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- Artificial intelligence (AI)
A set of techniques that let a program perform tasks we associate with human intelligence: understanding text, recognising images, planning, solving problems. The word covers very different systems, from spam filters to chat assistants.
Example : An assistant that answers a written question and software that spots a tumour on an X-ray both count as AI.
See also : Machine learning, Language model
- Machine learning
A method where rules are not written by hand: a program infers its own rules from examples. The more varied the examples, the better it tends to generalise to new cases, within limits.
Example : To recognise cats, you show the program many labelled photos instead of describing what a whisker is.
See also : Neural network, Training, Dataset
- Neural network
A family of models made of many small computing units linked in layers. Each link carries a number that is adjusted during training. The name is an image: it does not work like a brain.
Example : A network reading the pixels of a photo passes them through layer after layer until it outputs an answer such as “cat” or “dog”.
See also : Parameter, Transformer, Machine learning
- Language model
A neural network trained on very large amounts of text to predict what comes next. This simple task gives rise to useful abilities: answering, summarising, translating, writing code. It can also be wrong with confidence.
Example : When you type the start of a sentence and an assistant completes it, a language model is choosing the words one at a time.
See also : Transformer, Foundation model, Hallucination
- Foundation model
A large model trained once on very broad data, then adapted to many uses. It serves as a base, instead of starting from scratch for each task.
Example : The same base model can be tuned into a writing assistant, a coding tool or a scientific research system.
See also : Language model, Multimodal, Training
- Transformer
A neural network architecture that lets the model weigh how much each piece of the text matters relative to the others. It underlies most current language models.
Example : In “the ball bounced off the table, then it fell”, the model links “it” to “the ball” thanks to this attention mechanism.
See also : Neural network, Language model
- Training
The phase where a model adjusts its parameters by looking at examples, to reduce its errors. It takes a lot of data and computing power. Once it is done, the model is frozen and ready to use.
Example : The model predicts a word, the prediction is compared with the real word, the parameters are nudged, and the loop repeats very many times.
- Inference
The moment a model that is already trained is used to produce an answer to a request. The parameters no longer change. It happens each time you ask an assistant a question.
Example : Sending a photo to an app that describes it triggers inference. The model is not retrained.
- Parameter
An internal number of a model, adjusted during training. Together, the parameters hold what the model has learned. Large models have a great many, but that count alone does not tell you whether a model is good.
Example : You can picture parameters as the knobs of a very large mixing desk, set by training.
See also : Training, Open weights, Neural network
- Dataset
A collection of examples (texts, images, measurements, problems) used to train or evaluate a model. Its makeup matters: a model reflects in part what it has seen, including biases and errors.
Example : A collection of X-rays annotated by doctors serves as a dataset for learning to detect an anomaly.
- Benchmark
A standardised test used to compare models on the same questions. Useful but limited: a good score does not prove a model will succeed elsewhere, and the questions may have leaked into training data.
Example : A set of conjectures whose status is known lets you measure how many a system can solve.
- Agent
An AI system that does more than answer: it chains actions towards a goal, using tools (search, code, files) and taking the results into account. The more it acts on its own, the more human oversight matters.
Example : A research agent reads papers, runs a computation, fixes its mistake, then writes up a report.
See also : Reasoning, Language model
- Reasoning
The ability to chain logical steps to solve a problem. Some models first produce intermediate steps before answering. Whether those steps reflect real reasoning is still debated.
Example : For an olympiad problem, a system can try several approaches and check each one before proposing a solution.
See also : Agent, Proof, Hallucination
- Hallucination
An answer from a model that sounds confident and well written but is false or made up: a source that does not exist, a proof with a gap. The tone says nothing about accuracy.
Example : A model cites a paper with a plausible title and real authors, but the paper does not exist.
See also : Language model, Formal verification, Claim
- Open weights
Said of a model whose parameters (the “weights”) are published: anyone can download and run them. It is not always open source: the training code, the data and the licence may stay closed.
Example : A lab publishes a model's weights: a researcher can inspect it and run it on their own hardware.
See also : Parameter, Foundation model
- Multimodal
Said of a model that handles several kinds of data at once: text, image, audio, video. It can, for example, answer a question about a photo.
