Minimal Sufficient Semantic Representation

• Minimal sufficient semantic representation is a framework that retains only the task-relevant semantic content while eliminating redundant, nuisance details.
• It spans various fields—from statistics and self-supervised learning to natural language processing—by targeting representations that are both compact and sufficiently expressive for tasks like generation and prediction.
• Empirical studies in semantic coding, deep neural architectures, and communication theory demonstrate that minimalist representations enhance efficiency, robustness, and generalization in practical applications.

Minimal sufficient semantic representation denotes a family of related ideas rather than a single canonical object. Across statistics, self-supervised learning, natural-language semantics, communication, scene understanding, and knowledge representation, it refers to a representation that preserves the information needed for a specified semantic, generative, or inferential task while discarding nuisance variation, redundancy, or detail judged irrelevant to that task. The decisive qualification is that both “minimal” and “sufficient” are target-relative: contrastive minimal sufficiency is defined relative to another view, quotient-based sufficiency relative to an invariant likelihood, MRS-based sufficiency relative to faithful surface realization, and communication-oriented sufficiency relative to downstream reconstruction or decision objectives (Wang et al., 2022, Stewart, 5 Jun 2026, Hajdik et al., 2019, Qin et al., 24 May 2025).

1. Scope of the concept

In the statistical literature, minimality typically means “coarsest among sufficient representations,” whereas in modern representation learning it usually means removing non-shared, nuisance, or domain-relevant information while preserving task-relevant content. In communication theory, minimality is often operationalized as reducing token count, latent-code count, or bitrate while keeping semantic adequacy. In symbolic semantic formalisms for language, by contrast, the question is not maximal abstraction but whether the representation preserves exactly those distinctions that generation would otherwise have to guess, such as tense, number, quantification, or determiner structure (Stewart, 5 Jun 2026, Wang et al., 2022, Qin et al., 24 May 2025, Hajdik et al., 2019).

This diversity leads to a recurrent distinction between two senses of “minimal.” One sense is formal and order-theoretic: the quotient by a symmetry action, or the smallest sufficient statistic in an exponential family. The other is practical and task-driven: a representation that is compact enough for learning or transmission but still adequate for faithful realization, prediction, or communication. Several papers explicitly reject the equation of semantic adequacy with maximal invariance or maximal abstraction; a representation can be sufficient for one target and insufficient for another, and a representation that is minimal for one supervision signal may omit information needed for future tasks (Wang et al., 2022, Qin et al., 24 May 2025).

A further recurring theme is that semantic sufficiency is frequently established indirectly. In some cases it is demonstrated by reconstruction or generation quality; in others by downstream accuracy under distribution shift, compression-distortion tradeoffs, or psychophysical interpretability. This suggests that “minimal sufficient semantic representation” is best understood as an empirical and formal design principle whose exact content depends on the semantics one intends to preserve.

2. Formal statistical and information-theoretic formulations

A fully explicit formulation appears in invariant statistical models. If a Lie group $G$ acts on an observation space $\mathcal X$ and the likelihood satisfies

$p_\theta(gx)=p_\theta(x),$

then the quotient map $\pi:\mathcal X\to \mathcal X/G$ is sufficient; if distinct orbits are statistically distinguishable, the orbit quotient is minimal sufficient. On compact groups and homogeneous spaces, this invariant content admits harmonic realization through Fourier coefficients, and for finite-band harmonic exponential families the empirical harmonic coefficients

$$T_N(X_1,\dots,X_n)=\left(\sum_{i=1}^n \rho_\lambda(X_i)^\dagger\right)_{\lambda\in\widehat G_N}$$

are minimal sufficient statistics (Stewart, 5 Jun 2026).

Algorithmic statistics gives a different formalization. For a finite set $S\subseteq 2^n$, a sufficient statistic for a string $x$ satisfies

$K(S)+\log |S| =^+ K(x),$

with analogous forms for computable semimeasures and computable functions. That paper shows that ordinary minimal sufficient statistics need not reduce purely to Halting information; they can contain substantial non-Halting information. To repair this, it introduces weak sufficient statistics, replacing $K(Z)$ by $C(Z)$, and shows that a minimal weak sufficient statistic is equivalent, up to constant terms, to a minimal typical model and to the Halting problem up to BB-depth (0911.4521).

