# Interpretable Semantic Gradients in SSD: A PCA Sweep Approach and a Case Study on AI Discourse

arXiv: https://arxiv.org/abs/2603.13038 · HTML: https://mlsanity.com/paper/2603.13038/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 18 references that are in the map.
- First posted on arXiv 13 Mar 2026.

## Builds on (most cited first, 5 of 5)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Discovering Language Model Behaviors with Model-Written Evaluations](https://mlsanity.com/paper/2212.09251/) (2022)
- [Word Embeddings Quantify 100 Years of Gender and Ethnic Stereotypes](https://mlsanity.com/paper/1711.08412/) (2017)
- [All-but-the-Top: Simple and Effective Postprocessing for Word Representations](https://mlsanity.com/paper/1702.01417/) (2017)
- [The Geometry of Culture: Analyzing Meaning through Word Embeddings](https://mlsanity.com/paper/1803.09288/) (2018)

## Built on by (most cited first, 2 of 2)

- [The Shared Latent Structure of LLM Psychometric Responses](https://mlsanity.com/paper/2605.05080/) (2026)
- [Semantic Gradients Interactions in SSD: A Case Study in Racial Identity and Hate Speech](https://mlsanity.com/paper/2605.27322/) (2026)

## Abstract (arXiv)

Supervised Semantic Differential (SSD) is a mixed quantitative-interpretive method that models how text meaning varies with continuous individual-difference variables by estimating a semantic gradient in an embedding space and interpreting its poles through clustering and text retrieval. SSD applies PCA before regression, but currently no systematic method exists for choosing the number of retained components, introducing avoidable researcher degrees of freedom in the analysis pipeline. We propose a PCA sweep procedure that treats dimensionality selection as a joint criterion over representation capacity, gradient interpretability, and stability across nearby values of K. We illustrate the method on a corpus of short posts about artificial intelligence written by Prolific participants who also completed Admiration and Rivalry narcissism scales. The sweep yields a stable, interpretable Admiration-related gradient contrasting optimistic, collaborative framings of AI with distrustful and derisive discourse, while no robust alignment emerges for Rivalry. We also show that a counterfactual using a high-PCA dimension solution heuristic produces diffuse, weakly structured clusters instead, reinforcing the value of the sweep-based choice of K. The case study shows how the PCA sweep constrains researcher degrees of freedom while preserving SSD's interpretive aims, supporting transparent and psychologically meaningful analyses of connotative meaning.