Antifragility in complex dynamical systems | Hacker News Reader

Antifragility in complex dynamical systems

nature.com

173 pointsRafelMri113 comments

I've found that intentionally causing abrupt (but reasonable) changes to hyperparameters in evolutionary spiking neural network simulations (I.e between each generation) results in far more robust simulations that will meet fitness criteria with less likelihood of getting stuck somewhere. The tradeoff being that simulating will take longer, but this may be worth things like reducing the chances of your resource requirements going asymptotic half way through.

My current method of perturbation is to cap the total # of activations per candidate globally. When at least 3 improvements in the best global fitness score have been achieved, I cut the global activation limit in half. Obviously, this is fairly catastrophic for the current population. Each generation can increase the limit by 1% if no improvements made. This provides aggressive selection pressure for more efficient networks and forces a different kind of partial restart of the training process (I.e. do what you just did with 50% resources now). Very often this does result in optimization of the network. It also seems to make the networks rebound faster after restarts. At first, a restart can take 10-20 generations to recover. By generation 1000, this is closer to 1-2.

I am quite curious about your approach, Do you have an example code somewhere?

I'd start here: https://arxiv.org/abs/2406.12552

I will say that less is more and "The Bitter Lesson" applies here. Chasing biologically-inspired rabbits, such as STDP and LIF (see paper above/wikipedia), does seem to be a waste of time, especially when we have this thing entirely outside of biology that can arbitrarily replicate, serialize, mutate and simulate billions of instances of the same parent candidate in minutes-hours.

Leaky charge carriers and inability to persist learned weights between candidate instantiations are limitations, not features to emulate. Imagine if you could be reincarnated with all of the exact knowledge you have today. Then clone that 1000 times and apply subtle mutations to it. Then, put these clones in an FFA arena and see who wins based upon a very well crafted fitness function. Then, do all of that over and over thousands of times per hour.

>Chasing biologically-inspired rabbits, such as STDP and LIF (see paper above/wikipedia), does seem to be a waste of time

Unless physiological compatibility with a biological brain is considered an interesting endpoint? If you think about Neuralink for example, wouldn’t it be interesting if our brains could directly engage the model? Not just a translation layer but perceive it directly and natively though some kind of synaptic modem that converts analog exchanges of neurotransmitters to the synthetic network in the digital domain.

> Unless physiological compatibility with a biological brain is considered an interesting endpoint?

Excellent point. I am focused entirely on synthetic simulations without biological integration (for now).

I think that could be an interesting next step - determining a way to modify a SNN that was trained in a synthetic time domain such that it can process real time signals. Training these things online is not really an option. You have to run a large # of offline simulations before you can find the right networks. Learning rules like STDP could theoretically address the online learning problem, but I couldn't find any traction down that path yet.

I had heard about spiking neural networks but I didn't really think about them until your post here. Lately I've been kind of deep diving into biological neurons (just a lay perspective) and what we know about their mechanism of action at the individual cell level. I'd also just watched the 8hr episode of Lex Fridman's podcast with the folks from Neuralink, so my brain was primed to make this connection and holy moly it's exciting to think about the possibilities.

Thanks for sharing your work, would love to see a post on here down the road when you've found some light in the dark forest.

> Lately I've been kind of deep diving into biological neurons (just a lay perspective) and what we know about their mechanism of action at the individual cell level

I've been doing the same for a long time, it's a really fun and interesting topic. I really like reading about each new discovery about something that is computationally important, people don't realize how complex a neuron is and that the scientists don't have the full picture yet.

If you haven't looked into it, check out how astrocytes are involved in computation (e.g. visual processing), their internal calcium wave signaling and their control of neurons.

> Then clone that 1000 times and apply subtle mutations to it. Then, put these clones in an FFA arena and see who wins based upon a very well crafted fitness function. Then, do all of that over and over thousands of times per hour.

I spent many years on an ALife+ANN simulation that did this. For each new generation, I kept the top X% unchanged, the next Y% were changed a little, next Z% changed a lot, etc.

It was pretty fun and I wish I had the time+money to continue on a larger scale.

Very cool, but I'm surprised you're sharing this on here and not in a job interview with a deep learning startup and/or an arXiv paper.

> a job interview with a deep learning startup

I am not aware of any DL startups that are interested in techniques which are incompatible with GPUs and back propagation. I think this is a solo journey through the dark forest for now.

Eloquent, realistic, and sad. I'm living my own version of this (in biotech). The journey is the wonder.

