It's worth reading this one to the end- the point of this paper isn't about the math involved, it's that this math was the result of the federal funding of maths research.
> The cost-benefit ratio of Mathematical research has been off-scale. The Federal government spends about $250 Million/year on mathematics research. Yet in the US there are 40 Million MRI scans per year, incurring tens of billions in Medicaid, Medicare and other Federal costs. The financial benefits of the roughly 10-to-1 productivity improvements now being seen in MRI could soon far exceed the annual NSF budget for mathematics research
It's the thing people don't get when they see odd studies being funded and try to judge if they're worthy of being funded. Either it's just they don't understand where the study fits into a larger problem or simply that esoteric studies sometimes leads to surprising findings that are far more useful than anyone could reasonable predict.
If folks are interested, I recently published a paper [1] demonstrating that fMRI activity in the visual cortex is remarkably high-dimensional!
Specifically, using a linear approach (like PCA, but slightly fancier), we find that stimulus-related information is present along many, many dimensions of the neural response---much more than previously expected/reported.
Yeah, there's a ton of criticism of fMRI as a method, largely because of a lot of results that are statistically unsound (to say the least)!
I tend to think of fMRI data as some highly nonlinear transform of whatever neural activity is occurring in a particular region of the brain, at pretty coarse spatial resolution (~1-3 mm) and pretty bad temporal resolution (~5-15 s).
Sure, it's no direct measure of neurons firing, but that doesn't mean there isn't information in the signal that we can interpret and maybe use (see [1] for a recent example of reconstructing seen images from brain activity)
As a cognitive neuroscientist, I tend to abstract away a ton of the details (neurons, molecules) and focus on more general computational principles: how do we get complex behavior from many simple interacting units---voxels in fMRI, for instance?
Regarding the specific paper you posted, I saw some of the discourse around it but haven't read it carefully myself (it's not my area of expertise). I saw some recent re-analysis of that data [2] that argues that the result isn't valid, but need to look at it more carefully.
It sounds like it's a claim along the lines that you can't tell "I love Lucy" is on because you are listening to the audio and not looking at the screen.
Recent studies have demonstrated using fMRI data to reconstruct the images of what the person being scanned is seeing. There's enough information there to produce a highly plausible reconstruction - if someone is seeing a picture of a zebra, the software shows a zebra, but it's not going to get the stripe patterns exactly right.
fMRI provides a great proxy and noisy set of signals. Fortunately, the brain is redundant enough that a bunch of regions getting activated creates a sufficiently differentiable pattern at large that you can get enough good information to do things like MindEye and so on. Fortunately, recent AI breakthroughs have allowed extremely high dimensional geometry to be handled relatively simply, with millions or billions of dimensions being processed into semantically useful tools.
I don't immediately see how that paper's assertion (that some areas' fMRI response is influenced by baseline oxygenation and cerebral blood flow) relate to the reliability of an information modeling experiment?
I wouldn't say "called into question", as if the whole idea is bunk.
MRI is, in general, a lot harder than people often imagine. It uses complicated physics to measure convoluted physiological changes to indirectly measure brain activity, which is obviously stupifying involved--and then relate that to other, often complicated factors like behavior, lifestyle or disease state.
I think it's reasonably well-known that the BOLD response is complex and doesn't directly reflect "average" spiking activity. Some studies find that it's sensitive to the amount of synchrony (=more neurons firing together in time) rather than the rate. The paper you mention shows another dissociation: neurons can get more fuel by extracting oxygen more efficiently OR have having more overall oxygen to extract at the same rate. Thus, it's not noise, but it is complicated.
You can do a lot better than this if you redefine the problem from directly generating images with certain contrasts to maximizing information gain, even with weak magnets. They've since basically run out of money and are on life support, but Q Bio [0] had that tech working years ago, able to quickly derive many different image types from an entropy-maximizing scan, though they never deployed that in prod IIRC (again, they're broke).
A couple of months ago I wrote a small post [1] (in Spanish) about subsampled MRI image reconstruction using compressed sensing and how it relates to government funding issues. At the time Tao had written some posts [2] about how the IPAM, where Terrence Tao was working, was losing some funding because UCLA wouldn't follow some new federal government policies.
