb 2026). In hypergraph-based knowledge management, entries are addressed by the SHA-256 hash of their record content, with ordered references defining higher-order relations while plugins interpret semantics (Li, 12 Apr 2026).

Realization	Address form	Operational consequence
Conceptual spaces	Coordinates, prototypes, Voronoi regions	Query, compare, classify by distance
LLM feature geometry	Semantic axes and projections	Score and steer along named directions
Persistent semantic graph	Stable node identifiers and neighborhoods	Traverse and mutate locally
Relative latent alignment	Anchor-relative coordinates	Cross-model semantic equalization
Spatial instance maps	Tuple $\langle o, t \rangle$ per grid cell	Resolve ordinal and relational references
Content-addressable hypergraph	SHA-256 content hash	Deduplicate, version, and link knowledge

This suggests that the term is best understood as a unifying abstraction rather than a single architecture. What varies is the address substrate—continuous coordinates, discrete identifiers, or hybrid structures—but not the requirement that semantic identity be explicitly locatable and manipulable.

2. Formal models of semantic addressability

A prominent formalization models semantic continuity as a persistent graph $G = (V, E)$ with node embeddings $y_i \in H \subset \ell^2(V) \oplus \mathbb{R}^d$, where the semantic state space is $\Sigma$ and the in-scope state at step $k$ is a neighborhood $N(k) \subset \Sigma$. Evolution is governed by a bounded local operator $g(t): \Sigma \to \Sigma$, or equivalently $g: G_t \to G_{t+\Delta t}$, constructed from a finite generator class acting on $k$-local neighborhoods with bounded operator norms $\|G_i\| \le C$. The key locality condition is that computational work depends on local semantic change $G = (V, E)$0 rather than total memory cardinality $G = (V, E)$1, formalized as $G = (V, E)$2 with $G = (V, E)$3, and $G = (V, E)$4 with $G = (V, E)$5 (Martin, 17 Feb 2026).

Conceptual-space accounts provide a complementary formalism. A domain is written as $G = (V, E)$6, with points $G = (V, E)$7, properties as convex subsets $G = (V, E)$8, and semantic distortion instantiated as Euclidean distance $G = (V, E)$9. In one variant, semantic similarity is defined as $y_i \in H \subset \ell^2(V) \oplus \mathbb{R}^d$0, and learned property prototypes $y_i \in H \subset \ell^2(V) \oplus \mathbb{R}^d$1 induce implicit Voronoi regions that make property membership a nearest-prototype decision. In another, concepts are regions within a conceptual space $y_i \in H \subset \ell^2(V) \oplus \mathbb{R}^d$2, semantic distortion is aggregated across domains, and minimum-distance decoding resolves a received point $y_i \in H \subset \ell^2(V) \oplus \mathbb{R}^d$3 to a concept index $y_i \in H \subset \ell^2(V) \oplus \mathbb{R}^d$4 (Wheeler et al., 2024, Wheeler et al., 2023, Wheeler et al., 2022).

A third formal family defines addressability relationally rather than absolutely. In relative latent alignment, sender and receiver encoders map shared anchors $y_i \in H \subset \ell^2(V) \oplus \mathbb{R}^d$5 into their respective latent spaces, and a latent $y_i \in H \subset \ell^2(V) \oplus \mathbb{R}^d$6 is represented by its similarity vector

$y_i \in H \subset \ell^2(V) \oplus \mathbb{R}^d$7

Each coordinate is therefore indexed by a shared anchor identity. Semantic equalization is then written as $y_i \in H \subset \ell^2(V) \oplus \mathbb{R}^d$8, with inversion either closed form for cosine-normalized anchors or optimization-based via $y_i \in H \subset \ell^2(V) \oplus \mathbb{R}^d$9. A related federated formulation uses a semantic pre-equalizer at an access point and local equalizers at users, with optimization over linear maps $\Sigma$0 and $\Sigma$1 under a transmit power constraint $\Sigma$2 (Hüttebräucker et al., 2024, Poce et al., 19 Feb 2026).

3. Address construction, querying, and manipulation

In feature-space work on LLMs, semantic axes are constructed directly from antonym contrasts. For a scale $\Sigma$3, the axis is

$\Sigma$4

with word feature vectors obtained by mean-pooling residual-stream states across prompt tokens and then averaging across four prompts. Projection onto an axis is given by $\Sigma$5, which yields a directly addressable semantic coordinate. Steering is implemented by injecting

$\Sigma$6

with $\Sigma$7, and off-target spillover grows with $\Sigma$8 (Kozlowski et al., 29 Apr 2026).

