How many dimensions does emotion have?

Emotion research offers competing answers to what the space of feelings looks like. Each theory predicts a different geometry — and that makes the question testable.

Across all twelve models, two independent nearest-neighbour estimators agree: the emotion vocabulary lives on roughly 10–15 effective dimensions. That is far below the hundreds of nominal dimensions the models could use — the emotion lexicon occupies a thin slice of embedding space. But it is also clearly above the 2–4 dimensions of classical psychometric theories. The geometry that language learns is richer than core affect, leaner than a category per emotion. How much of that structure the twelve models share with one another — about eleven dimensions, with a four-dimensional nameable core — is a later scene's question.

The neighbourhood readout generalizes to the GRID's full four-dimensional structure — the study's main test. Reading each dimension purely from each model's distance table (a held-out word gets the mean rating of its seven nearest neighbours; a permutation test supplies the chance band), all four dimensions clear chance in 11–12 of the twelve models: valence (R² 0.53–0.88), power (0.38–0.70), arousal (0.29–0.51) and novelty (0.28–0.54). The single failure is novelty under RoBERTa without a template — the pre-declared degenerate control. Novelty is the critical case: power closely mirrors the dominance axis VAD already had, but novelty is the dimension the classic scheme genuinely lacks — and it, too, is written into the neighbourhoods. The last row is the machine consensus: the rank-average of the twelve tables recovers the four dimensions at the top of the list under every metric we tried, with the sharpest novelty of any space (0.56).

Arousal is the weakest dimension in most spaces — but remember the previous scene: how weak depends on the instrument (0.30 vs 0.50 on identical words). Fine rankings among the top models are not adjudicated at n = 77; top and bottom are stable, the middle reorders with the metric.

Independent human instruments measuring the same words agree with each other at RSA ≈ 0.6 — that is the realistic reference level, not 1.0. Normalizing every space by that level (bootstrap over terms, 95% CIs): the best individual models reach 71–74% of human-level agreement with the GRID, and in all twelve the gap is significantly above zero. The top row is the machine consensus — rebuilt from scratch inside every bootstrap resample, so nothing leaks: it reaches 76%, at the top of the list (its interval overlaps the best individual models' — the honest claim is "at the top", not "above every member"). A diverse committee pools twelve partially independent perspectives on the same structure; yet even the pooled agreement stops measurably short of how well two human instruments agree with each other.

And the agreement is not generic semantics: recompute the same model-to-model matrix on frequency-matched neutral words and it drops to half (median RSA 0.22 vs 0.43). Emotion is an unusually consensual domain of language.

There are two natural ways to read directions out of twelve models: align the twelve clouds into shared coordinates and read the common axes, or draw the consensus distance table as a map and read its variance-ordered axes. Match either reading to the GRID's four dimensions and something odd happens: in the aligned-coordinate reading, power owns a clean axis (0.74) and arousal is the weak one — but in the raw relational reading, power collapses to 0.30 and arousal keeps a signal. Which reading is right? Both — and neither. The power information is in the distance table all along: predicting a word's power from its nearest neighbours works at R² = 0.70, and an unrotated regression on the map's coordinates reaches 0.74 — exactly the height of the coordinate-frame axis. Only the raw axis-matching loses it, because variance-ordered axes cannot give a separate axis to a dimension that correlates 0.64 with valence — and the same raw reading applied to the GRID's own distances loses power identically (0.29). Give both frames the same reading — a rotation fitted on two-thirds of the words, tested on the held-out third — and they converge to the same point: 0.75 vs 0.75. The axes were properties of the reading convention; the geometry was one all along. What remains genuinely graded is each dimension's unique share of the distances: power adds almost nothing beyond valence in the models — less than in the GRID itself.

Could a cherry-picked committee of models have manufactured this? We swept every committee of three or more models — 4,017 of them — plus a control arm where committees grow with term-shuffled models (same geometry, zero structure). Real committees improve with size and family diversity; shuffled members dilute monotonically; and no curated subset beats the full twelve beyond resampling noise. Rank aggregation is hard to game. Finally, how big is the structure the twelve models share? Confront the consensus spectrum with its own null — each model's table term-shuffled independently before averaging — and eleven dimensions exceed chance, not four. The four GRID dimensions are the interpretable core, carrying about half the shared variance; the rest is shared too, mostly lexical (word frequency, concreteness). The right summary: models share an ~11-dimensional structure whose leading, nameable directions are the GRID's four.

Every model, every word, every rating — each cloud drawn in the three leading axes of that model's own distance table. Pick a model, color by valence, arousal or dominance, drag to rotate, and hover the points. Notice how valence paints a clean gradient across the cloud in most models — and how the same coloring by arousal is far blurrier. The last entry in the picker is the machine consensus: the same map with everything model-specific averaged away.

The experiment opened with three questions. Here is each one again, with its answer and the evidence behind it.

Pretrained embeddings — trained only to predict words in context — converge on a shared geometry of emotion: about 10–15 dimensions per model, dominated by valence, organized as gradients rather than categories, and rich enough to carry all four dimensions of the GRID, including novelty, the axis classical VAD lacks. That shared geometry is where the psychometric maps live too, and it has a name in this study: the machine consensus, the twelve models merged into one map. The measurement has no analytic machinery for the answer to hinge on — models are compared only through their distance tables, no dimensions chosen, nothing rotated, nothing fitted, and no human data enters the construction; the conclusion is the same in all 25 ways of building the consensus. The four dimensions recover from neighbourhoods alone, the consensus sits at the top at 76% of the human-to-human agreement level (the best single models reach 71–74%), and the structure the models share spans about eleven dimensions, with the GRID's four as its nameable core. Even the one apparent disagreement — which axis is weakest — dissolved on inspection into a property of how axes are read, not of the geometry. Distributional semantics recovers most of the affective structure psychologists measure, sharpest where the models agree — and the last stretch to human-level agreement remains open.

This site accompanies ongoing PhD research on the intrinsic dimensionality of the emotion lexicon in pretrained embedding spaces. Figures and statistics are computed from the research pipeline; the interactive views use the same data as the paper.