Correct me if im wrong, this is just a question originating from my own curiosity, but could you not apply the same or similar techniques to classical NN architectures? I dont see exactly how the differentiability of the architecture matters? I.e. in between epochs randomly perturb weight values (similar effect I understand to introducing scheduled noise or non-isomorphic transforms on the features), implement a scheduled causal drop in/out scheme etc? I know of people that train models these ways as a form of regularisation and they claim better fits too.

Enjoy your adventures in the Dark Forest.

> I dont see exactly how the differentiability of the architecture matters?

I don't know that classical architectures are infeasible to perturb as noted in other comments. I just think we have a really interesting knob to turn in this specific case that doesn't seem to exist in other architectures.

How would you go about constraining the resource consumption (by up to half!) of a classical ANN while preserving realistic hopes that it will recover between training epochs? And, we are talking real resource reduction here not some academic thing. You can see the difference in task manager. That's actually the primary tool I've been using to determine how to tune the parameters of this scheme.

There has been some work to dynamically reduce the compute required by a network.

See for example: https://arxiv.org/abs/2404.02258

They have a fixed compute budget which is lower than what the LLM need, and dynamically decide to allocate this compute budget to different part of the network.

So its not exactly what you propose since here the compute budget is fixed (that's the point of the paper: to make the network learn how to allocate the resources by itself) but its dynamic for each part of the network, so it shows that its possible.

> I think this is a solo journey through the dark forest for now.

In academia there's quite a bit of stuff on neuromorphic computing going on.

Your surprise breaks my brain. Why would someone "keep it to themselves" outside some white paper they won't have time to promote or for a job interview that they might not need?

Is your thought that it is some novel approach that nobody is doing and has obvious market implications? Even then, the implications matter only if you are in a position to take advantage.

The Internet used to be a place people shared cool shit because it was cool, not for some monetization scheme or personal gain beyond the joy of sharing. Content creators (as a job) and hustle culture are a blight.

They are sharing it here?! It’s not like OP is keeping it to themselves

As I'm sure you're aware deep learning work better is the most hot and highly funded thing right now... there is nothing wrong with making sure you get the credit for a new technique, and it in no way precludes widespread free sharing of the idea.

I am an academic researcher (not in this field) and everything I do is 100% free and public, but I still either patent or publish it, because getting the credit is what allows me to keep doing what I love. I actually hate that part, and would rather just do the work, but I already push that line too far sometimes, and risk losing my funding aka "publish or perish."

Respect to the OP as spiking networks are a different domain, but the field of Graceful Degradation and Perturbations itself is almost older than the field of Neural Networks itself. Generally, the bitter lesson occurs - these techniques show some kind of useful robustness at parameter M, but fail to show as much of a useful robustness relatively as parameter M*100. For example, before attention, using Drop out (in essence a form of forcing robustness) was one of the most common techniques. The quality of robustness or its resulting sub parts (e.g. the tradeoff between precision and recall) is incorporated as a measure in some of the fields basic scores, such as harmonic F1 score.

Still it, like alternate activation functions, data beyond matrices and vectors and non-linear networks, remain very unstudied.

Firstly, I'm coming at this from the pint of view of standard feed forward NNs, rather than spiking neural networks, so apologies in advance if I am way off-base.

By global activation limit, I assume you mean the total sum of neuron activation during one forward pass? So halving it would strongly encourage sparsity? How do you enforce the reduced limit? Just put it in the loss function? Or does the spiking nature allow you to "sparsify" the spiking by raising a threshold?

Very very interesting stuff. I'm working with differential evolution, and incorporate correlation measures between candidates to (try to) allow for multiple divergent solutions, and it also feels fairly off the beaten track, compared to mainstream AI. But who cares, let's enjoy the dark forest! :-)

> By global activation limit, I assume you mean the total sum of neuron activation during one forward pass?

Yes. For each candidate network I keep a counter of the total # of neuron activations. This figure is constrained by a global limit (which varies based on prior performance). We simply break out of the simulation loop once the allotted resources are exhauted. This means that more efficient networks are more likely to score higher.

> I've found that intentionally causing abrupt (but reasonable) changes to hyperparameters in evolutionary spiking neural network simulations (I.e between each generation) results in far more robust simulations that will meet fitness criteria with less likelihood of getting stuck somewhere.

