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.
But have the scans got cheaper?
It’s possibly that acceleration techniques have prevented the cost being greater, but key parts of the cost are not getting cheaper. Staffing costs are just so high.
Pricing a scan based on scanner time doesn’t really work.
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.
fMRI is a step above dowsing rods. It's plugging a multimeter into an outlet and guessing what type and brand of appliances you are running in your house.
I was at a talk maybe 15 years ago in which the speaker gave pretty convincing evidence that given a time series of voltages you could learn a lot of things about what kind of appliances you've got running.
There are a lot of devices that have reasonably distinct patterns to their power consumption. Motors- especially well pumps, but also large central air fans and some others- are going to look very different from a microwave or vacuum cleaner or refrigerator, especially if you have time of day on your readings.
Constant lower draw devices- chargers, lights, speakers and such- are going to be harder to distinguish, though.
I'd say you're right about any given individual channel: the activation of a single voxel doesn't tell us much about all the fancy computation happening in that ~1 mm^3 of tissue.
But the pattern of activity of thousands of voxels across cortex does contain reliable information! And a decent amount of it too, at least in sensory cortices.
Caveat: brain-computer interfaces are not quite my field, but I think the consensus is (judging from some conversations with folks who know more):
Neuralink is doing interesting BCI research, with decent hardware, but it's not really a step-change above and beyond the rest of the field.
There's definitely a lot of promise in using BCIs for rehabilitation of patients with brain injuries but their input-output capabilities are still incredibly crude: for example, we can't reliably "write" to the brain to make people perceive things beyond very simple stimuli (e.g. a phantom touch sensation, or a visual phosphene).
This is understandable: the brain has a bajillion neurons and we only have ~1,000 electrodes that aren't particularly precise in how/where they zap the brain---and even if they were, we don't really know well enough how the brain works to "control" perception finely.
Other problems for BCIs include (i) "representational drift", where the brain's code changes over time, so you need to keep fine-tuning your interface in some sort of closed loop fashion and (ii) damage/scarring to neural tissue.
> Is there enough signal for this to really work?
I'm not quite sure what Neuralink's marketing claims are, so I'm not sure what you mean by "this" here. But intracranial electrodes do have a surprising amount of signal, especially relative to non-invasive methods (I'm currently collecting some iEEG data myself!)
I really want the sci-fi future where we have brain-computer interfaces that augment our cognition and perception, but we're nowhere close---though we're getting better.
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?
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 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.
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.
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).
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.
I'm not convinced this is a problem. For example, all the folks who developed convex analysis for its pure geometric and mathematical beauty in the land of pure Platonic forms, well their work was still useful downstream for all of us doing convex optimization and dealing with log-concave probability distributions. So no harm, no foul.
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.
Between this and blipped-CAIPI in 2011, there hasn’t been much change from an acquisition perspective in the industry. Mostly everyone shifted to AI reconstruction, workflow improvements, and reducing helium use. Those are the low-hanging fruit. I’d be happy to be proven wrong but I don’t see any major breakthroughs coming from advanced math in the near future. ISMRM was this week though so maybe something came out of it.
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.
Our universe is multi-dimensional and we are only 3 dimensional. The only way to understand more about our universe is to try to understand multi-dimensions.
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.
It would be instructive to actually look at the studies in question and whether or not they were odd or esoteric.
It’s probably more
But have the scans got cheaper? It’s possibly that acceleration techniques have prevented the cost being greater, but key parts of the cost are not getting cheaper. Staffing costs are just so high.
Pricing a scan based on scanner time doesn’t really work.
Sounds more like the point is that math research has high ROI compared to most federally funded research
As the Soviets knew, apparatus are expensive but pencils are cheap.
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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.
[1] https://journals.plos.org/ploscompbiol/article?id=10.1371/jo...
Hasn't fMRI as a whole been called into question? https://www.nature.com/articles/s41593-025-02132-9
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.
[1]: https://www.nature.com/articles/s41598-025-89242-3 [2]: https://www.biorxiv.org/content/10.64898/2026.04.21.719913v1
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.
fMRI is a step above dowsing rods. It's plugging a multimeter into an outlet and guessing what type and brand of appliances you are running in your house.
