Contextual Lexical Classifiers

• Contextual Lexical Classifiers are models that combine token embeddings and their surrounding context to assign precise semantic labels.
• They employ local topological measures and manifold-based transformations to capture geometric relations and global corpus context.
• Empirical studies show enhanced sequence tagging performance, enabling robust entity recognition and effective domain adaptation.

A contextual lexical classifier is a machine learning or rule-based system that assigns semantic or syntactic labels to tokens or spans in text, where label assignment leverages not only the lexical item itself but also the context in which it is embedded. Recent research foregrounds the limitations of traditional sequence tagging frameworks—primarily their insulation from global corpus statistics and manifold structure in high-dimensional embedding spaces—by advancing new paradigms that characterize local latent space topology, geometric relation, and corpus-level context for more expressive and robust lexical classification. This article synthesizes technical advancements, methodologies, and empirical findings from the recent literature, with an emphasis on frameworks that go beyond both context-agnostic representations and purely in-sequence context, notably the integration of local topological descriptors and geometric transformation processes in contextual lexical classification.

1. Formal Definition and Motivating Limitations

A contextual lexical classifier maps input tokens $t_i$—modeled as embedding vectors $\mathbf{v}_i$ generated by a contextual LLM $e$—to an output label space (e.g., BIO labels, semantic classes, or entity types), with model decisions conditioned on the token's embedding and its broader context. Standard approaches typically employ a classifier $c$ (e.g., an MLP, transformer, or CRF layer) directly atop $\mathbf{v}_i$ (possibly aggregated within windows or sentential context) to predict the label $y_i$.

Traditional systems exhibit two primary limitations (Ruppik et al., 7 Aug 2024):

1. Sequence-local isolation: Instance-level classifiers process single input sequences but lack mechanisms to relate $\mathbf{v}_i$ to embedding vectors across the entire corpus, thus underutilizing global distributional and relational context.
2. Dependency on joint fine-tuning: Optimal performance is often achieved by co-training the classifier and the underlying embedding model, but this is computationally prohibitive or impossible if embeddings are generated by fixed, inaccessible, or large foundation models.

2. Topological and Geometric Approaches: Local Structure Descriptors

Recent advancements address these deficits by incorporating local topology measures—summarizing the structure of embedding space neighborhoods—and manifold-based transformations, situating each token’s representation not just in its local sentential context but relative to the latent topology carved out by the full corpus embedding datastore (Ruppik et al., 7 Aug 2024, Vassilis et al., 12 Feb 2025). Key techniques include:

a. Construction of the Embedding Neighborhood:

Given a corpus $C$ and contextual encoder $e$, a datastore of all embeddings is built. For each token embedding $v$, select its $n$-nearest neighbors $_n(v)$ using a suitable distance metric (cosine or Euclidean).

b. Persistent Homology and Persistence Images:

Apply persistent homology (typically $H_0$, $H_1$) to the neighborhood point cloud, yielding persistence diagrams that summarize topological features (connected components, cycles) over multiple spatial scales. Transform diagrams to numerical features via persistence images ($PI^d(v) \in \mathbb{R}^{100}$), which are invariant to permutation, translation, and rotation.

c. Wasserstein Norms:

Compute the first-order Wasserstein distance between the persistence diagram and the empty diagram, quantifying overall topological complexity of the neighborhood.

d. Codensity:

Codensity is defined as the radius to the $(n+1)$-th neighbor from $v$, operationalizing local sample density (higher codensity implies sparser, less densely packed neighborhoods).

These features robustly summarize geometric and corpus-level context, and are stable under global reordering—crucial for semantic interpretation in multi-domain corpora and tasks requiring label stability across data permutations.

3. Complementarity and Empirical Advantage over Conventional Classifiers

These local geometric features are largely orthogonal to standard measures such as LLM perplexity or masked token probabilities, and are not captured by direct fine-tuning of context encoders (Ruppik et al., 7 Aug 2024). Empirically, integrating these descriptors as feature augmentations offers statistically significant and robust improvements for sequence tagging problems:

Model Variant	F1 (MultiWOZ2.1)
Baseline LM Only	52.39
+ Static Persistence Images	53.62
+ Contextual Persistence Img	53.97

Ablation and transfer experiments reveal the augmentation especially benefits:

• Recognition of multi-word expressions, long or ambiguous entity names.
• Extraction/recognition robustness in domain adaptation or low-resource settings.
• Generalization to previously unseen domains due to the features' global, corpus-aware nature.

