About Continuous Function

Waterbirds is a benchmark of bird photographs placed on land or water backgrounds; in its training set most waterbirds appear on water and most landbirds on land, so a classifier can score well by reading the background. A frozen ImageNet ResNet-50 with a logistic-regression readout is right 97% of the time on Waterbirds photos mixed in the same proportions as its training data, yet gets only 37 of 69 validation photos of waterbirds on land right (on a 64-dimensional projection of its features). The workspace takes that failure through the steps of a careful experiment: predict the outcome, set limits a fix must respect, approve a plan, refit the last layer in your browser, look once at the held-out test images through a separate check, narrow the claim to what the evidence supports, and export a file that anyone can replay run by run or adapt. The test suite checks the in-browser fits against scikit-learn for every run of the reference plan, to within one image per group.

The Lab follows a transformer in eight steps, from one gradient update to a claim about a serving trade-off: rotary position embeddings, grouped-query attention and the KV cache, long context, batching and decoding, speculative decoding, evaluation design, and a final step where you state a systems claim and what it does not cover. Where a step asks for your prediction, it does so before it shows the calculation.

The attention notebook is built around one small example: a query, three sources, and the scores, weights and output they produce. The explanation, the equations, the Python and the interactive figure describe the same calculation, so a statement made in one of them can be checked in the others.

A variant scored higher than a baseline on the same items. Verify examines what that paired comparison supports under the assumptions you declare: which direction counts as better, what the items represent and the smallest difference that would matter.

It applies McNemar’s test with a Newcombe interval to exact 0/1 pairs, and a paired Student-t interval only when the declared assumptions support one. Repeatability is a separate test across at least five independent matched reruns. Based on your declarations, it declines designs outside its supported assumptions, such as clustered, weighted or repeated-generation evaluations, rather than approximating them; it does not verify the declarations.

The site is a statically generated Next.js and TypeScript application with no accounts, advertising or analytics; interactive state stays in your browser. Two checks show how correctness is handled:

• The attention notebook’s Python export is executed by the test suite and compared with the in-browser calculation and with an independently worked example.
• The gradient-descent lesson once misclassified the critical step size, where the iterates neither shrink nor grow. The fix came with a test that checks all 1,288 slider settings against exact rational arithmetic.

Continuous integration is set up to run the unit tests, browser tests at desktop and phone widths (including keyboard use), content validation and a production build on every pull request. Much of the code is written with AI coding assistants under our direction, and it has to pass the same checks as any other change; How this site is written describes this in full.

Status. This proposal has not been run. It is presented here as a design example, separate from the current research question on the Research page.

When AI agents act for different people or organizations, a handoff between them crosses an authority boundary. This proposal asks whether two controls that each participant can enforce locally can contain a seeded failure without anyone having to see or govern the whole system, and whether the failure can then be attributed.

1. People decide. A person chooses the question and its assumptions, what would count as evidence, how a result is read, and what is published.
2. AI may propose, within limits. In the intended design, an AI system could suggest, search, write code and run work, but only inside limits a person sets, and it could not change the question, the standard of evidence, the conclusion or what is published. None of this is built: no AI agent works on this site, and no service runs experiments for you.
3. Predict before you look. Some investigations ask for your prediction before they show a result and record it first, so that the result has something honest to be compared with; others ask you to inspect, change, compare or explain instead. There is no score. In Verify you may calculate first, but its questions about the design stay open until you answer them.
4. Say what a result does not show. In the lab, each toy result is calculated in your browser from the settings shown; it is not a measurement from a production model. Where a page cites a paper, the source is linked next to the claim it supports.
5. Carry forward only what was reviewed. In the intended design, only work a person has reviewed would feed into later work. No shared record of this kind exists yet.

Five parts of the site exist today. One investigation, the workspace, takes a single question from a first look to a result someone else can rerun; the other parts stand alone, and together they are not yet one connected research environment.