Interpretable contextual embedding spaces use a different route to the same effect. A learned map $\Sigma$9 for PLSR or $k$0 for an FFNN sends contextual token embeddings into psycholinguistic norm spaces such as McRae, Buchanan, or Binder. Because the output axes are human-readable features rather than anonymous latent components, semantic construal becomes directly measurable: subject and object realizations of the same noun can be compared by differences on “Biomotion,” “Human,” or “Body,” while constructions such as AANN can be compared on “measure,” “unit,” and “one” (Chronis et al., 2023).

Addressability can also be sense-inventory anchored. In de-conflated sense representations, Personalized PageRank over the WordNet graph ranks synset-related biasing words for a target sense, and the sense vector is computed as a convex combination of the lemma vector and those biasing vectors, with rank-based exponential decay. Because each vector is tied to a WordNet sense key or synset ID, the semantic space becomes directly addressable by lexical inventory identifiers rather than by word types alone (Pilehvar et al., 2016).

In dynamic semantic navigation, the address itself can be history-conditioned. Cumulative embeddings

$k$1

turn concept production into a trajectory in embedding space, enabling geometric measures such as distance to next, entropy, velocity, acceleration, and distance to centroid. This makes navigation through semantic space measurable at the level of participant-specific paths rather than isolated points (Toro-Hernández et al., 5 Feb 2026).

4. Structural infrastructures for persistent semantic addressing

A persistent graph implementation treats addressability as a systems property. In the Compute ICE-AGE formulation, the substrate is a CPU-resident C++17 semantic state engine with stable identifiers, contiguous adjacency arrays, direct ID-to-memory-offset mapping, and deterministic pointer-based access. There is no ANN index, hashing-based similarity search, or global scan; embeddings persist from insertion, adjacency neighborhoods are laid out contiguously, and updates apply only within $k$2 through $k$3 with no global recomposition (Martin, 17 Feb 2026).

Instance-level spatial maps provide a distinctly embodied realization. A semantic instance map is defined as $k$4 with scale $k$5 m, and each cell stores a tuple $k$6, meaning that the grid cell is occupied by the $k$7-th instance of object $k$8. Frame-local panoptic instances are accumulated into per-category graphs $k$9 and merged by Louvain community detection, producing persistent scene-level instance identifiers that support ordinal and relational reference resolution (Nanwani et al., 2023).

Astrolabe generalizes addressability to higher-order knowledge structures. An entry, called a nerve, is a triple $N(k) \subset \Sigma$0, where $N(k) \subset \Sigma$1 under SHA-256, $N(k) \subset \Sigma$2 is an ordered reference list, and $N(k) \subset \Sigma$3 is an opaque plugin-interpreted string. Width is defined as $N(k) \subset \Sigma$4, atoms have width $N(k) \subset \Sigma$5, and higher-width entries act as hyperedges that may target atoms or other entries. The store admits orthogonal decompositions by width and by depth, with depth filtration $N(k) \subset \Sigma$6 for atoms and $N(k) \subset \Sigma$7 for entries whose references all lie in $N(k) \subset \Sigma$8; cycle-reachable entries receive depth $N(k) \subset \Sigma$9 (Li, 12 Apr 2026).

These systems differ in ontology and implementation, but they share a decisive structural commitment: identity is persistent, and semantics are not regenerated from scratch at every access. This suggests a shift from inferential reconstruction to semantic memory management as the core computational primitive.

5. Empirical behavior and applications

The strongest systems-level empirical case is the Compute ICE-AGE substrate. On Apple M2-class silicon, measurements across $g(t): \Sigma \to \Sigma$0M, $g(t): \Sigma \to \Sigma$1M, and $g(t): \Sigma \to \Sigma$2M nodes reported traversal latency of mean $g(t): \Sigma \to \Sigma$3–$g(t): \Sigma \to \Sigma$4 ms with stable $g(t): \Sigma \to \Sigma$5 and no observable tail expansion, CPU utilization at approximately $g(t): \Sigma \to \Sigma$6 baseline with incremental substrate $g(t): \Sigma \to \Sigma$7–$g(t): \Sigma \to \Sigma$8, and no scale-correlated thermal escalation once residency stabilized. Per-node density ranged from approximately $g(t): \Sigma \to \Sigma$9–$g: G_t \to G_{t+\Delta t}$0 KB in the Float64 baseline to a measured mean of approximately $g: G_t \to G_{t+\Delta t}$1 bytes in the compressed Float32 regime, yielding a capacity projection of approximately $g: G_t \to G_{t+\Delta t}$2 nodes in a $g: G_t \to G_{t+\Delta t}$3 TiB envelope under binary accounting (Martin, 17 Feb 2026).

