Semantic-Preserving Feature Partitioning (SPFP)

• SPFP is a feature partitioning paradigm that uses information-theoretic criteria to create semantically consistent views for enhanced multi-view ensemble learning.
• Its methodology combines entropy, mutual information, and conditional mutual information to maximize relevance, minimize redundancy, and capture useful feature interactions.
• Empirical studies demonstrate that SPFP improves computational efficiency and prediction uncertainty metrics while supporting interpretable surrogate modeling in high-dimensional settings.

Searching arXiv for the core SPFP paper and closely related usage/interpretation papers. arxiv_search(query="Semantic-Preserving Feature Partitioning for Multi-View Ensemble Learning", max_results=5, sort_by="relevance") Searching by arXiv identifier for the principal SPFP source and adjacent papers mentioning SPFP. arxiv_search(query="(Khorshidi et al., 2024) OR (Khorshidi et al., 16 Sep 2025) OR (Hüttebräucker et al., 2024)", max_results=10, sort_by="submittedDate") Semantic-Preserving Feature Partitioning (SPFP) is a feature partitioning paradigm whose central objective is to divide a representation into views or partitions that remain semantically consistent and information-preserving for a downstream task. In its explicit algorithmic form, SPFP was introduced for Multi-View Ensemble Learning (MEL) as an information-theoretic procedure that partitions datasets into multiple semantically consistent views while preserving semantic and predictive integrity and improving computational efficiency (Khorshidi et al., 2024). Subsequent work applied SPFP to frozen transformer embeddings to obtain disjoint, information-preserving views for cooperative genetic-program surrogates, and related literatures developed semantically preserving partition mechanisms for task interaction, object-centric representation learning, semantic communication, robotic manipulation, and high-resolution vision-language modeling (Khorshidi et al., 16 Sep 2025).

1. Conceptual definition and scope

In the MEL formulation, SPFP addresses the feature partitioning problem that arises when expansive yet sparse datasets make direct learning difficult. The method treats feature partitioning as a principled construction of artificial views rather than as an arbitrary split. Its stated objective is to partition a dataset’s features into multiple semantically consistent views for MEL, while preserving semantic and predictive integrity and improving computational efficiency (Khorshidi et al., 2024).

The conceptual novelty lies in how “semantic preservation” is operationalized. Conventional random-based, pattern-based, and clustering-based partitioning approaches may reduce computation, but they do not ensure that each view is informative or semantically faithful. Optimization and wrapper-based methods may improve predictive performance, but they are computationally expensive and lack explicit semantic guarantees. SPFP replaces those heuristics with a direct information-theoretic criterion: each view should preserve the information content of the full feature space and its relation to the target variable (Khorshidi et al., 2024).

This notion of semantic preservation later appeared in a broader sense. In surrogate modeling of frozen embeddings, SPFP was used to create multiple disjoint, information-preserving views so that each view retained enough task-relevant information to contribute nontrivially to prediction while remaining non-redundant with other views (Khorshidi et al., 16 Sep 2025). Across these uses, SPFP is not merely dimensionality reduction; it is a structured decomposition in which each partition is expected to remain meaningful for the learning problem.

2. Information-theoretic formulation

The core SPFP algorithm is grounded in entropy, mutual information, conditional mutual information, and interaction gain. The entropy of a variable $X$ is

$H(X) = -\sum_{x_i} p(x_i)\log p(x_i),$

and the mutual information between a feature $X$ and target $Y$ is

$I(X;Y)=H(X)+H(Y)-H(X,Y).$

Conditional mutual information is used to quantify redundancy or complementarity among features given the target, and interaction gain measures whether feature interaction is synergistic or redundant (Khorshidi et al., 2024).

SPFP adapts the Conditional Likelihood Framework by setting $\alpha=\beta=1/|S|$ and by adding Pearson correlation. For a candidate feature $f_c$ and the currently selected subset $S$, the SPFP score is

$$J_{\mathrm{SPFP}}(f_c)=|R(f_c,Y)|+I(f_c;Y)-\frac{1}{|S|}\sum_{f_s\in S} I(f_s;f_c)+\frac{1}{|S|}\sum_{f_s\in S} I(f_s;f_c\mid Y).$$

This objective combines four pressures: relevance to the target, linear association with the target, penalization of redundancy with already selected features, and reward for conditional complementarity. In the terminology of the original paper, the method is designed to maximize relevance, minimize redundancy, and capture useful joint interaction effects among selected features (Khorshidi et al., 2024).

The stopping criteria are likewise information-theoretic. Let $F$ denote the full feature set and $H(X) = -\sum_{x_i} p(x_i)\log p(x_i),$0 the subset selected for the current view. SPFP uses the following criteria:

$H(X) = -\sum_{x_i} p(x_i)\log p(x_i),$1

$H(X) = -\sum_{x_i} p(x_i)\log p(x_i),$2

$H(X) = -\sum_{x_i} p(x_i)\log p(x_i),$3

The theoretical rationale is that the entropy and mutual information of the full set are always greater than or equal to those of any subset, so a subset can be regarded as information-preserving only when it matches the full set on the relevant information-theoretic quantity. This makes the stopping rule part of the semantic-preservation claim rather than a purely engineering heuristic (Khorshidi et al., 2024).

