How do we know this?

Many of the companies (including OpenAI) have even claimed the opposite. Inference is profitable; it's R&D and training that's not.

It's not reasonable to claim inference is profitable when they've also never released those numbers. Also the price they charge for inference is not indicative of the price they're paying to provide inference. Also, at least in openAI's case, they are getting a fantastic deal on compute from Microsoft, so even if the price they charge is reflective of the price they pay, it's still not reflective of a market rate.

DeepSeek on GPUs is like 5x cheaper then GPT

And TPUs are like 5x cheaper then GPUs, per token

Inference is very much profitable

You can do most anything profitability if you ignore the vast majority of your input costs.

OpenAI hasn't released their training cost numbers but DeepSeek has, and there's dozens of companies offering inference hosting of open weight models for the very large models that keep up with OpenAI and Anthropic, so we can see what market rates are shaking out to be for companies that have even less economies of scale. You can also make some extrapolations from AWS Bedrock pricing and can also investigate inference costs yourself on local hardware. Then look at quality measures of quantizations that hosting providers do and you get a feel for what hosting providers are doing to manage costs.

We can't pinpoint the exact dollar amount OpenAI categorically spends but we can make a lot of reasonable and safe guesses, and all signs points to inference hosting being a profitable venture by itself, with training profitability being less certain or being a pursuit of a winner-takes-all strategy.

Statistically this is obvious. Most people use the free tier. Their total losses are enormous and their revenue is not great.

No, it’s not obvious. You can’t do this calculation without having numbers, and they need to come from somewhere.

Sam has claimed that they are profitable on inference. Maybe he is lying but I don't think speaking so absolutely about them losing money on that is something you can throw around so matter of fact. They lose money because they dump an enormous amount of money on R&D.