I remember one of my diploma students continued with discrete tomography as PhD, topic "Binary Tomography by Iterating Linear Programs" and I found it super interesting to get down the number of shots and at the same time increasing the accuracy a lot.
Having worked through Geometric Tomography by Gardner, one of the big names in the field, I am pretty confident in asserting that the folks in the field have little to no interest in tomography or other applications. It's merely a grant winning ruse. The same field rebrands as "high dimensional probability/stats" by casting the uniform measure on convex bodies in the language of log-concave densities, but you talk to the folks themselves and they smirk about the extent to which they care about whether their work has any relation to the applications they claim.
There are some notable exceptions -- Donoho, Vershynin -- but most of them are doing good old fashioned Brunn-Minkowski theory, which is fundamental but a hard sell in its most truthful form.
It's a nice review but the end reads like a funding pitch.
The most important Mathematicians like donoho and Tao in the US seem to currently experience budget cuts and start to address the public.
> The cost-benefit ratio of Mathematical research has been off-scale. The Federal government spends about $250 Million/year on mathematics research. Yet in the US there are 40 Million MRI scans per year, incurring tens of billions in Medicaid, Medicare and other Federal costs. The financial benefits of the roughly 10-to-1 productivity improvements now being seen in MRI could soon far exceed the annual NSF budget for mathematics research
Specifically, using a linear approach (like PCA, but slightly fancier), we find that stimulus-related information is present along many, many dimensions of the neural response---much more than previously expected/reported.
[1] https://journals.plos.org/ploscompbiol/article?id=10.1371/jo...
I tend to think of fMRI data as some highly nonlinear transform of whatever neural activity is occurring in a particular region of the brain, at pretty coarse spatial resolution (~1-3 mm) and pretty bad temporal resolution (~5-15 s).
Sure, it's no direct measure of neurons firing, but that doesn't mean there isn't information in the signal that we can interpret and maybe use (see [1] for a recent example of reconstructing seen images from brain activity)
As a cognitive neuroscientist, I tend to abstract away a ton of the details (neurons, molecules) and focus on more general computational principles: how do we get complex behavior from many simple interacting units---voxels in fMRI, for instance?
Regarding the specific paper you posted, I saw some of the discourse around it but haven't read it carefully myself (it's not my area of expertise). I saw some recent re-analysis of that data [2] that argues that the result isn't valid, but need to look at it more carefully.
[1]: https://www.nature.com/articles/s41598-025-89242-3 [2]: https://www.biorxiv.org/content/10.64898/2026.04.21.719913v1
https://medarc-ai.github.io/mindeye/
Recent studies have demonstrated using fMRI data to reconstruct the images of what the person being scanned is seeing. There's enough information there to produce a highly plausible reconstruction - if someone is seeing a picture of a zebra, the software shows a zebra, but it's not going to get the stripe patterns exactly right.
fMRI provides a great proxy and noisy set of signals. Fortunately, the brain is redundant enough that a bunch of regions getting activated creates a sufficiently differentiable pattern at large that you can get enough good information to do things like MindEye and so on. Fortunately, recent AI breakthroughs have allowed extremely high dimensional geometry to be handled relatively simply, with millions or billions of dimensions being processed into semantically useful tools.
I don't immediately see how that paper's assertion (that some areas' fMRI response is influenced by baseline oxygenation and cerebral blood flow) relate to the reliability of an information modeling experiment?
MRI is, in general, a lot harder than people often imagine. It uses complicated physics to measure convoluted physiological changes to indirectly measure brain activity, which is obviously stupifying involved--and then relate that to other, often complicated factors like behavior, lifestyle or disease state.
I think it's reasonably well-known that the BOLD response is complex and doesn't directly reflect "average" spiking activity. Some studies find that it's sensitive to the amount of synchrony (=more neurons firing together in time) rather than the rate. The paper you mention shows another dissociation: neurons can get more fuel by extracting oxygen more efficiently OR have having more overall oxygen to extract at the same rate. Thus, it's not noise, but it is complicated.
[0] q.bio
[1] https://fintualist.com/chile/ciencia/los-efectos-de-las-pole... [2] https://mathstodon.xyz/@tao/114956840959338146
There are some notable exceptions -- Donoho, Vershynin -- but most of them are doing good old fashioned Brunn-Minkowski theory, which is fundamental but a hard sell in its most truthful form.