---
title: DiscourseGeometry
emoji: 🧭
colorFrom: green
colorTo: blue
sdk: gradio
sdk_version: 5.49.1
app_file: app.py
pinned: false
license: apache-2.0
short_description: Compare text collections on semantic axes
---

# DiscourseGeometry

Reference implementation of the spatial-geometric framework for discourse comparison
(Vallego, 2026, [SSRN](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=6387958)). Part of the
[H4rmony Project](https://theh4rmonyproject.org).

Two collections of texts are placed in the semantic space of a sentence encoder and compared on a **primary axis**
and up to five **secondary axes**. Each axis is defined by two sets of exemplar texts (pole A, pole B); secondary
axes are orthogonalised with Gram-Schmidt in the order given. The default preset reproduces the paper's study
(TinyLlama-1.1B-Chat vs its H4rmony fine-tuned version on 60 prompts, four ecosophical axes). An extended preset
adds two secondary axes proposed in the paper's §9.2, Non-human Agency and Intergenerational Responsibility
(exemplars in `extra_axes.py`), appended after the paper's three so their results are unchanged.

**3D view.** Two modes. *Semantic map* (default, as in SpatialSemanticAnalysis): x = position on a chosen axis
(0–100%), y and z = the two main directions in which all texts differ once that axis is removed; the pole exemplars
are shown with the collections. *Chosen axes*: any three axes (primary or secondary), as raw projections or
orthogonalised in the chosen order, with each collection's centroid and first principal component.

**Documentation.** `DiscourseGeometry_Documentation.docx` explains every input, measure and output.

## The six layers

| Layer | Question | Reported |
|---|---|---|
| Axis validation | Are the axes well defined? | pole separation, separation ÷ mean SD, d′, leave-one-out check, angles between axes, primary–secondary overlap |
| 1 · Primary axis | Where does each collection sit, and did it move? | mean score and position, shift, t-test, Cohen's d, permutation p, optional neutral baseline |
| 2 · Secondary axes | Which dimensions moved? | Gram-Schmidt-projected shifts with Bonferroni correction |
| 3 · Order check | Do the results depend on the Gram-Schmidt order? | GS vs raw shifts and their ratio |
| 4 · Secondary Frobenius | How is the shift spread across the named dimensions? | column norms and shares |
| 5 · Full-space Frobenius | How large is the total difference, and how much do the named axes capture? | ‖ΔE‖_F, per-unit shift and consistency, coverage of the primary, secondary and combined subspaces vs random directions, residual |
| 6 · Eigenanalysis | Did the shape and orientation change? | eigenvalues, isotropy, effective dimensionality, PC1 loadings, PC1 angle to the primary axis, principal-axis rotation with permutation test and bootstrap intervals; also in the full space |

**Designs.** *Paired*: two sets of responses to the same prompts in the same order (paired t-test, Cohen's d_z,
sign-flip permutation, per-unit Frobenius as in the paper). *Independent*: two corpora (Welch t-test, Cohen's d,
label permutation, Frobenius as centroid separation with its share along the axes, plus shape difference).

**Robustness.** The encoder can be switched (all-mpnet-base-v2, bge-base-en-v1.5, e5-base-v2, a multilingual mpnet)
to check that findings do not depend on one model.

**Scales.** Score = dot product with the axis (positive = toward pole A), as in the paper.
Position = 0% at the pole B centre, 100% at the pole A centre. Eigenvector signs are arbitrary, so only angles
between directions (0–90°) are interpreted.

**Generation (optional).** The two collections can be generated in the app from a list of prompts with any two
Hugging Face causal language models (greedy decoding).

## Cite

Vallego, J. (2026). *A spatial-geometric framework for discourse comparison: Centroid projection, Frobenius norm,
and eigenanalysis in a constructed semantic measurement space*. SSRN.
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=6387958

Vallego, J. (2026). *DiscourseGeometry* [Software]. Hugging Face Spaces.
https://huggingface.co/spaces/neovalle/DiscourseGeometry