---
title: "Interpretable Semantic Gradients in SSD: A PCA Sweep"
description: "Supervised Semantic Differential (SSD) builds a semantic gradient in embedding space by regressing a continuous trait on… 16 references."
authors: ["Hubert Plisiecki", "Maria Leniarska", "Jan Piotrowski", "Marcin Zajenkowski"]
year: 2026
venue: "Findings of the Association for Computational Linguistics: ACL 2026"
source: "https://aclanthology.org/2026.findings-acl.446/"
doi: "10.18653/v1/2026.findings-acl.446"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/plisiecki-2026-interpretable-semantic-gradients-ssd-pca/"
---
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# Interpretable Semantic Gradients in SSD: A PCA Sweep Approach and a Case Study on AI Discourse

**Authors:** Hubert Plisiecki, Maria Leniarska, [Jan Piotrowski](https://md.research.elamur.ai/free/en/authors/jan-piotrowski/) and Marcin Zajenkowski · **Year:** 2026 · **Venue:** [Findings of the Association for Computational Linguistics: ACL 2026](https://md.research.elamur.ai/free/en/venues/findings/) ([Findings of the Association for Computational Linguistics 2026](https://md.research.elamur.ai/free/en/venues/findings/2026/)) · **Publisher:** [Association for Computational Linguistics](https://md.research.elamur.ai/free/en/publishers/association-for-computational-linguistics/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2026.findings-acl.446/) · [PDF](https://aclanthology.org/2026.findings-acl.446.pdf) · [DOI 10.18653/v1/2026.findings-acl.446](https://doi.org/10.18653/v1/2026.findings-acl.446) · [OpenAlex](https://openalex.org/W7166821232)

**Citations:** 0 citations (OpenAlex, 2026-10-14)

## Summary
Supervised Semantic Differential (SSD) builds a semantic gradient in embedding space by regressing a continuous trait on PCA-compressed text vectors. Until now, users chose the number of retained components (K) by hand, which adds unnecessary analytic flexibility. The authors propose a PCA sweep that fits SSD over a range of K values and picks the smallest K with the best combined score. The score has two parts: cluster interpretability (coherence plus alignment with the gradient, detrended against variance explained) and gradient stability across neighbouring K values. Predictive fit is deliberately left out of the criterion.

They demonstrate the procedure on 349 short posts about AI from Prolific participants who also completed Narcissistic Admiration and Rivalry scales. For Admiration, the sweep produced a significant and interpretable gradient: hopeful, cooperative views of AI at one end and suspicious, mocking ones at the other. Rivalry showed no reliable association. A high-dimensional comparison run produced blurry, poorly structured clusters. The sweep therefore makes SSD analyses more transparent while preserving their qualitative value.

## Key points
- **How the sweep works:**
  - It tracks three things per K: cumulative explained variance (used only for detrending), a cluster-size-weighted interpretability z-score, and gradient change (1 − cosine between consecutive gradients).
  - Both the interpretability and stability curves are smoothed with a local neighbourhood average (AUCK), so broad plateaus are favoured over isolated peaks.
- **Case study setup:**
  - Corpus of N = 349 posts, about 30 words each, preprocessed with spaCy 3.8.7 (en_core_web_sm).
  - Posts were embedded with the 300-dimensional Dolma GloVe model, using SIF weighting (a = 10⁻³) and removal of the top principal component.
  - Whole posts were used instead of a concept lexicon, since all texts answered the same AI-focused prompt.
- **Sweep settings:** K from 1 to 119 in steps of 2; cluster number chosen by silhouette within 2–5; 100 nearest neighbours per pole; AUCK radius of 3; median-smoothed gradient change with a window of 7.
- **Results:**
  - Admiration: adjusted R² = .19, F = 6.32, p \< 10⁻¹⁰.
  - Rivalry: adjusted R² = .03, p = .095, so it was not interpreted.
  - A counterfactual run at K = 120 gave diffuse clusters.
- **Limitations and resources:**
  - The authors flag a small survey sample, purely correlational interpretation, and other open pipeline choices such as the embedding model and window size.
  - Code is available at github.com/hplisiecki/acl2026-ssd-pca-sweep.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [University of Warsaw](https://md.research.elamur.ai/free/en/universities/university-of-warsaw/) — University, Warsaw, Poland · 8 works · 575 citations
- [Warsaw University of Technology](https://md.research.elamur.ai/free/en/universities/warsaw-university-of-technology/) — University, Warsaw, Poland · 3 works · 256 citations

Also on the byline: [VIZJA University](https://ror.org/00523a319).

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## Cite

Cite as: Hubert Plisiecki, Maria Leniarska, Jan Piotrowski and Marcin Zajenkowski. 2026. Interpretable Semantic Gradients in SSD: A PCA Sweep Approach and a Case Study on AI Discourse. Findings of the Association for Computational Linguistics: ACL 2026.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{plisiecki2026interpretable,
  title = {{Interpretable Semantic Gradients in SSD: A PCA Sweep Approach and a Case Study on AI Discourse}},
  author = {Hubert Plisiecki, Maria Leniarska, Jan Piotrowski and Marcin Zajenkowski},
  booktitle = {Findings of the Association for Computational Linguistics: ACL 2026},
  year = {2026},
  doi = {10.18653/v1/2026.findings-acl.446},
  url = {https://doi.org/10.18653/v1/2026.findings-acl.446}
}
```

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## References

16 references, 3 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

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*Updated 1 November 2026*