Example : You send a photo of a chart and ask what it shows: the model reads the image and answers in writing.
See also : Foundation model, Robotics and VLA model
- Robotics and VLA model
A VLA model (vision, language, action) links what a robot sees and a written instruction to an action to carry out. The idea is to command a robot in plain language. Lab demonstrations do not guarantee reliability in the real world.
Example : You tell a robot arm “put the cup on the shelf”: the model looks at the scene and picks the movements.
See also : Multimodal, Agent
- Reinforcement learning
A method where a system learns by trial and error: it tries actions, gets a reward when the outcome is good, and adjusts its strategy. It works well when the result can be checked automatically, as in a game or a machine-checked proof.
Example : A formal-proof system gets a positive signal when the proof assistant accepts its proof.
See also : Reasoning, Lean (proof assistant)
- Preprint
A scientific paper posted online before any peer review, on a platform such as arXiv. It spreads results quickly, but nobody has formally checked its content yet.
Example : A lab announces a result in a preprint; the community reads and criticises it, and a journal may later send it for review.
See also : Peer review, Scientific journal
- Peer review
Examination of a paper by experts in the field, independent of the authors, before or during publication. It catches many errors but not all: a reviewed paper can still contain a mistake.
Example : Specialists read the proof, put questions to the authors and ask for corrections before accepting the paper.
See also : Scientific journal, Preprint, Independent third party
- Scientific journal
A periodical that selects research papers after peer review. Not all journals are equally demanding: the journal's name matters, and so does the date.
Example : A result published in a peer-reviewed journal has passed a check that a blog post has not.
See also : Peer review, Preprint
- Conjecture
A mathematical statement that is believed true, but that nobody has yet proved or disproved. It can stay open for a long time. Solving a conjecture means proving it, or showing it is false.
Example : A conjecture says “all objects in this family have this property”; a single object without it is enough to refute it.
See also : Proof, Counterexample
- Proof
A logical demonstration, step by step and from established results, that a mathematical statement is true. A proof must be checkable by others. In practice, long proofs can hide errors that are hard to spot.
Example : An AI can propose a proof; until someone independent has checked it, it is a proposed proof.
See also : Conjecture, Formal verification, Lean (proof assistant)
- Counterexample
A specific case that shows a general statement is false. It is often easier to check than a proof: you verify that the case exists and breaks the rule.
Example : To refute “all swans are white”, one black swan is enough.
See also : Conjecture, Proof
- Bound
A limit proved for a quantity: it cannot be larger (upper bound) or smaller (lower bound) than a given value. Improving a bound brings it closer to the true value, without always reaching it.
Example : Knowing a number is at least some value is a lower bound; finding a larger valid value tightens the range.
See also : Record, Conjecture
- Record
The best known value for a given problem, for example the largest known construction with a given property. Beating a record does not necessarily solve the problem: it only does better than earlier attempts.
Example : A program finds a construction larger than any published one; it still has to be checked that it follows the rules.
See also : Bound, Reproduction
- Reproduction
Redoing a result by another person or tool, with the same data or code, to see whether the same thing comes out. A reproduced result is sturdier than one seen once.
Example : A third party reruns the published code of a computation and gets exactly the announced value.
See also : Independent third party, Formal verification
- Lean (proof assistant)
Software in which a mathematical proof is written in a form the machine can check step by step. If Lean accepts it, no step is wrong. It does not say whether the written statement matches what was meant to be proved. Coq and Isabelle play a similar role.
Example : An AI can propose a proof in Lean; the software rejects it if a step does not hold.
See also : Formalisation, Formal verification, Statement fidelity
- Formalisation
Translating a mathematical statement or proof into a language a machine can check. When the result was already known, it is a verification, not a discovery: DiscoverIA tells them apart.
Example : Rewriting a famous, long-established theorem in Lean so that the machine validates each step.
See also : Lean (proof assistant), Formal verification
- Formal verification
Checking by a machine, following fixed logical rules, that a proof is correct. It is the strictest form of proof checking. It covers the statement as written: it does not replace reading that statement.
Example : A third party runs a proof in Lean on their side and publishes that the machine accepts it.
