Find the law behind your data
NAI (No-Ansatz Inference) finds a formula that fits your table without fixing its form in
advance: you give the measurements, it gives the law, with its accuracy on rows it has not seen.
No language model, no GPU.
- 60.3 %exact Feynman laws, SRBench 20211st of 15 systems
- 0.9925real-data R², SRBench 20251st of 28 systems
- 0.775scaling-law R², SLDBench1st of 12 systems
- 72.07 %within 10 %, LLM-SRBench1st of 13 systems
Places against the results each benchmark publishes for other systems. Details and caveats: benchmark reports.
A law, not a curve fit
Eleven measurements of a drug in plasma, over the first eight hours after a dose.
NAI, a cubic polynomial and a regression tree are fitted to them.
Then the next sixteen hours, which none of them saw.
Examples
Each was solved by NAI from the table shown, with no hint of the formula.
The tables are synthetic, in the shape of the laws each field uses.
Pick one; move the sliders where a law has more than one variable.
An honest answer
NAI says what it has found: the law, a formula within the noise, or no law at all.
It does not present a fit as a discovery.
NAI in your pipeline
NAI is one step between the data you already collect and the decisions you make with them.
A table goes in; a law comes out, with its accuracy and its forecast.
Four typical pipelines:
- 01Training runs
Small models of three families, each trained to the end: one final loss per run.
36 runs - 02A table
One row per run; the error of the loss in its own column, the family as a group.
N,L,sigma,group - 03 · NAIThe law
One form for every family, chosen by how well it predicts the largest runs, held out.
L = c₁ + c₂·log(N)³/√N - 04Forecast
The loss of a ten times larger model, with its uncertainty band, before it is trained.
--predict, --band - 05Decision
Which size to train for the budget, and which family is worth scaling.
size, data, compute
--next- 01Lab samples
Plasma concentration after three intravenous doses, sampled over 24 hours.
36 samples - 02A table
Time, dose, concentration, and the assay's error in its own column.
t,D,C,sigma - 03 · NAIThe law
The decay law and its constants, with a statement: exact, or within the noise.
C = 0.0251·D·θ^t, θ = 0.840 - 04Model
Half-life about 4 h, concentration proportional to the dose: schedules can be explored within the range of the data.
--predict, --band - 05Review
One input for the study team; the choice of dose and interval stays with them and the protocol.
for review
--nextAn illustration on synthetic data. NAI is a research tool, not a medical device: it is not meant for diagnosis or for treatment decisions.
- 01Wear tests
Tool life at twelve cutting speeds, with the 5 % scatter that wear tests have.
12 tests - 02A table
Cutting speed, tool life, and the scatter in its own column.
V,T,sigma - 03 · NAIThe law
Taylor's steep power law and its exponent, judged on the fastest cuts, held out.
T = 2.70·10¹⁰ / V^3.92 - 04Forecast
Tool life at speeds not tested yet, with its uncertainty band.
--predict, --band - 05Decision
The cutting speed and the tool change interval: the cost per part against the downtime.
speed, change interval
--next- 01Turbine records
Power of turbines of three sizes at three air densities, against the wind speed.
72 records - 02A table with units
The units in the header, so that only dimensionally consistent laws are searched.
rho[kg/m^3],A[m^2], v[m/s], P[W] - 03 · NAIThe law
Power as a number times ρ·A·v³; the number is half the power coefficient.
P = 0.2098·ρ·A·v³ - 04Model
The power coefficient, 0.42; a site's yield from its wind record, with its band.
--predict, --band - 05Decision
Which turbine for which site, and when the measured power falls below the law: wear, icing.
turbine, site, service
--nextnai_cli --data table.csv --predict grid.csv out.csv
The full build of NAI: one program, a processor and no GPU; a table in, the law and its forecast out. It fits a cron job, a notebook or a CI step.
POST /api/jobs
The HTTP interface this page uses: the table and the settings in JSON, the law, its accuracy and the simpler alternatives back.
on-premises
The same program inside your network, for data that must not leave it. Nothing is sent anywhere.
Try it with your data
A table with a header row; the last numeric column is the quantity to explain. See data format.
The live demo is being set up. The form already reads your table and shows how NAI will see it; the search itself opens soon. The examples above were computed by NAI in advance.
Data format
- Text table, UTF-8, the first line is the header. Separator: tab,
;,,or spaces. Lines starting with#are comments. - The last numeric column is the quantity to explain, the others are its variables.
- Reserved names:
sigma(orsd,se,err,error) is the standard error of each value;trialsis the number of trials behind a frequency;grouplabels groups that share one law with their own constants. Do not use these names for anything else. - Precision. Without a
sigmacolumn, the precision is read from how the numbers are written:0.1172is known to four decimals, integers and full-precision numbers are exact. Do not round exact data; give noisy data their error. - Units, optional, in brackets after each name, for every column or none:
v[m/s],F[N],n[1]. NAI then searches only dimensionally consistent laws. - At least 4 rows; with 8 or more, part of them is held out to check the formula.
L[m],g[m/s^2],T[s] 0.25,9.81,1.003 0.50,9.81,1.4185 1.00,9.81,2.0061 …
Questions
How is NAI different from fitting a curve or training a neural network?
A curve fit has its form chosen in advance, a polynomial or an exponential, or no form at all, like a tree or a network: it describes the data it saw. NAI searches for the form itself and returns a formula you can read, check against theory and carry beyond the data. Section 01 shows the difference on one drug.
How is it different from PySR, AI Feynman or systems built on language models?
The goal is the same: symbolic regression. NAI uses no language model and no GPU, and it says whether its answer is exact, within the noise, or an approximation. Its places on public benchmarks, against the results those benchmarks publish for other systems, are in the benchmark reports.
Do I need a GPU or a cloud service?
No. NAI runs on an ordinary processor; this demo gives each search two cores. The full build runs on your own machines, with no network.
How many rows does it need?
At least 4; with 8 or more, part of them is held out to check the formula. Noisier data need more rows. This demo takes up to 2000 rows and 6 variables.
What if my data have no law?
NAI says so: “Approximation: no law found”, with the best short formula it has, marked as an approximation. Section 03 shows it on random numbers.
How do I check an answer?
Each answer comes with its error on rows NAI did not fit to and with the simpler and more accurate alternatives it kept; with units in the header, it considers only dimensionally consistent laws. Copy the formula as Python, Excel, MATLAB, LaTeX, C, Mathematica or SymPy and test it on new data.
How far can I trust a forecast beyond the data?
The band on the charts shows it: where the forms that predict the held-out rows nearly as well disagree. An exact law has none. NAI can also propose the next measurements that narrow the band the most for their cost: see the scaling-law example.
Can I use it on data that must not leave my organisation?
Yes: NAI runs on your own machines, and nothing is sent anywhere. In this demo, tables and results are deleted after 24 hours.
Does it work on integer sequences?
Yes, on exact sequences: it finds recurrences and generating functions. Its results led to seven accepted edits in the OEIS; see the OEIS findings.
How do I get NAI for my work?
Write to lab@mindscan.org: a pilot on your data, or the full build on your own machines.
Limits and privacy
Limits of this demo
- up to 2000 rows, 6 variables, 2 MB
- 10, 30 or 60 seconds of search on 2 CPU cores
- one search at a time; up to 10 an hour from one address
- NAI on your own machines has none of these limits
Your data in this demo
- tables and results are deleted after 24 hours
- nothing is shared or used for training
- data that must not leave your premises: NAI runs on your own machines, ask for an on-premises version
NAI is a research tool, not a medical device: it is not meant for diagnosis or for treatment decisions.