Qualitative inspection demonstrates improved ability to segment complete entity expressions and to disambiguate tokens with corpus-specific semantic distributions (e.g., "Prince" as a name vs. title in different datasets).

4. Integration with the Manifold Hypothesis and Dynamic Reconfiguration

These approaches extend and empirically ground the manifold hypothesis for contextual embeddings—the notion that representation spaces consist of locally low-dimensional manifolds, with semantic classes and content words exhibiting distinct manifold structure and curvature. Persistent homology not only quantifies topological invariants but can also reflect differential-geometric properties (e.g., varying neighborhood curvature), capturing nuances inaccessible to density- or proximity-only metrics.

Further, architectural advances in Lexical Manifold Reconfiguration (LMR) (Vassilis et al., 12 Feb 2025) instantiate a framework wherein token embeddings are treated as points on a dynamically evolving differentiable manifold, whose geometry is continuously modulated by context-aware transformation flows:

• Embedding evolution is described by

$$\frac{d\mathbf{e}_i}{dt} = -\nabla_{\mathbf{e}_i} \mathcal{L}(\mathbf{e}_i, \mathbf{e}_j)$$

where $\mathcal{L}$ encodes contextual potential between tokens.

• Geodesic updates and curvature terms (via Christoffel symbols) ensure that the update trajectories respect the manifold’s intrinsic geometry.
• A Hamiltonian formalism propagates minimal-energy, context-preserving transformations, regularized by a partition function over the manifold, achieving efficient adaptation without semantic drift.

This allows token representations to shift fluidly across context boundaries, improving contextual coherence, reducing repetitive outputs, and enabling more granular and robust lexical classification in dynamic or structured domains.

5. Computational Considerations, Generalization, and Practical Deployment

Local topological descriptors (e.g., $PI^d(v)$, $W_n^d(v)$, codensity) are low-dimensional and computationally tractable, requiring only access to the precomputed datastore of embeddings, and not to model internals or training processes. The integration is operationalized simply as feature concatenation—pluggable in any token-level classification pipeline without model retraining.

In the case of manifold reconfiguration, training complexity increases due to iterative geometric updates, but inference remains efficient, benefiting from sparsity constraints and parallel computation. Downstream models benefit from both sets of innovations due to:

• Permutation and rotation invariance, guaranteeing stability.
• Minimal resource footprint for feature generation at inference time.
• No requirement for direct access to or fine-tuning of upstream LLMs.

6. Applications, Empirical Results, and Broader Implications

These methodologies have demonstrated superior performance in dialogue term extraction (BIO tagging in MultiWOZ2.1, SGD), particularly for out-of-domain generalization and in settings where only frozen LLM features are available (e.g., LLMs as static black boxes). The architectural paradigm of LMR facilitates increased lexical diversity, sharper contextual adaptation, and lower perplexity across general, technical, news, and dialogue domains.

Domain	Perplexity (Static)	Perplexity (LMR)	Lexical Diversity (+%)
General	35.2	28.4	+9.5
News	31.5	24.3	+22.8
Dialogue	45.6	37.2	+18.4

A plausible implication is that such methods lay the groundwork for robust context-sensitive lexical inference and tagging in real-world scenarios where data is heterogeneous and model access is limited—e.g., zero-shot domain adaptation, terminology mining in specialized corpora, or post-hoc analysis of LLM-generated content.

7. Synthesis and Outlook

Contextual lexical classifiers have evolved from static, sequence-local models to frameworks that exploit intrinsic geometric and topological properties of the latent space, incorporating both neighborhood structure (persistent homology, Wasserstein, codensity) and dynamic, curvature-aware embedding transformation (LMR) (Ruppik et al., 7 Aug 2024, Vassilis et al., 12 Feb 2025). This yields classifiers that are:

• More expressive and contextually sensitive,
• Robust under permutation and corpus partitioning,
• Easily extensible to new domains, languages, or downstream tasks.

Future directions involve further integration of these topological and manifold-based features into unified architectures, the exploration of their interaction with architectural innovations such as attention and retrieval, and the extension to tasks beyond dialogue term extraction—including semantic role labeling, entity normalization, and context-adaptive language generation.