See also : Lean (proof assistant), Independent third party, Statement fidelity
- Independent third party
A person or organisation separate from the one announcing a result, with no stake in defending it, that has checked it. DiscoverIA requires a named third party for the “formally verified” status: a proof supplied by its author alone is not enough.
Example : A lab announces a proof, then an outside group has it checked and publishes its report.
See also : Formal verification, Reproduction, Status: formally verified
- Statement fidelity
The question of whether the statement written in formal language says what the source claims. A proof accepted by Lean may be about a weaker, or different, statement than the one people assume. DiscoverIA assesses this separately from the status.
Example : A source announces a theorem for all numbers; the formal statement proves it only for positive numbers. The machine is satisfied, the announcement is too broad.
See also : Lean (proof assistant), Formal verification, Formalisation
- Claim
What a person or organisation says it has achieved, before any independent check. DiscoverIA records the claim, its author, its source and its date, then follows what happens to it: review, challenge, withdrawal.
Example : A lab writes that it solved an open problem: that is a claim until others have examined the proof.
See also : Hallucination, Status: not evaluated, Independent third party
- Status: formally verified
A named third party has checked the proof by machine (for example in Lean). A Lean file supplied by the claimant alone is not enough. The status says nothing about statement fidelity, which is assessed separately.
Example : A Lean formalisation checked by a named outside group gets this status; the same formalisation seen only at its author's does not.
See also : Formal verification, Independent third party, Status: peer reviewed
- Status: peer reviewed
The result is published in a journal or has been reviewed by named experts. It is a solid human check, but less strict than a formal verification.
Example : A paper in a peer-reviewed journal about an AI system gets this status once the publication is confirmed.
See also : Peer review, Scientific journal, Status: under review
- Status: under review
A public review is under way, with no verdict yet. The result is neither confirmed nor dismissed: wait, or follow the discussion.
Example : A batch of manuscripts is released and mathematicians begin reading them in public, without having concluded.
See also : Status: disputed, Status: not evaluated
- Status: disputed
A sourced public objection exists, without an established refutation. The result is not declared false: the objection is flagged and the follow-up is tracked.
Example : An expert publishes a reasoned critique of an announced proof; the authors have not yet answered or the matter is unsettled.
See also : Status: withdrawn, Status: under review
- Status: withdrawn
The result was withdrawn or abandoned by its author, or classified as incorrect by the reference source. It stays in the registry, with the date and the reason, so that the error remains visible.
Example : A manuscript is withdrawn after a sign error is found; the entry keeps the trace of the withdrawal.
See also : Status: disputed, Claim
- Status: not evaluated
No third-party evaluation has been found. This does not mean the result is wrong, nor that it is right: as far as we know, nobody has published a check.
Example : A lab posts a result on its own blog and nobody else has examined it yet: the entry reads “not evaluated”.
See also : Claim, Status: under review, Independent third party
- Product and model statuses
For a product or a model, DiscoverIA uses another set of statuses: announced (nothing shown), demo only, available, tested by a third party, abandoned. The labels are provisional. They say where a product stands, not whether it is good.
Example : A robot shown in a video but not on sale is “demo only”; when a named third party publishes a trial, it can become “tested by a third party”.
See also : Status: not evaluated, Robotics and VLA model
- Reading reliability: PAGE
The source page was read in full and the quotation was taken word for word. It is the highest reading confidence: the fact reported rests on the text itself.
Example : The entry quotes a sentence from an article, copied as is from the page consulted on a given date.
See also : Reading reliability: PAGE-WF, Reading reliability: search-engine snippet
- Reading reliability: PAGE-WF
The page was read through a summary produced by a model. The quotation was not re-checked word for word on the page: it is probable, not guaranteed.
Example : A tool summarised a long page; the entry keeps one quotation from it, flagged as not re-checked.
See also : Reading reliability: PAGE, Reading reliability: search-engine snippet
- Reading reliability: search-engine snippet
The information was seen only in the snippet shown by a search engine, without opening the page. It is the weakest level. A status resting on a snippet alone is marked as unconfirmed.
Example : A search engine shows two lines hinting at a withdrawal; until the page is read, the entry says so.
See also : Reading reliability: PAGE, Reading reliability: PAGE-WF