What 10²⁶ Actually Means

The number that defines a “frontier model” in US and California law, in terms of time, hardware, money, and the handful of training runs that have crossed it.

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The recent wave of AI laws shares a definition. A frontier model is one trained using more than 10²⁶ operations. California’s SB 53 uses it, and so does the federal AI diffusion rule. In the statutes, the figure reads like a technical condition. That condition decides which companies the law reaches, and most write-ups leave it sitting there as a row of zeros.

The number

Written out, 10²⁶ is 100,000,000,000,000,000,000,000,000. A hundred septillion. Each unit is one arithmetic step, an addition or a multiplication, performed during training. What the model learns is the accumulated result of those steps, run over and over against the training data until the weights settle.

Counting it

Count them by hand, one per second, and you would need roughly 230 million times the current age of the universe. Recruit help. Put all eight billion people on Earth on the job, each doing one operation every second with no breaks and no sleep, and a single training run still takes about 400 million years.

On real hardware

The work happens because machines do not count one per second. A current high-end AI chip, an NVIDIA H100, performs on the order of 10¹⁵ operations per second, about a quadrillion. Run one of them flat out and it reaches 10²⁶ in roughly 3,000 years, and longer once you account for the fact that a chip is rarely kept perfectly busy. So nobody uses one. A run at this scale spreads across a cluster. Meta has described assembling a cluster of around 100,000 H100-class chips for its largest models. A cluster that size covers 10²⁶ operations in something like a month, depending on how efficiently the chips stay fed. The newest chips are faster, which shortens the clock again.

The cost

The compute by itself costs somewhere in the range of tens to hundreds of millions of dollars, before salaries, data, or the building it sits in. Reaching the threshold takes a budget only a few organizations on the planet can currently cover. That is part of what the line was chosen to do.

What training does

So far this is a count of operations with no sense of what they are for. A model is a very long list of numbers, called weights or parameters. A frontier model has hundreds of billions to trillions of them. At the start of training, they are set at random, and the model can do nothing useful. Training is the work of finding good values for every one of them.

It runs as a loop. The system shows the model a stretch of text from its training data and asks it to predict what comes next, one token at a time, where a token is a word or a fragment of a word. The model produces a guess. The system measures how far the guess was from the real next token, then adjusts every weight by a tiny amount in the direction that would have made the guess a little better. Then it repeats with the next stretch of text, and again, and again. The model passes over trillions of tokens this way, nudging billions of weights a little at a time, until the values stop improving.

That loop is where the 10²⁶ goes. A standard way to estimate training compute, used by groups like Epoch AI, is to multiply a model’s parameter count by its number of training tokens and then by about six, because each parameter gets touched roughly six times for every token the model reads. A trillion parameters, times ten trillion tokens, times six, comes to roughly 10²⁶. The number in the law comes straight out of the sizes the models already are and the text they already read.

When the loop finishes, what remains is the final list of numbers, not a transcript of everything the model saw, and not a stored index of it. For a frontier model, that list is a file somewhere in the range of hundreds of gigabytes to a few terabytes. That file is the whole product of the run. Every one of the 10²⁶ operations existed to set those numbers.

What a query does

Querying the model is a different kind of event, and a far smaller one. When you send a prompt, your text runs through that fixed list of numbers a single time. The weights do not change. They were frozen the moment training ended, and they stay frozen no matter how many questions arrive. Your prompt goes in as numbers, flows through the weights in one pass, and comes out as a set of probabilities for what the next token should be. The system picks one, attaches it to your text, and runs the whole thing through again to get the token after that. It assembles the answer one token at a time, which is why you often watch a response appear word by word.

The cost of that is small next to training. One pass through the weights for a single token takes on the order of two operations per parameter, so a couple of trillion operations for a trillion-parameter model. A long answer of a few thousand tokens still totals only a few quadrillion operations, billions of times below the 10²⁶ that produced the model. The training run happens once. After that, answering happens billions of times over, each instance cheap, all of it drawing on the same frozen numbers, which is how a single model can serve millions of people at once. The expensive part already finished before you typed anything.

Training versus inference

People reach for the same word, using the model, to cover both phases, and that is where the confusion usually starts. Training and inference are two different activities, and the difference comes down to whether the model itself changes. Training changes it, rewriting the weights step by step, while inference leaves every weight untouched and only runs text through them.

The gap in their per-token cost comes from one extra step. To answer, the model runs your tokens forward through the weights a single time, which costs about two operations per weight. To learn, it runs that same forward pass, then a second pass backward through the weights to work out how each one pushed the guess wrong and which way to move it, and then applies the change. The backward pass costs roughly twice the forward one, so learning from a token runs to about three times the work of answering with it. Put that heavier per-token cost on top of the trillions of tokens read during training, set against the few thousand tokens of prompt in a query, and the two totals separate by a factor in the billions.

Because the weights are frozen, your conversation does not change the model you are talking to. The weights are the same for you and for everyone else using it in that moment, and they hold steady through the whole exchange. When the context window fills and earlier text scrolls out, the model keeps nothing of it, because none of it was ever written into the weights. A memory feature, where one exists, is a separate system that stores some of your text and pastes it back into a later prompt, not the model learning. Companies may feed collected conversations into a future training run, but that run produces a different file of numbers, shipped later as a new model. The one in front of you is not learning from you as you type.

The two also grow in opposite directions. Training is paid once, in a single concentrated run, to bring the model into existence. Inference is paid steadily, a sliver at a time, for as long as anyone keeps using it. Each query is cheap, and they keep coming. It takes something like tens of billions of answered prompts to match the compute of one training run, and a heavily used model can field that many within days, so over its deployed life, the compute spent answering it can quietly pass the compute spent creating it. The compute threshold in the law counts what it took to build the model, paid once. Inference is the other cost, what it takes to run the model, charged per token every time someone uses it.

Models above the line

On the model side, the scale is easier to feel against systems people know. GPT-4, the release that made the public pay attention in 2023, came in at an estimated 2×10²⁵ operations, about five times under the line. By Epoch AI’s tracking, the first model estimated to cross 10²⁶ was xAI’s Grok-3, in February 2025. As of early 2025, around two publicly available models had passed it, against roughly thirty above the 10²⁵ mark one order of magnitude below. Epoch projects the count of models above 10²⁶ rising to roughly thirty by 2027 and past two hundred by 2030. Fable 5 and Mythos 5 sit well above the line.

A moving line

The figure first entered US policy in October 2023, in the Biden administration’s executive order on AI, as the trigger for a reporting requirement on dual-use foundation models. That order was revoked in January 2025. The number outlived it. It carried into the Commerce Department’s AI diffusion rule, then California’s SB 53, and the vetoed SB 1047 before either. The European Union drew its own line a power of ten lower, presuming systemic risk for general-purpose models trained above 10²⁵ operations.

The number stays fixed while training compute for the largest models keeps growing, several-fold per year for more than a decade. A line that sits above all but a couple of models today sits below dozens within a few years, on Epoch’s projection, without anyone changing a word of the statute. Both SB 53 and the diffusion rule let the relevant agency adjust the threshold over time, which tells you the drafters already expected the number to move.