Preparation is under way for a first walkthrough with consenting participants. It would test only whether the path is understandable: whether a person can build intuition from a notebook, make a prediction in the lab, turn the open point into a research draft, and see which evidence would settle it and what decision comes next. It has not happened, and our own rehearsals are not evidence that the path works.

The intended loop has eight steps. People own every one of them; two are not built, and the site has no service that runs experiments for you.

1. Learn: a person builds an intuition for the idea.
2. Frame: a person states the question and its assumptions.
3. Predict: a person commits to an expected result before seeing one.
4. Delegate: AI systems would carry out bounded work inside the person’s limits. Not built.
5. Experiment: small training runs can happen in your browser; larger runs happen outside this site today.
6. Inspect: a person examines the evidence.
7. Decide: a person decides what the result supports.
8. Carry forward: only reviewed work would feed later work. Not built.

Verify stores nothing: it creates no account, no saved record and no export.

Some lab pages and lessons keep your predictions, saved comparisons, place in a reading route or research drafts in this browser; others save nothing. None of it is shared with anyone, and it is kept apart from Verify. Your work lists your questions, projects, research drafts, saved investigations and ideas to review; some exercises keep your answers on their own page. Opening Your work reads those records and changes none of them.

The Research Workbench saves a draft in this browser automatically when storage is available and the draft passes its checks, and restores it when you return. The blank workbench and each starter draft are saved separately. Nothing is uploaded or synced to an account. If saving fails, the latest edits may exist only in the open tab. Resetting a draft asks for confirmation first, and exporting downloads a JSON file that you keep. A draft creates no run, evidence, approval or publication.

The workspace keeps your work in this browser’s storage, so after a successful save it is there when you return; a failed or cleared save, or a workspace replaced in another tab, is not recovered. “Forget this workspace” deletes it. Its package is a download you start. Clearing this site’s storage also resets the workspace’s one look at the test images.

Clearing this site’s browser data removes everything stored here, but not files you downloaded. The privacy notice also covers what the hosting provider processes when you visit.

On the research side, no study protocol is fixed, no study with participants is running, no independent review has taken place and no empirical evidence exists. An earlier question on alignment evidence is kept as a record but set aside; its earlier schedule no longer applies. Our full report of an earlier model-fusion case is not published and is not an accepted result. Where a page offers different points of view on an idea, such as a learner’s or a researcher’s, those are fixed texts, not people or contributions. A new capability will be described here as current only after it has been built and checked.

Verify. The version on this site is experimental. A revised version will replace it only after it has been reviewed and has passed further checks, including accessibility. The test that matters is whether someone outside the project can bring a real result to Verify, and whether it changes a decision they make.

Research. The feasibility check must stop the proposal, or send it back for revision, if any of these cannot be settled: earlier work on the same question, the exact sources and the rights to use them, keeping the compared conditions identical apart from the links, ethics, a route to qualified reviewers, the outcome measure, statistical power and the resources needed. A named person who did not design or carry out the check must then assess it, and even a favourable assessment would not by itself approve a study. Whatever happens to Verify, the earlier alignment-evidence question stays set aside. The Research page shows the absence of evidence as prominently as the question itself, and keeps proposed, set-aside and future work visibly separate.

Learning, sources, predictions, study designs, evidence, decisions and reviewed corrections would stay attached to the same question, so that later teaching and later research build on what survived review rather than on an unexamined answer. AI systems might propose, challenge and carry out bounded work; people would keep authority over the question, the assumptions, the standard of evidence, the interpretation, the decision and publication.

If real use justifies it, the same records could support collaboration between people, between people and AI systems, and between AI systems acting with permission, and in time an open research institution whose shared knowledge consists of reviewed records and explicit disagreements rather than a feed of conversations or unreviewed AI output.

None of that exists today: there are no accounts, identities or permissions, no shared community, no live AI on the site, no agents running, no shared memory, no independent review workflow, no publishing and no automatic changes to the curriculum.

Continuous Function sets its own direction and is responsible for everything the site says publicly. How the site is written is described below, and how to reach us at the end of this page. Independent review, wherever this site mentions it, means review by a named person who did not design the work.