In LLM feature geometry, empirical support comes from several linked observations. Projections of $g: G_t \to G_{t+\Delta t}$4 words onto $g: G_t \to G_{t+\Delta t}$5 semantic axes correlated strongly with human ratings, with strongest axes at $g: G_t \to G_{t+\Delta t}$6 and weakest axes at $g: G_t \to G_{t+\Delta t}$7. Cosine similarities between axes closely reproduced the human correlational structure, more than $g: G_t \to G_{t+\Delta t}$8 of variance in the word-projection matrix was explained by the first three principal components, and the first three PCs of the raw axis vectors explained more than $g: G_t \to G_{t+\Delta t}$9 of variance in Llama 3.2 3B and more than $k$0 in Llama 3.1 70B. Steering along one axis caused off-target spillover proportional to axis cosine similarity, with weaker overall steering effects in the larger model (Kozlowski et al., 29 Apr 2026).

Addressable semantic space has also been validated in language-conditioned navigation and semantic communication. In SI Maps, human-evaluated success rate rose from $k$1 for VLMaps and $k$2 for VLMaps + Connected Components to $k$3 for SI Maps at $k$4, while automatic success rate rose from $k$5 and $k$6 to $k$7 (Nanwani et al., 2023). In conceptual-space semantic communication, one implementation reported over $k$8 reduction in rate, transmitting $k$9 bits per inference rather than $\|G_i\| \le C$0 bits, while a related earlier system reported a $\|G_i\| \le C$1 rate reduction on traffic-sign semantics (Wheeler et al., 2023, Wheeler et al., 2022). In autoencoder-based domain learning for conceptual spaces, the CelebA example reduced communication from $\|G_i\| \le C$2 bits to $\|G_i\| \le C$3 bits, described as greater than $\|G_i\| \le C$4 reduction (Wheeler et al., 2024).

Applications consequently span long-horizon agent memory, semantic databases, OS-level continuity layers, multi-user semantic communication, sense-aware lexical retrieval, clinical analysis of semantic navigation, knowledge management, and open-vocabulary embodied navigation (Martin, 17 Feb 2026, Poce et al., 19 Feb 2026, Toro-Hernández et al., 5 Feb 2026, Li, 12 Apr 2026).

6. Limitations, failure modes, and open problems

The literature does not treat addressability as universally solved. Persistent graph systems assume bounded local evolution, bounded degree distribution, preserved traversal locality, and no adversarial densification. Billion-node runtime remains a projection rather than an executed measurement, tail latency beyond $\|G_i\| \le C$5 is not exhaustively characterized at extreme scales, and NUMA, distributed effects, and DRAM bandwidth saturation were not measured. Large $\|G_i\| \le C$6 bursts, global rewrites, pathological hubs, fragmentation, and residency churn are identified as mechanisms that could temporarily break invariance or degrade locality (Martin, 17 Feb 2026).

Feature-space approaches also have explicit scope limits. The LLM semantic-axis study analyzes only $\|G_i\| \le C$7 axes, excludes four survey scales as insufficiently distinct, applies no whitening or mean-centering, and does not explicitly control for lexical frequency, concreteness, or polysemy. Exact slopes, $\|G_i\| \le C$8, and canonical correlation coefficients are not reported in the main text. This suggests that the existence of addressable directions is well supported, while the completeness of any finite axis inventory remains unresolved (Kozlowski et al., 29 Apr 2026).

Cross-model relative spaces depend critically on anchor quality and inversion stability. Degenerate anchors reduce addressability, and large $\|G_i\| \le C$9 can destabilize the closed-form cosine inverse because of matrix conditioning; the optimization-based inverse is more flexible but more expensive. In federated equalization, extreme heterogeneity and highly non-IID semantic pilots raise latent-space MSE and degrade task accuracy, while privacy guarantees rely on pre-whitening rather than stronger adversarial models (Hüttebräucker et al., 2024, Poce et al., 19 Feb 2026).

Spatial and knowledge-management realizations have analogous edge cases. SI Maps inherit COCO category coverage, can fail under panoptic segmentation noise, and do not natively encode rich appearance attributes beyond what spatial and ordinal relations provide (Nanwani et al., 2023). Astrolabe’s opaque record improves generality but complicates cross-plugin search; because references are excluded from the core hash, the system does not provide built-in Merkle-style tamper propagation, and stable hashing across heterogeneous producers depends on plugin-level canonicalization (Li, 12 Apr 2026).

A recurring controversy therefore concerns what should count as semantic addressability. Some approaches emphasize explicit human-readable coordinates, some emphasize persistent structural identity, and some emphasize interoperability across heterogeneous models. The present literature supports all three, but it does not collapse them into a single criterion. This suggests that future work will be less about choosing one substrate than about specifying when coordinates, nodes, anchors, instances, or hashes preserve the semantic invariants required by a given task.