In supervised deep learning, DeepIn defines a minimal predictive representation through a learnable matrix $\mathcal X$0 in models of the form

$\mathcal X$1

The minimal representation dimension is

$\mathcal X$2

and the framework jointly selects $\mathcal X$3, the number of relevant variables, and the minimal sufficient network architecture. The resulting estimator is proved to achieve an adaptive rate of order

$\mathcal X$4

so generalization depends on the learned minimal dimension rather than the ambient dimension (Tan et al., 25 Mar 2026).

These formal accounts share a common structure: sufficiency is defined relative to a target parameter or task, and minimality removes all distinctions that do not change that target. What differs is the target itself—likelihood equivalence classes, algorithmic structure, or predictive risk.

3. Symbolic semantic representations in natural language

In NLP, the question has often been whether a linguistically expressive representation is also practically sufficient for generation and parsing. A central result is that Minimal Recursion Semantics and its graph form Dependency MRS preserve enough information for high-quality generation. DMRS retains lexical predicates, node attributes such as tense, sentence force, perfectivity, mood, person, number, and individuation, and explicit relations such as ARG1-NEQ, ARG2-NEQ, and RSTR-H-of. A sequence-to-sequence DMRS-to-text model reaches a BLEU score of 77.17 on the full test set and 83.37 on the subset of test data most closely matching the silver-data domain. The ablation study is especially relevant: removing node attributes lowers BLEU from 72.06 to 59.37, keeping only number and tense yields 67.34, while removing edge features reduces BLEU only to 71.27. The result suggests that a practically sufficient semantic interface must preserve distinctions such as tense, number, and determiner structure, whereas some scopal edge features are less critical for realization (Hajdik et al., 2019).

The parsing literature reaches a complementary conclusion. A neural transition-based parser for MRS-derived graphs achieves 86.69% Smatch on DMRS, which the paper notes is higher than the upper-bound on AMR parsing cited from the AMR literature. The representation used is not raw variable-based MRS but graph encodings such as EDS and DMRS; of these, DMRS is inter-convertible with MRS and preserves enough information to recover full underspecified semantics. The paper does not claim that MRS is formally minimal, but it does argue that a semantically richer, syntax-coupled representation can still be parseable at scale (Buys et al., 2017).

A more aggressive compression of semantic roles is proposed by EAT, a format based on Event, Agent, and Theme. EAT discards semantic metapredicates and represents roles entirely via positional encoding in triplets such as $\mathcal X$5. In MRS-to-text generation, reducing a 52-role MRS representation to an EAT-inspired 9-role version improves BLEU-4 from 64.22 to 64.76 and exact match from 20.2% to 23.8%; a 3-role version lowers BLEU-4 to 61.06 while retaining much of the performance (Gröndahl, 2019).

At the same time, event-semantics work shows a clear boundary to such compression. An analysis of VerbNet role co-occurrence argues that semantic roles are necessary but not sufficient for event representation, especially for result and change-of-state structure. The paper therefore proposes a hybrid role-scalar approach, using roles for participant structure and scalar structure for changes such as $\mathcal X$6 (Huminski et al., 2018).

Taken together, these papers support a specific NLP interpretation of minimal sufficiency: not the sparsest possible predicate-argument skeleton, but a representation that preserves exactly those semantic and semantically relevant morphosyntactic distinctions required for faithful realization and event interpretation.

4. Learned representations for generalization and synthesis

In representation learning, the main controversy is whether minimal sufficiency relative to one supervision signal is the right target for downstream tasks. A theoretical analysis of contrastive learning argues that the standard objective approximately learns a representation sufficient for one view to predict another, but that this may be too compressed when task-relevant information is not fully shared across views. The key quantity is

$\mathcal X$7

the non-shared but task-relevant information. When this term is non-negligible, a minimal sufficient representation in the contrastive sense is not sufficient for the downstream task. The proposed remedy is to increase

$\mathcal X$8

alongside the contrastive objective, yielding

$\mathcal X$9

This paper therefore treats “minimal sufficient” as view-relative rather than task-relative (Wang et al., 2022).

