Manifold Atlas

Tier: comparative tool. Object: output embeddings across models.

github.com/vector-lab-tools/manifold-atlas · All tools

Manifold Atlas compares multiple embedding models’ output geometries on the same inputs. It is the comparative cartographic instrument of the Vector Lab: the tool that operationalises vector theory empirically, turning what a model has learned about democracy, care work, negation, or intelligence into a testable geometry rather than a metaphor.

Why Manifold Atlas

Without vector theory, a cosine similarity of 0.95 between “fair” and “not fair” is a curiosity. With it, the same number is evidence for the negation deficit, for geometric ideology, for the proprietary encoding of human language that a particular training regime has produced. Atlas lets claims of that kind be tested against the geometry directly, across multiple models on the same inputs, with outputs that are comparable and exportable.

Operations

The tool packages seventeen operations for the critical testing of vector-theoretic claims, with Calibration establishing the scale against which the others are read:

• Calibration. Per-model, per-register measurement of the manifold’s usable scale. Reports the floor (mean pairwise cosine over unrelated texts, measured separately for bare terms, short declaratives, and prose), the topical ceiling, the cone half-angle, dispersion and percentiles, and the norm behaviour. Every downstream operation declares the register it works in and is read against the appropriate floor; the full calibration record sits in each operation’s Deep Dive.
• Concept Distance. Cosine similarity for two terms across enabled models, with angular separation, euclidean distance, vector norms, and top contributing dimensions.
• Neighbourhood Map. The local structure of the manifold around a concept, rendered as an interactive 3D scatter plot with cluster detection, connection mesh, and cross-domain analysis.
• Negation Gauge. A statement and its auto-generated negation, measured for similarity. How much space the manifold actually gives to negation.
• Negation Battery. Automatic runs of 10-40 negation tests, with report card, collapse rate, and CSV export.
• Semantic Sectioning. Interpolation between two anchor concepts to reveal what lies between them.
• Vector Drift. How context warps the manifold’s positioning of a concept, visualised as a drift cloud.
• Hegemony Compass. A contested concept placed between two competing ideological clusters; which side does the manifold pull it toward?
• Real Abstraction Test. Contrasts a concrete use-value description with its abstract exchange-value equivalent, after Sohn-Rethel.
• Silence Detector. Local density across domains. Dense regions are low-resolution (diverse realities compressed); sparse regions are high-resolution (fine-grained distinctions preserved).
• Distance Matrix. A pairwise cosine similarity heatmap across concepts and models, with contested-geometry detection when multiple models are enabled.
• Agonism Test. Pre-loaded philosophical debates. Does the manifold preserve genuine opposition, or collapse it into proximity?
• Vector Logic. A − B + C = ?, the narrowest test of vector logic. Applied to modern embedding models with critical intent.
• Vector Walk. A particle walking through the manifold from one concept to another, built with Three.js.
• Persistent Homology. Topological features of the manifold above cosine geometry: connected components, loops, and voids across scales, with the persistence of each feature reported as evidence for genuine structural presence rather than sampling artefact.
• Text Vectorisation. Embedding and inspection of arbitrary text.
• Grammar of Vectors. A critique-tier operation that maps discursive quirks of LLM prose onto cosine geometry. Ships with five antithesis grammars (Not X but Y, Not just X but Y, It’s not X it’s Y, While X, Y, and What matters is not X but Y) across four register batteries (Marketing, AI pedagogical, Political op-ed, Technology discourse), around 240 curated constructions in total. The gap between rhetorical opposition and geometric reality, what the tool calls synthetic dialectic, is the empirical object. Cosines are reported with observation-only labels rather than interpretive verdicts.

Each operation makes a theoretical claim empirically testable against the geometry a given model has learned.

Test library and standardisation

Each operation ships with a curated library of pre-built tests. These form a stable instrument against which any model can be measured, and against which models can be compared to each other. Because the tests are fixed, the same battery can be fired at different models at the same moment, at the same model across versions of its embedding API, or at the same model across dates. The result is a standardised testing regime that lets findings be reproduced across research groups and held durable across model generations.

The library

Representative items in the library:

• Hegemony Compass: pre-loaded tests for Freedom (market liberalism vs emancipatory politics), Democracy (liberal proceduralism vs radical democracy), Intelligence (techno-rationalism vs embodied cognition), Security, and Progress. A new Hegemonic Defaults Sweep test (research tier) runs three axis presets in one go, Political Compass (economic-left / right, libertarian / authoritarian), Technology Compass (commons / proprietary, human-centred / techno-solutionist), and Knowledge Compass (critical / empiricist, qualitative / quantitative), followed by a pairwise Distance Matrix over an 18-concept political vocabulary.
• Negation Battery: pre-built sets for political claims, ethical statements, factual assertions, and epistemological claims, runnable 10-40 at a time.
• Agonism Test: forty-eight pre-loaded philosophical debates organised in eight themes (six pairs per theme) including Marx vs Burke, Hegel vs Kierkegaard, and Arendt vs Schmitt, with thematic filtering and observation-only labels rather than interpretive verdicts.
• Real Abstraction Test: twelve concrete use-value to abstract exchange-value pairs after Sohn-Rethel, across domains from clothing to care work.
• Silence Detector: density comparisons across contested domains, such as financial derivatives vs subsistence farming, Silicon Valley vs indigenous ecological knowledge, and corporate management vs care work.
• Vector Logic: pre-loaded analogies including ‘capitalism minus exploitation plus cooperation equals ?’
• Neighbourhood Map and Vector Walk: curated concept sets across Philosophy, Carpentry, Critical Theory, Democracy, and other domains, with eight distant-pair presets for walks.

