Semantic Surrogates: Enhancing AI Interpretability

• Semantic Surrogates are models and formalisms that substitute or augment primary semantic representations with interpretable proxies, ensuring semantic fidelity and operational efficiency.
• They are applied in neuro-symbolic communication, metric-aligned optimization, adversarial robustness, continual learning, and interpretable transformer systems.
• Utilizing these surrogates leads to improved performance metrics, lower computational overhead, and heightened model interpretability, driving further AI innovation.

A semantic surrogate is a model, system, or formalism that replaces or augments primary semantic representations with interpretable, structured, or otherwise functionally equivalent proxies. Semantic surrogates have been deployed in diverse contexts—neuro-symbolic communication frameworks, surrogate losses for optimization, adversarial robustness, continual learning, and interpretable post-hoc modeling. Their principal objective is to achieve semantic fidelity, auditability, generalizability, or accessibility, often when direct semantic modeling is infeasible, opaque, or not aligned with the end goal. Representative instantiations include ideographic metalanguages for inclusive communication, differentiable metric-aligned losses, synonym encoding layers for adversarial defense, memory surrogates for efficient continual learning, and symbolic genetic-programming models for interpretable classifier calibration.

1. Semantic Surrogates in Communication: Ideographic Metalanguages

The NIM framework ("Neuro-symbolic Ideographic Metalanguage for Inclusive Communication" (Sharma et al., 12 Oct 2025)) exemplifies semantic surrogates in digital communication. NIM's formal core is a hierarchically structured metalanguage: Semantic Classes (SC), Semantic Templates (ST), and Semantic Variable–Molecule pairs $(sv,sm)$, where utterances are decomposed into ideographic units and binding text. This decomposition is governed by neuro-symbolic AI principles: a symbolic layer derived from Natural Semantic Metalanguage (NSM) heuristics, and a neural layer leveraging LLMs prompted via a two-stage Tree-of-Thought workflow to cover out-of-vocabulary concepts.

NIM achieves semantic surrogacy by (1) mapping complex tokens to atomic, cross-culturally validated ideographs, and (2) allowing interactive decomposition into universal semantic components. This surrogate representation exhibits high semantic comprehensibility (METEOR $=0.81$ by Day 5, LCR $=0.38$), cross-domain adaptability, and rapid learnability, substantially outperforming conventional pictographic systems and remaining robust to linguistic diversity. The mechanism is formalized as: $$w_j^{id} \rightarrow (sc_k, st_\ell, \{(sv_p, sm_q)\})$$ with surface grammar rendering icons per $sc$/$st$, and interaction yielding further semantic detail.

2. Surrogate Losses for Metric Alignment in Optimization

In semantic segmentation and other metric-driven training contexts, surrogate losses are essential when metrics (e.g., mIoU, BF1) are non-differentiable or misaligned with popular losses. The Auto Seg-Loss approach ("Searching Metric Surrogates for Semantic Segmentation" (Li et al., 2020)) formalizes surrogate construction by parameterizing non-differentiable metrics into differentiable analogues:

• Replacing hard $\arg\max$ quantization by softmax probabilities
• Substituting logical operators AND/OR with parameterized continuous functions, $g(y;\theta)$, respecting endpoint and monotonicity constraints

Surrogates $\widetilde{\xi}_\Theta$ are optimized via PPO2-based AutoML, delivering metric-specific, generalizable loss surfaces. These surrogates yield measurable improvements (e.g., $+2.3$ mIoU over cross-entropy on VOC), outperform manual designs, and scale efficiently across datasets and network architectures.

Loss Type	mIoU (VOC)	BF1
Cross-Entropy	78.69	65.30
Searched mIoU	80.97	68.86
Searched BF1	1.93	74.83

3. Semantic Surrogates for Adversarial Robustness

Adversarial perturbations exploiting synonym substitution challenge the semantic integrity of NLP models. The Synonym Encoding Method (SEM) ("Natural Language Adversarial Defense through Synonym Encoding" (Wang et al., 2019)) embodies semantic surrogacy by pre-processing inputs: constructing synonym clusters using counter-fitted GloVe embeddings, and deterministically mapping all synonyms within each cluster to a canonical code-word before model ingestion. The encoder, $E: W \rightarrow W$, ensures that adversarial synonym substitutions produce identical encoded sequences, provably blocking attacks and transferability.