Have you heard of time-domain reflectometry? A $20,000 multimeter could have the "impossible" feature you describe all but built in.
I was at a talk maybe 15 years ago in which the speaker gave pretty convincing evidence that given a time series of voltages you could learn a lot of things about what kind of appliances you've got running.
There are a lot of devices that have reasonably distinct patterns to their power consumption. Motors- especially well pumps, but also large central air fans and some others- are going to look very different from a microwave or vacuum cleaner or refrigerator, especially if you have time of day on your readings.
Constant lower draw devices- chargers, lights, speakers and such- are going to be harder to distinguish, though.
Turns out it's a (somewhat) active area of research.
https://ubicomplab.cs.washington.edu/pdfs/electrisense.pdf
https://www.researchgate.net/publication/266461208_Multimedi...
https://www.mdpi.com/1996-1073/14/9/2485
I'd say you're right about any given individual channel: the activation of a single voxel doesn't tell us much about all the fancy computation happening in that ~1 mm^3 of tissue.
But the pattern of activity of thousands of voxels across cortex does contain reliable information! And a decent amount of it too, at least in sensory cortices.
Try it with a crude task - eg finger tapping. It’s pretty convincing.
Could you share your thoughts about neuralink? Is there enough signal for this to really work?
Caveat: brain-computer interfaces are not quite my field, but I think the consensus is (judging from some conversations with folks who know more):
Neuralink is doing interesting BCI research, with decent hardware, but it's not really a step-change above and beyond the rest of the field.
There's definitely a lot of promise in using BCIs for rehabilitation of patients with brain injuries but their input-output capabilities are still incredibly crude: for example, we can't reliably "write" to the brain to make people perceive things beyond very simple stimuli (e.g. a phantom touch sensation, or a visual phosphene).
This is understandable: the brain has a bajillion neurons and we only have ~1,000 electrodes that aren't particularly precise in how/where they zap the brain---and even if they were, we don't really know well enough how the brain works to "control" perception finely.
Other problems for BCIs include (i) "representational drift", where the brain's code changes over time, so you need to keep fine-tuning your interface in some sort of closed loop fashion and (ii) damage/scarring to neural tissue.
> Is there enough signal for this to really work?
I'm not quite sure what Neuralink's marketing claims are, so I'm not sure what you mean by "this" here. But intracranial electrodes do have a surprising amount of signal, especially relative to non-invasive methods (I'm currently collecting some iEEG data myself!)
I really want the sci-fi future where we have brain-computer interfaces that augment our cognition and perception, but we're nowhere close---though we're getting better.
> Hasn't fMRI as a whole been called into question? https://www.nature.com/articles/s41593-025-02132-9
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?
fMRI is noisy, but there is definitely signal.
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 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.
I was expecting a link to this paper https://www.sciencedirect.com/science/article/abs/pii/S10538...
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.
[1] https://fintualist.com/chile/ciencia/los-efectos-de-las-pole... [2] https://mathstodon.xyz/@tao/114956840959338146
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).
[0] q.bio
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.
I'm not convinced this is a problem. For example, all the folks who developed convex analysis for its pure geometric and mathematical beauty in the land of pure Platonic forms, well their work was still useful downstream for all of us doing convex optimization and dealing with log-concave probability distributions. So no harm, no foul.
> by casting the uniform measure on convex bodies in the language of log-concave densities
Can you tell more ? I find the idea very intriguing. I don't know of the connection between the two.
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.
Given that this was published nearly a decade ago, I'd be very interested to see what the SOTA is today.
Between this and blipped-CAIPI in 2011, there hasn’t been much change from an acquisition perspective in the industry. Mostly everyone shifted to AI reconstruction, workflow improvements, and reducing helium use. Those are the low-hanging fruit. I’d be happy to be proven wrong but I don’t see any major breakthroughs coming from advanced math in the near future. ISMRM was this week though so maybe something came out of it.
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.
It may be a funding pitch, explicitly. It's not a paper - it has no abstract, no citations, works cited, etc.
That must be the thing that Terence Tao advertises in every podcast I watch with him in it.
Our universe is multi-dimensional and we are only 3 dimensional. The only way to understand more about our universe is to try to understand multi-dimensions.
quick scroll and saw no math in the paper
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