Tests

Tests bundle operations into named sequences, runnable in one click and exportable as a single composite dataset. Eight tests ship with the current version:

• Grammar of Vectors Sweep (research). All five antithesis grammars across all four register batteries in eleven steps, around 280 embeddings per model per run. Empirical backbone for the Grammar of Vectors argument on synthetic dialectic in LLM prose.
• Hegemonic Defaults Sweep (research). Three Hegemony Compass probes plus a Distance Matrix over eighteen political concepts. Tests which ideological framings the manifold has naturalised as defaults.
• ‘Fake’ News Test (research). All four pre-built batteries plus the eight-pair Agonism Test, ninety-six claim-and-counter-claim tests per model. Exposes the structural condition behind the fake-news problem, a medium whose geometry cannot sustain truth-and-falsehood.
• Political Contestation Test (research). Ten steps mixing Concept Distance, Semantic Sectioning, and Negation Gauge across politically contested pairs.
• Vector Logic Test (research). Six A − B + C analogical inferences run in one batch, each producing a per-model top-eight nearest-concept table.
• Negation Audit (critique). Ethical battery, three contested-claim gauges, and the full agonism battery. Establishes the negation deficit empirically and at scale.
• Concept Distance Demo and Vector Logic Demo (demos). Minimal runs intended as working demonstrations of the pipeline.

Users can also author their own tests as markdown files with YAML front matter, persisted in localStorage and round-trippable through a text editor.

Testing across models and versions

Atlas runs any test against any combination of enabled embedding models. Supported providers cover OpenAI, Anthropic, Google, Hugging Face, Cohere, and local Ollama. The Distance Matrix operation, running across multiple enabled models at once, flags the pairs where models most disagree, surfacing contested geometry for critical analysis.

Export and archive

Operations export to CSV, JSON, PDF, or PNG depending on the visualisation. Exports carry enough metadata (model identifier, date, test preset, parameter values) to reconstruct the run. These exports form the raw material for a longitudinal, comparative archive, a historical resource documenting how large language models have encoded contested concepts over time. Rather than a single ephemeral run against a single version of a single model, findings can be accumulated into a durable record.

Theoretical background

Manifold Atlas operationalises Berry’s Vector Theory (Philosophy & Technology, 2026), together with the Stunlaw essays The Vector Medium and What Is the Manifold?. The tool names operations after vector-theoretic concepts (negation gauge, hegemony compass, real abstraction test) rather than statistical generics, so the connection between theory and instrument is explicit.

Verdict vocabulary. Since v1.17.0, every operation reports its finding on a single five-phrase scale, “Almost the same, Barely different, Somewhat different, Clearly different, Far apart”, read against the register’s calibrated floor and ceiling. Earlier per-operation vocabularies had drifted toward interpretive verdicts (“Fully abstracted: the manifold has completed the real abstraction”) that handed down the theoretical conclusion as though it were the measurement. The tool now reports distance; the theoretical reading belongs in the interpretation.

Stack

Next.js 16, React 19, TypeScript 5, Tailwind, Three.js. Talks to the major embedding APIs: OpenAI, Anthropic, Google, Hugging Face, Cohere, and local Ollama.

Status

The most mature instrument in the Vector Lab. Currently at v1.17.2, with seventeen operations live and a deep-dive panel on every visualisation-heavy operation. Two lines of work have dominated since v1.8:

Calibration (v1.9.0–v1.14.2). Every operation is now read against a measured scale rather than against the raw cosine axis. Calibration reports the floor per register (bare terms, short declaratives, prose), the topical ceiling, the cone half-angle, dispersion and percentiles, dimension statistics against a sample ceiling, and norm behaviour. Live calibration reporting, a model radius, a foldable scale, cache provenance and verification, and the bridge rendered as a dimension line arrived across this series. The full calibration record sits in each operation’s Deep Dive.

One verdict vocabulary (v1.15.0–v1.17.2). Every operation now reports its finding on a single five-phrase scale, “Almost the same, Barely different, Somewhat different, Clearly different, Far apart”, read against the register’s calibrated floor and ceiling. Earlier per-operation vocabularies had drifted toward interpretive verdicts that handed down the theoretical conclusion as though it were the measurement. Negation verdicts now describe distance, not recognition; Real Abstraction no longer declares that abstraction has been completed. v1.17.2 also drops the pre-print Stunlaw citation for Vector Theory in favour of the published version in Philosophy & Technology.

Other recent additions include Persistent Homology as an operation on the manifold’s topology above cosine geometry; the Grammar of Vectors expansion from two grammars to five (with the synthetic dialectic concept now named in the tool); the canonical Vector Lab branding (navy V mark, v1.8.1); and a Runner Library of seven built-in protocols spanning Demo, Critique, and Research categories. In active use for research and teaching.

Siblings

Manifoldscope is anatomical on a single manifold; Atlas is cartographic across many. The two are complementary. Vectorscope opens the model internals that Atlas compares at the output. Theoryscope applies comparable methods to corpora of theory rather than models. LLMbench handles the prose surface.