Vector Lab Vector methods for vector theory

To start with, let us make no assumptions at all about the nature of the [Black] Box and its contents, which might be something, say, that has just fallen from a Flying Saucer. We assume, though, that the experimenter has certain given resources for acting on it (e.g. prodding it, shining a light on it) and certain given resources for observing its behaviour (e.g. photographing it, recording its temperature)… We now see the experimenter much like the engineer in a ship, who sits before a set of levers and telegraphs by which he may act on the engines, and who can observe the results on a row of dials. The representation, though it may seem unnatural, is in fact, of course, capable of representing the great majority of natural systems, even if biological or economic.

W. Ross Ashby (1956)

Large language models, the neural networks behind contemporary AI systems such as ChatGPT, Gemini, and Claude, reorganise meaning as a vector space. Every token, every concept, every sentence is assigned a position in a high-dimensional mathematical space called a manifold. What any given model can say about democracy, about politics, the economy, society, or everyday life is filtered through this vector space. Questions even about contested ideas of intelligence are constrained by the geometry that model has learned. And that geometry carries the sedimented assumptions of the corpus (i.e. its training data), the labour regime, and the economic pressures that produced it. We could call this the geometrisation of thought. What has been missing is the corresponding set of tools. Reading papers about the manifold is not the same as being able to inspect the manifold. Claiming that a model has naturalised market-liberal notions of democracy is not the same as measuring the internals of a vector space and being able to explore the structure of the vector field. To do this we need a critical-empirical method, and vector tools are designed to address this.

Vector Lab is a toolkit of tools that give different ways of seeing into the manifold. The instruments are arranged in two tiers. The first tier opens single objects for intensive inspection: a single language model, a single manifold, a single corpus of theoretical texts. The second tier works across models, asking comparative questions at the level of output embeddings (Manifold Atlas), generated prose (e.g. LLMbench), and diffusion trajectories. The first tier supplies the anatomical detail. The second tier provides the comparative grounds on which theoretical claims might be tested.

The family

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Comparative tools

Manifold Atlas

Object: output embeddings across models.

Concept distance, negation gauge, hegemony compass, silence detector, agonism test, vector logic. The comparative cartographic instrument.

LLMbench

Object: generated prose across models.

Dual-panel close reading, annotation, logprobs, probability visualisation. The hermeneutic surface instrument.

Diffusion Atlas (alpha)

Object: generative trajectories and compositional fidelity across diffusion image models.

Denoise trajectory, guidance sweep, latent neighbourhood, compositional bench. Atlas and Bench registers in one instrument.

Single-model scopes

Vectorscope (beta)

Object: a single open-weight model.

Layer-by-layer weights, hidden states, attention, precision regimes. The anatomical instrument of the lab.

Manifoldscope (beta)

Object: a single manifold.

Intrinsic dimension, curvature, density, topology, and the political reading of what a geometry sediments or refuses. Measure and critique bound together.

Theoryscope (beta)

Object: a corpus of theoretical texts.

Renormalisation-group flow, eigendirections, fixed points, universality classes. A navigable geometry of theory space.

Theoretical Background

Neither machines nor programs are black boxes; they are artifacts that have been designed, both hardware and software, and we can open them up and look inside. We can relate their structure to their behavior and draw many lessons.

Allen Newell and Herbert A. Simon (1987: 36)

The vector lab tools are designed to open the “vector box” of artificial intelligence. The key argument is that there is a shift from the digital to the vector. Our tools and approaches have to correspondingly shift also. Commercial embedding APIs return sentence-level composites from separately-trained embedding models, the output of a pipeline rather than a window into the representations themselves. This is fine for some tasks. It is inadequate for critical work. If we want to know what the geometry of a particular model has sedimented, we have to work with open-weight models where the weights, activations, and token embeddings can be read at every layer. Vector Lab tools therefore privilege open-weight models wherever the question requires internal access, and treat commercial outputs as a separate object, the retrieval surface, with its own interest.

The result is a set of instruments that do things other research tools do not. Vectorscope runs the same inputs across precision regimes, FP32 through BF16, INT8, INT4, FP4, INT2, to observe how signal degrades as the medium is quantised, on the principle that the material substrate of a representation shapes what it can hold. Manifoldscope treats each manifold as a geometric object (intrinsic dimension, curvature, density) and as an ideological object (what it naturalises, suppresses, sediments), binding measure to critique so that no interpretive claim goes without its attestation. Theoryscope applies renormalisation-group and eigenvector methods to corpora of theoretical texts, asking which positions are fixed points under coarse-graining and which traditions are universality classes of one another. Manifold Atlas runs fifteen operations across multiple embedding models, turning particular vector-theoretic claims into empirically testable propositions. LLMbench sets two models’ prose outputs side by side and enables the dual-panel close reading that hermeneutic work requires.

The tools are designed to explore the new media-theoretic terrain of AI, which are listed in each repository’s documentation and developed in the essays that motivate them. Critical work on large language models has, for a decade, been constrained by a tooling deficit. Either work with commercial APIs, and accept the interpretive costs, or do without tools and write essays that assert what a geometry looks like without ever seeing one. Vector Lab is an attempt to close that gap, to produce instruments that are continuous with the theoretical project rather than imported from outside it, and to make them public so that others can use, extend, or disagree with the work they do.

How the instruments relate

The instruments work at two scales and across two modalities. The single-model scopes are anatomical: they open one object (a model, a manifold, a corpus) and read its internal geometry at depth. The comparative tools are cartographic: they survey across many objects (across language models, across diffusion models, across generated outputs) and ask what each kind of geometry has naturalised. Anatomical and cartographic readings are complementary; a finding flagged at the comparative level is sharpened by an anatomical attestation, and an anatomical reading needs the comparative ground to know whether what it has found is local or generic.

The modality split is doing work too. Language models and diffusion models share the underlying vector regime, but their geometries are not interchangeable. The manifold framing migrates more cleanly to diffusion than it does to autoregressive text, and that asymmetry is itself an argument the lab is set up to develop. Theoretical corpora sit alongside the model registers as a third object whose geometry can be read with comparable methods, opening reflexive comparisons between the eigendirections of a body of theory and the model trained on it.

Generated prose is the hermeneutic surface that sits above the geometric work. It is the level at which models are usually encountered, and it is often the presentation layer for findings that begin lower down: a claim tested geometrically can be illustrated, read closely, and compared across models in prose form.

Further reading

Whilst voltage is the physical materiality of the digital configuration, vector space is a form of mathematical materiality, a materiality of relation rather than substance which creates the conditions of possibility for new forms of computation I call vector theory.

David M. Berry (2026: 2)

The tools operationalise claims developed across the vector theory sequence on Stunlaw and in the wider research programme. The essays are the conceptual statements; the tools are the empirical instruments that test, extend, and sometimes contradict them.

The vector theory sequence (Stunlaw)

Books and longer work on Vectors

Further reading

Wider background in media theory, critical theory of technology, and the pre-history of AI.

Using the tools

Each repository contains full documentation, dependencies, and setup instructions. Tools are research instruments and are offered as-is under permissive licences. If Vector Lab tools support published research, please cite the specific tool and version, and cite the relevant theoretical essays where the claims being tested are developed.

References