Formally: $E_{seq}(x) = (E(w_1),...,E(w_n))$ with $F_\theta(E_{seq}(x_{adv})) = F_\theta(E_{seq}(x))$ for any synonym-substitution adversarial $x_{adv}$.

SEM preserves original model accuracy (within $1$-$2\%$ of baseline), scales to large architectures, and is limited only to lexical-level synonym attacks, highlighting the specificity and sufficiency of this surrogate mapping.

4. Surrogates in Continual Learning: Semantic Memory Consolidation

Continual learning frameworks must preserve acquired knowledge efficiently. SPARC ("Continual Learning Beyond Experience Rehearsal and Full Model Surrogates" (Bhat et al., 28 May 2025)) introduces semantic memory surrogates by maintaining cross-task, task-agnostic filter sets ($\tilde{K}^c$) via exponential moving average updates of task-specific filters: $$\tilde{K}^c \leftarrow \alpha \tilde{K}^c + (1-\alpha) \tilde{K}^{(t)}$$ These semantic surrogates avoid the memory/computation costs of full-model surrogates while retaining and consolidating essential semantic knowledge required for strong Class-IL (class-incremental learning) performance. SPARC uses roughly 6% of the parameters of full-model-based rehearsal or surrogate methods (e.g., $1.04$M vs. $33.7$M for 5 tasks on CIFAR100) and matches or exceeds their classification accuracy.

5. Interpretable Surrogates for Frozen Transformer Embeddings

Symbolic surrogate modeling of high-dimensional, frozen embeddings enables post-hoc interpretability and auditability. The GP-surr pipeline ("From Embeddings to Equations: Genetic-Programming Surrogates for Interpretable Transformer Classification" (Khorshidi et al., 16 Sep 2025)) proceeds by semantic-preserving feature partitioning (SPFP) and cooperative multi-population genetic programming (MEGP). Surrogates are globally additive programs: $$z_c(x) = \sum_{v=1}^{V} f_c^{(v)}(x_{V_v}),\quad p_c(x) = \frac{\exp(z_c(x))}{\sum_k \exp(z_k(x))}$$ Each $f_c^{(v)}$ is a closed-form symbolic tree over a semantically coherent feature subset.

Post-selection calibration via temperature scaling significantly reduces overconfidence without sacrificing discrimination. These semantic surrogates offer explicit global explanations of classifier decisions, quantified via F1, AUC, ECE, symbolic complexity, and attribution analyses.

Dataset	F1	ECE (pre/post-T)
MNIST	0.982	0.029 / 0.010
CIFAR-10	0.973	(analogous)
SST2G	0.950	(analogous)
20NG	0.776	(analogous)

6. Surrogacy of Embeddings: Emergent Semantics in Transformer LMs

Recent empirical studies challenge the notion that input embeddings are the fundamental seat of semantics in Transformer architectures. "Emergent Semantics Beyond Token Embeddings" (Bochkov, 7 Jul 2025) demonstrates that frozen, purely visual Unicode-derived embeddings (with no semantic initialization) can serve as effective structural primitives. The semantic locus shifts to the compositional interaction of self-attention and MLP layers. Models with frozen visual embeddings:

• Converge identically to trainable-embedding baselines
• Double the reasoning scores of conventional models on MMLU
• Display semantic emergence as an architectural—not embedding—property

Visualization of embedding spaces confirms that semantic clustering arises within deeper layers, not the input. This reframes semantic surrogacy: embedding layers function as standardized structural proxies, while the Transformer’s composition mechanism is the true generator of high-level semantic representations.

7. Implications, Limitations, and Future Directions

Semantic surrogates represent a foundational tool in bridging semantic accessibility, interpretability, and operational efficiency. Their deployment enables metric alignment, adversarial resilience, cross-task memory consolidation, post-hoc interpretability, and inclusive communication. Empirical performance gains, calibration improvements, and user comprehension metrics substantiate their effectiveness across modalities. However, limitations persist: context-sensitive paraphrasing and domain-specific nonlinearities may not be captured by surrogate mappings designed for specific perturbation classes; mapping symbolic surrogates back to original input features remains nontrivial.

A plausible implication is that future research will further modularize semantic surrogate architectures, refine surrogate mappings for richer forms of context sensitivity, and extend these models to domains such as audio, graph, or multi-modal time-series representations. Broader adoption of semantic surrogates may recalibrate our view of where meaning, explanation, and semantic fidelity fundamentally reside in modern AI systems.