I use conditional formatting to color cells according to the probability that I can lift them—if I lifted 50kg for 10 reps then I can definitely do 50kg for 9 reps, so that cell is green. But if e1RM(50,10) > e1RM(40,15) then I can probably do that too so it's light green. The visualization naturally becomes Pareto-like.
If I'm feeling strong I can aim for higher weight, lower reps. Or if I'm feeling weak I can close out a (weight, reps) that's below my current e1RM but I haven't accomplished yet. The end result is that I'm always "accomplishing" some sort of PR no matter how I feel.
I call this e1RM Bingo.
My main finding for “pick whatever weight you want today” was that picking a lot of different weights made the curve less identifiable, so my latest iteration encourages you to pick a ladder for a few sentinel exercises per mesocycle in order to improve the statistical power. In addition, strength improves more quickly at >80% of 1RM, and hypertrophy depends on proximity to failure, so if you pick a lower weight, you really need to go to failure, which burns you out for the rest of your session, where leaving 1-2 reps in reserve is probably sufficient for hypertrophy and leaves a lot more gas in the tank for the rest of the session. Definitely open to suggestion/discussion here.
https://curvefit.app (it runs on Cloudflare free tier, so I won’t have to start running ads or charging until I hit a couple thousand users)
If pursued, good luck!
Please don't make an app based on this.
Some nuance here: the latest research shows that proximity to failure is the main hypertrophy driver regardless of load and rep count; high rep count makes proximity to failure harder to gauge; so high load/low reps close to failure is probably better for hypertrophy (there are other good reasons to do higher reps/lower load work though)
If you want the most 'optimal' form of this (aka, hell on earth), you should purchase a rowing machine. Being able to engage with very aggressive, full-body exercise every single day without exceptions is almost like cheating biology. You can maintain a 2-3x VO2 max premium over your peers with very little risk of injury.
But they go even a step further, they extend into 3 dimensions to also add body weight as a variable. So your graph would really have to be a 3D volume. Because different levels of body weight have different capabilities.
Maybe in vein but did anyone already figure this one out? The closest I got was PT sans, open-licensed commissioned by the Russian ministry for communication (I found it surprising that a country that doesn't use Latin script made the best font!), but it's not widely shipped so you need to figure out how to include font files whenever you want to use it
"The Pareto Front today claimed responsiblity for...."
[1] - http://montypython.50webs.com/scripts/Life_of_Brian/8.htm
ss02 disambiguation seems to be the one I'd be wanting to turn on, with tnum for monospace numbers being a good option as well that I hadn't even realised I wanted from a font!
Tabular numbers are awesome!
Anyways I'll namedrop Iosevka as perfect monospace font for working on 13" laptop
They apparently released Hyperlegible Next in 2025 which, flipping between tabs on Google Fonts (since the original website doesn't show the fonts), is nearly identical but has five new weight settings (nobody should imo ever use thin fonts though, it noticeably harms readability for me and my sight is only the tiniest bit below normal vision, but ok it's an option) and improved kerning (the original font had extremely little space between 'll', for example)
The 2025 version sadly doesn't ship with my version of TexLive, but the original (from 2020) already does so that makes it easy to use as well! Cool stuff, thanks for the tip :)
When explaining it to some coworkers, I stumbled on a fairly intuitive explanation: "I've run farther before, and I've run faster before, but I've never run _this_ far, _this fast."
There was some pushback about why not just call it a PR (personal record), but I would only use that term for fixed distances (1mi, 5k, 10k, etc.) or a consistent route that I've run many times before. Nobody would say "I set my 7.40 mile PR today." More importantly, it misses the comparison to all farther (and faster) runs—it's not exciting to set a 5k PR just because you've barely run that distance before, and the pace is actually slower that a 10k you've done.
(Had a Pareto run of 7.40 miles @ 6:28/mi last week!)
ChatGPT 5.6 Luna on the right (cheaper) cover most of the frontier, with a point for Deepseek flash, and higher performance overlapping heavily between 5.6 Sol and Fable.
That DeepSeek point will probably move back towards Luna as deepseek announced a "significant" price increase coming to their API [1], which kind of demonstrates that beating the Pareto frontier is where the difficulty actually is).
[1] https://www.bloomberg.com/news/articles/2026-08-06/deepseek-...
I think it's great and hope the price can stay the same.
Going from 81GB of weights to 79GB of weights can mean a 50% reduction in GPU capacity required.
If you can fit a model in just one GPU (or rack) as opposed to across an entire datacenter, the latency gains can be substantial too. If you can reduce token latency by half, that would double the amount of customers you could support.
As the number of objectives (dimensions) increases, the number of samples you need to cover the frontier increases exponentially. You will very rarely find solutions that actually dominate other solutions in many practical optimization scenarios. With 2 dimensions you have a 25% chance of domination. With 10 dimensions it's a .098% chance.
The most useful cases I've seen tend to occur where we just optimize for two things at once. The chances of domination are high, it's easy to visualize and very efficient to implement. As we get into higher dimensional spaces, things get weird really fast.
The geometric problem of computing a d-dimensional Pareto set of cardinality n
https://en.wikipedia.org/wiki/Maxima_of_a_point_set
has a truly weird property not covered by the computational complexity discussion on that page. It says there's an algorithm achieving O(n log(n)^(d-3) log log n), which is true and also a lie. The algorithm that achieves that asymptotic form is a galactic algorithm; and not an ordinary one in the sense of "has a large constant multiplicative factor", but one with this property (I've never found any other algorithm which exhibits it):
The runtime is within a bounded constant factor of n^2, for all n up to some critical N whose size is exponential in d (I think it was exactly 2^d or something).
I.e. the runtime has "two shapes": it's purely quadratic up to a galactically-large constant, and thereafter has a transition into to a slower function. The asymptotic version in the textbooks isn't achievable in the real world (for all but very small dimension).
There's an elementary proof using generating functions.
edit to add: If anyone's curious about it, a simplified version of the recurrence relation that's enough to exhibit this behavior (you can instantly see it if you graph this numerically) is
f(n,d=0) = 1
f(n=1,d) = 1
f(n,d) = n + 2f(⌊n/2⌋, d) + 2f(⌊n/2⌋, d-1)I've built large, deep product evaluation frameworks, and it is 100% of the time a running argument with stakeholders, inside and out, "well you should have measured it this way" or "I think we should be targeting X not Y" or "why didn't you consider Z in the metric??"
The Pareto Front in practice is squishy, fuzzy, and often quite moist and moldy.
As you say, the most useful things happen in low-dimensional spaces.
The 80/20 “rule,” as far as I know, is meant to be descriptive after the fact. It can’t be used as a planning assumption. To be fair to those managers, they don’t really mean to be rigorous. They are just trying to justify cutting scope.
Is your planet accepting immigrants? I think I'd like it there
If one option is at least as good on every relevant dimension and better on one, just pick it. That's not really a trade-off, and it shouldn't need escalation. Eg, if two SaaS tools cost the same and have similar support, but one fits your use case better, you choose that one. Otherwise, you just suck at your job!
The interesting decisions only start once you're already on the frontier, where getting more of one thing means giving up something else. If the better tool costs 50% more, now you're trading capability against cost, and that may need sign-off.
Basically, everyone should be able to get to the frontier on their own. Coordination and arbitration at higher levels of the org / between different departments should happen on the frontier, where the trade-offs involve several people or teams.