3. View construction and partition geometry

Algorithmically, SPFP receives as input the dataset $H(X) = -\sum_{x_i} p(x_i)\log p(x_i),$4, the minimum number of features per view $H(X) = -\sum_{x_i} p(x_i)\log p(x_i),$5, the number of views $H(X) = -\sum_{x_i} p(x_i)\log p(x_i),$6, and a fraction $H(X) = -\sum_{x_i} p(x_i)\log p(x_i),$7 of features to remove between view constructions. The unused feature pool is initialized as $H(X) = -\sum_{x_i} p(x_i)\log p(x_i),$8. For each view, the algorithm begins with an empty subset $H(X) = -\sum_{x_i} p(x_i)\log p(x_i),$9, computes $X$0 for each candidate feature in the current pool, adds the top-scoring feature, and repeats until a stopping criterion is satisfied. The resulting subset is stored as a view $X$1 (Khorshidi et al., 2024).

A distinctive design choice is that only a fraction of selected features is removed from the global pool after a view is completed. After storing a view, SPFP randomly eliminates a fraction $X$2 of its selected features from $X$3 to increase diversity between views. As a consequence, views may overlap. The original formulation states that larger $X$4 means less overlap and greater view diversity, at potential cost to information coverage (Khorshidi et al., 2024).

The embedding-based SPFP variant in interpretable surrogate modeling keeps the same general logic but emphasizes disjointness more strongly. Given a standardized embedding matrix $X$5 and labels $X$6, it initializes the pool $X$7 and builds one view at a time using a greedy relevance–redundancy criterion. A view is finalized when it passes an information-preservation test or reaches a feature budget $X$8. When a view $X$9 finishes, a fraction $Y$0 of its dimensions is removed from the pool, promoting inter-view diversity, and the output is a set of disjoint index sets $Y$1 (Khorshidi et al., 16 Sep 2025).

This difference in overlap policy is instructive. In MEL, controlled overlap is part of the view-diversity tradeoff. In embedding surrogates, the emphasis shifts toward disjoint, low-redundancy views that can support additive symbolic decompositions. This suggests that SPFP is better understood as a family of semantics-preserving partition strategies than as a single immutable partition geometry.

4. Empirical behavior in multi-view ensemble learning

The original MEL evaluation used eight real-world datasets varying from 756 to 75,994 samples, 129 to 20,531 features, and binary to 26-class outputs. The protocol used 30 runs per dataset and model with random 67/33 train/test splits. For each run, views were constructed on the training data via SPFP, hyperparameters were tuned with 5-fold cross-validation, XGBoost and Logistic Regression were trained on the views and on the full feature set, and ensembles were formed by combining predictions from the first 2–5 views through weighted average by AUC (Khorshidi et al., 2024).

The evaluation covered micro-averaged $Y$2, AUC, log-loss, mean entropy of correct predictions (MEC), mean entropy of wrong predictions (MEW), and training time. Statistical analysis used the Friedman test, the Conover post-hoc test, and Cliff’s Delta for effect size. The experimental parameters were $Y$3, $Y$4, and $Y$5, or lower for the extremely high-dimensional GECR dataset (Khorshidi et al., 2024).

The reported findings are specific. SPFP typically selected 1–27% of total features per view while matching entropy or joint entropy constraints. For XGBoost, differences in accuracy versus the benchmark were minor but significant, while improvements in MEC, MEW, and training time were more substantial; the ensemble of all views, $Y$6, often outperformed the benchmark in AUC and log-loss. For Logistic Regression, the gains were larger, especially on complex high-dimensional data. The abstract summarizes the overall pattern as follows: SPFP maintains model accuracy while significantly improving uncertainty measures in scenarios where high generalization performance is achievable, and conversely retains uncertainty metrics while enhancing accuracy where high generalization accuracy is less attainable (Khorshidi et al., 2024).

The effect-size analysis is central to how the original work positions the method. Cliff’s Delta was frequently larger than $Y$7, indicating large practical effect sizes, and running time was consistently lower for SPFP-based views than for all-feature benchmarks. In this sense, SPFP is presented not only as a semantic constraint on partition quality but also as a computational strategy for high-dimensional ensemble learning (Khorshidi et al., 2024).

5. SPFP for frozen embeddings and interpretable surrogate models

A later use of SPFP places it at the front end of symbolic surrogate modeling for frozen Transformer embeddings. In that pipeline, embeddings from ModernBERT, DINOv2, and SigLIP are partitioned on the training split into disjoint, information-preserving views via SPFP, and a cooperative multi-population genetic program (MEGP) learns additive, closed-form logit programs over those views (Khorshidi et al., 16 Sep 2025).

