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.
Principal component analysis (PCA) finds orthogonal directions of greatest variance for data compression, visualization, denoising, and feature discovery.
We introduce interaction SSD, an extension of Supervised Semantic Differential that models how semantic meaning varies across moderators such as groups, traits, or conditions making this variation testable and interpretable. The method estimates a main semantic gradient, an interaction gradient, and conditional gradients, all interpretable through standard SSD tools. We illustrate it on the UC Berkeley Measuring Hate Speech corpus, testing whether annotator racial identity moderates hate-speech judgments of comments targeting people of color. The interaction model detects a significant moderation effect: the shared gradient contrasts dehumanizing hostility with counter-speech, while the interaction gradient reveals smaller group-linked differences in which semantic cues predict hate-speech ratings. Interaction SSD makes moderated meaning-outcome relationships statistically testable and interpretable.
Cross-cultural comparison of psychological meaning requires methods that go beyond word-level translation and examine how semantic dimensions are organized across languages. We introduce a cross-lingual extension of the Supervised Semantic Differential (SSD), which estimates supervised semantic gradients in embedding space and compares them across aligned multilingual word embeddings. The method tests gradient alignment and difference using permutation procedures and bootstrap intervals, and interprets residual differences through clustering around the difference gradient. We demonstrate the approach on Polish, English, and French affective norm lexicons, modeling Valence, Arousal, and Dominance where available. Affective dimensions were significantly recoverable across languages and model settings. Cross-lingual comparisons showed broad alignment together with structured residual differences: Valence appeared mostly shared, whereas Arousal and Dominance produced more interpretable contrasts involving bodily threat, aesthetic stimulation, internal emotionality, macro-level authority, and everyday control. Several clusters also reflected corpus-specific artifacts, underscoring the need for cautious interpretation. Cross-lingual SSD offers an explainable framework for testing semantic alignment, identifying divergence, and generating hypotheses about cross-cultural differences in psychological meaning.
Jan Sikora, Paweł Lenartowicz, Hubert Plisiecki
University of Warsaw · Society for Open Science Centre for Brain Research, Jagiellonian University · IDEAS Research Institute
Data attribution methods using gradient similarity are widely used to analyze and select training data for large language models, but what gradient similarity actually measures is debated. Some interpret it as identifying task-relevant skills, while other work reports that surface form is the main factor. We resolve this debate for supervised fine-tuning examples by varying task and answer format independently. Specifically, we render benchmarks in different answer formats, such that datasets can share a task without a format or a format without a task. We find that gradient alignment follows the answer format, as benchmark pairs sharing an answer format align strongly (disattenuated cosine near 0.4), while same benchmarks rendered with different answer format classes show no alignment (near 0.0). We demonstrate that this ordering holds from the earliest pretraining checkpoints through post-training, and across model scales and families. We then analyze the released selections of LESS, a gradient-based data selection method for instruction tuning, and find that each target's selections over-represent the target's own answer format. Hence, we demonstrate that gradient-based attribution methods track format similarity more than task semantics, meaning that such methods, as well as the semantic interpretation of the gradient, should be tested on data where answer format and task vary independently for greater robustness and reliability.