For unsupervised domain generalization, MS-UDG explicitly formalizes the target as a minimal sufficient semantic representation. It defines a sufficient semantic representation as one preserving all semantic information shared across augmented views, and a minimal sufficient semantic representation as one minimizing

$p_\theta(gx)=p_\theta(x),$0

where $p_\theta(gx)=p_\theta(x),$1 is the semantic information. The practical loss is

$p_\theta(gx)=p_\theta(x),$2

combining an InfoNCE sufficiency term, a semantic-variation disentanglement term, and a reconstruction-based mechanism that forces variation to be captured outside the semantic code (Pan et al., 19 Sep 2025).

MEASURE adapts a similar idea to sleep-staging domain generalization. Its core claim is that contrastive alignment alone is insufficient because it does not explicitly mitigate “excess domain-relevant information.” The paper formulates the target through

$p_\theta(gx)=p_\theta(x),$3

then implements a multi-scale pretraining loss that combines supervised contrastive alignment with conditional-entropy regularization $p_\theta(gx)=p_\theta(x),$4. On SleepEDF-20 and MASS, the full multi-scale minimal-sufficient variant reaches $p_\theta(gx)=p_\theta(x),$5 on both datasets and outperforms the minimal-only and multi-scale-only ablations (Jo et al., 14 Oct 2025).

DOMINO applies the same principle to domain-specific data synthesis for LLMs. It learns a shared soft prompt $p_\theta(gx)=p_\theta(x),$6 from reference examples through

$p_\theta(gx)=p_\theta(x),$7

where $p_\theta(gx)=p_\theta(x),$8 enforces sufficiency by maximizing $p_\theta(gx)=p_\theta(x),$9 and $\pi:\mathcal X\to \mathcal X/G$0 contrastively separates domain-level patterns from sample-specific noise using per-sample prompts $\pi:\mathcal X\to \mathcal X/G$1. The paper states that fine-tuning on data synthesized by DOMINO improves Pass@1 accuracy by up to 4.63% over strong, instruction-tuned backbones (Ye et al., 28 May 2026).

Across these works, minimal sufficiency is not identified with maximal invariance. Rather, it is treated as a constrained separation: preserve what is shared and predictive, while isolating or discarding what is domain-specific, sample-specific, or otherwise nuisance.

5. Communication, compression, and scene representations

Semantic communication work makes compactness explicit. One paper argues that ordinary neural coding is not automatically semantic, and defines semantic coding as a context-aware coding procedure that extracts “the basic attributes and concepts behind the data” while discarding much of the unnecessary signal detail. Its standardized workflow is raw data input, contextual modeling through tokenization, semantic extraction via reorganization, optional quantization, transmission, decoding, and downstream adaptation. In an image case study, an off-the-shelf ViT-B/16 is modified with bipartite soft matching so that images of size $\pi:\mathcal X\to \mathcal X/G$2 are represented using either 30 or 10 tokens instead of the standard 196 patch tokens, and semantic coding achieves 524 images/s FP16 throughput with only about a 5% Top-1 accuracy drop and nearly 1.5x throughput relative to vanilla ViT-B/16 (Qin et al., 24 May 2025).

A statistical-mechanical account of semantic compression formalizes the problem in Euclidean embedding space. Message meaning is modeled as

$\pi:\mathcal X\to \mathcal X/G$3

semantic distortion as

$\pi:\mathcal X\to \mathcal X/G$4

and the optimization as minimizing this distortion subject to a fixed compressed length $\pi:\mathcal X\to \mathcal X/G$5. The resulting phase diagram exhibits a first-order transition between lossy and lossless compression and a continuous crossover from extractive to abstractive compression. The paper also identifies a maximum $\pi:\mathcal X\to \mathcal X/G$6 for lossless compression, with peak approximately $\pi:\mathcal X\to \mathcal X/G$7 (Can, 1 Mar 2025).