The surrogate classifier has the form

$Y$8

The intended interpretability effect is explicit in the formulation: each view is assigned to a dedicated genetic-program population, each population can access only its own dimensions, and the final logit is an additive sum of per-view programs. This yields a decomposition in which each symbolic component is tied to a compact subspace of the embedding (Khorshidi et al., 16 Sep 2025).

The empirical study covered five benchmarks: SST2G, 20NG, MNIST, CIFAR10, and MSC17, with 30 runs per dataset. A canonical model was chosen by a one-standard-error rule on validation $Y$9 with a parsimony tie-break. The reported partition structures were dataset-dependent: 4 views for SST2G, 3 for 20NG, 4 for MNIST, 5 for CIFAR10, and 4 for MSC17. Canonical models used a small fraction of embedding dimensions overall, including 17/1024 dimensions for MNIST and 76/1024 for CIFAR10. Test discrimination reached macro-$I(X;Y)=H(X)+H(Y)-H(X,Y).$0 on MNIST, CIFAR10, and MSC17, and $I(X;Y)=H(X)+H(Y)-H(X,Y).$1 on SST2G, while 20NG remained the most challenging dataset (Khorshidi et al., 16 Sep 2025).

Calibration was also part of the SPFP-mediated outcome. The study reports that temperature scaling fitted on validation yields substantial expected calibration error reductions on test, with ECE reductions of 60–75% after temperature fitting. Contribution-based importances, dimension-usage and overlap statistics, reliability diagrams, and global effect profiles through PDP and ALE were used to analyze the resulting surrogates. In this setting, SPFP functions as a structural prior for interpretable decomposition, not only as a preprocessing step (Khorshidi et al., 16 Sep 2025).

6. Related formulations and recurrent misconceptions

Related literature addresses semantically preserving partition problems through different mechanisms, often without using the exact information-theoretic SPFP algorithm. The recurring pattern is that preservation of task-relevant semantics is treated as a property of the partition itself rather than as a side effect of downstream learning.

Setting	Partition unit	Preservation mechanism
Joint entity and relation extraction (Yan et al., 2021)	Entity, relation, and shared neuron partitions	Two gates segment neurons; the shared partition is evenly shared across tasks
Object-centric representation learning (Pervez et al., 2022)	$I(X;Y)=H(X)+H(Y)-H(X,Y).$2 disjoint partitions of scene features	Minimum $I(X;Y)=H(X)+H(Y)-H(X,Y).$3-$I(X;Y)=H(X)+H(Y)-H(X,Y).$4 graph cuts encode topology and neighborhood relationships
Semantic channel equalization (Hüttebräucker et al., 2024)	Atoms of the latent space	Clustering on action-value vectors captures one-to-many mappings
Generalist-specialist RL (Yuan, 2024)	Clusters of environment variations	Point cloud feature-based balanced clustering groups similar variations
High-resolution LVLMs (Liang et al., 24 Jan 2025)	Sub-images plus a global thumbnail	GSWA weights sub-images by semantic relevance to the entire image
Packetized semantic communication (Yang et al., 21 Nov 2025)	One-dimensional transmission units	Channel-dimension partitioning and Semantic Equalization Mechanism balance semantic representation

Several misconceptions recur across these works. First, semantic preservation is not equivalent to hard partitioning. In semantic channel equalization, hard partitioning based on hard inference results results in loss of information in one-to-many settings, whereas clustering Q-value vectors yields a more descriptive and regular partition of the space and enhances equalization performance (Hüttebräucker et al., 2024).

Second, semantic preservation is not equivalent to uniform treatment of partitions. In high-resolution large vision-LLMs, existing methods that process all sub-images uniformly are described as suboptimal, and GSWA instead dynamically allocates weights to sub-images based on relative information density (Liang et al., 24 Jan 2025). In generalist-specialist learning for robotic manipulation, random task partitioning can impede performance, whereas point cloud feature-based partitioning outperforms vanilla partitioning by 9.4% with a fixed number of specialists and reduces computational and sample requirements by 50% to achieve comparable performance (Yuan, 2024).

Third, the meaning of “semantic” varies by domain. In MEL it is defined information-theoretically through entropy and joint entropy preservation (Khorshidi et al., 2024). In joint extraction it is mediated by shared task partitions that support balanced two-way interaction (Yan et al., 2021). In topology-aware object-centric learning it is linked to contiguous object-like regions induced by graph structure (Pervez et al., 2022). In packet-loss-robust semantic communication it is linked to balanced channel contributions, where CNNs equipped with Semantic Equalization Mechanism retain about 85% of lossless PSNR at 40% packet loss, comparable to Transformer models (Yang et al., 21 Nov 2025). A plausible implication is that SPFP is best treated as a general design principle—partition features so that the decomposition itself retains the structure required by the task—rather than as a single domain-independent objective.