A more axiomatic communication formulation is given for “minimal structural semantics” in images. Under Monotone Invariance, Pairwise Stationarity, and Minimal Sufficiency, the family of pairwise rank-Copulas

$\pi:\mathcal X\to \mathcal X/G$8

is proved to be the minimal sufficient statistic for the dependency structure of the image. The associated distortion metric is

$\pi:\mathcal X\to \mathcal X/G$9

The framework also derives sample-complexity bounds, rate-distortion bounds, an SLA theorem, and a semantic source-channel separation theorem (Jian et al., 10 Nov 2025).

Higher-order relational semantics has likewise been compressed topologically. In joint semantic communication and inference, teacher-side data are mapped into a simplicial complex, and minimal structures are obtained by removing simplices selected by Hodge Laplacians without compromising query accuracy. On a coauthorship dataset, removing simplices by ranking Laplacian values yields an 85% reduction in payload size without sacrificing accuracy, and joint semantic communication and inference improves query accuracy by 25% compared to local-student querying and 15% compared to remote-teacher querying (Zhao et al., 2023).

A scene-understanding analogue appears in visual-inertial object detection, where the minimal sufficient representation is defined as the posterior over semantic and syntactic object attributes in 3-D space. The posterior is decomposed into a geometric term maintained by a localization-and-mapping filter and a likelihood function approximated by a discriminatively trained CNN, yielding a persistent scene-centric representation rather than framewise detections (Dong et al., 2016).

These communication and vision papers converge on a common operational doctrine: semantic sufficiency is whatever must be retained for faithful downstream interpretation or control, while minimality is achieved by collapsing nuisance marginals, redundant tokens, low-impact simplices, or raw sensor histories.

6. Human interpretation, modular knowledge, and unresolved questions

Some of the clearest behaviorally grounded evidence comes from vision. Minimal recognizable configurations are defined as image patches that can still be recognized by human observers, but become unrecognizable after further reduction in size or resolution. A structured model built from points, contours, square region primitives, and relations such as continuity, contour bridging, containment, and parallelism improves interpretation accuracy from 0.48 with basic relations to 0.62 with the extended relation set, against a human-human agreement upper bound of 0.78. This treats minimal sufficiency as the smallest visual structure that still supports detailed semantic interpretation rather than mere category recognition (Ben-Yosef et al., 2017).

Knowledge-graph work proposes a pragmatic modular counterpart: semantic units, defined as identifiable named subgraphs that encapsulate “smallest, independent propositions” or semantically meaningful compound units. The framework introduces four representational resource types—some-instance, most-instances, every-instance, and all-instances—to model assertional, contingent, prototypical, and universal statements, and explicitly supports mixed logic bases at the unit level. Here minimal sufficiency is proposition-relative and cognitively oriented: larger than isolated triples, but simpler and more local than OWL restriction encodings (Vogt, 2024).

The literature also records several persistent limits. One paper on semantic communication explicitly states that there is still no standardized mathematical criterion for semantic content or semantic distortion (Qin et al., 24 May 2025). The copula-based framework excludes “attribute semantics” such as color or absolute intensity values by construction (Jian et al., 10 Nov 2025). MRS-based semantics is empirically effective for generation, but “a more detailed meaning representation is harder to produce” (Hajdik et al., 2019). Event-role analysis shows that semantic roles alone have limited coverage for result-state structure (Huminski et al., 2018). In algorithmic statistics, ordinary minimal sufficient statistics can contain substantial information that is not Halting information, so minimality does not automatically coincide with a unique semantic core (0911.4521). In predictive deep learning, minimal predictive structure improves generalization and interpretability, but it is not identical to human semantic decomposition (Tan et al., 25 Mar 2026).

The overall picture is therefore plural rather than monolithic. The strongest recurring principle is not that the best semantic representation is the most abstract one, but that it must preserve exactly the distinctions required by the target use—generation, prediction, transmission, or human interpretation—while discarding everything else. This suggests that minimal sufficient semantic representation is less a single formal object than a disciplined way of specifying what a representation must keep, what it may remove, and which notion of semantics makes that judgment meaningful.