If I understand you correctly this is similar to the philosophy behind simulated annealing isn't it? The idea being that adding some peturbation can be enough to jog the evolution out of local minima and you probably want to reduce the amount of those jogs over time so it ends up converging.

https://en.wikipedia.org/wiki/Simulated_annealing

Not op but what they described is indeed sim annealing coupled with relaxing feedback loops. This approach would in theory result in prevention of stagnation, forced adaptation and over time, creating some form of resiliency. Pretty cool stuff!

I was actually thinking about simulated annealing as I got into this.

I've found that reducing this specific mode of perturbation over time has not been necessary. The simulation will oscillate its way right into a perfect fitness score assuming everything else is good.

Convergence seems to rely much more heavily on the quality of the fitness function and population management (i.e. size, selection criteria, mutation strategies). I apply random mutations to delays and weights, but using a spectrum of mutation each time (I.e. some clones are heavily mutated while others are barely touched). This spectra of mutation is constant all the way through the simulation.

Some of you may die... But that's a sacrifice i'm willing to make.

Random note: Antifragility is called hormesis in living organisms, a concept that existed since the 1950s when the wrong dose - too low - of herbicides made the plants stronger.

Mechanical engineering uses the term system resilience. I must admit I don't like antifragility, which sounds like a novlang and is poorly defined.

Resilience is not the same, a system is anti-fragile if it gets stronger under stress.

Resilience is just "not getting weaker".

Pedantically-not pedantic, but isn’t resilience the ability to quickly recover?

The first graphic in the paper has a good illustration of the differences between fragility, robustness, resilience, adaptiveness, and antifragility: https://www.nature.com/articles/s44260-024-00014-y/figures/1

When enduring successive hurricanes the most worthwhile effort might be to improve antifragility on more of a continuous basis than even recovery itself.

You can definitely benefit by increasing your antifragility in the face of a second hurricane long before recovery from the first hurricane has been very well completed at all, no matter how focused the recovery effort.

I never thought people needed a new term to be coined for this, but it doesn't sound so bad when you think about it.

It's just one of the things you inherently know your whole life.

I think you mean resilient or robust, not antifragile. I know of no building which gets stronger under/after hurricane force winds.

No, but the community and relevant economy can.

Exactly.

Plus the individual may have to make progress without a community or economy to fall back on.

Whether you have a building or not.

But you can do that with a simple growth model? Larger systems can already withstand larger shocks that would have been fatal when they were smaller.

Antifragile is a bit odd, the idea is supposed to be things that get stronger because of the shocks. Think how your muscles grow specifically from micro tears. In that regard, they must have resistance to grow. Though, I think that also misses on some of the definition?

Really, the more I try to defend the idea, the more I question it. :(

I'm not sure why you're talking about the size of systems, maybe I missed something.

I think the point is that the systems become stronger with negative stimuli. The community and relevant economy become stronger only because of the hurricane. They would not have done it otherwise.

I meant only that larger town/cities can take hurricanes a bit better than smaller ones can. Same reason that large trees weather the storm better than smaller trees do. If you increase the size of the system/thing, then it necessitates larger negative stimuli in most cases. Consider the size of a wave that would topple a canoe versus standard war ships.

At any rate, this is a hard analogy to stick with as it isn't the hurricane that makes things stronger. It is being ready for the hurricane. And, yeah, you can argue that getting hit by hurricanes is why the city was prepared, but that is kind of silly. Are non-coastal towns that don't have to evacuate for large storms somehow weaker than the ones that do? Not really, they are prepared for other shocks.

Again, muscle growth would kind of follow an antifragile model. In that you have to have some resistance for most growth. Maybe the old SR-71 was an even better example. Literally needed the resistance of flight so that it wouldn't leak. The saying for it was the faster it went, the faster it could go.

> I meant only that larger town/cities can take hurricanes a bit better than smaller ones can. Same reason that large trees weather the storm better than smaller trees do. If you increase the size of the system/thing, then it necessitates larger negative stimuli in most cases. Consider the size of a wave that would topple a canoe versus standard war ships.

I don't know anything about that but it's an empirical question that you can't answer with a priori reasoning like you're trying to do. We need actual data.

> At any rate, this is a hard analogy to stick with as it isn't the hurricane that makes things stronger. It is being ready for the hurricane.

No, the point was that they are not ready the first time, but they are the second time. The hurricane is what causes them to be ready the second time. If their preparations were not good enough the second time, they will be even better the third time.

I'm not sure I follow. You don't need heavy logic to explain why a single person can capsize a canoe rather easily, but would be unable to capsize something like a ferry.

As a similar example, we know that you can't just scale up an ant body to be human sized, as it would crumble under its own weight. Look up the "square-cube law". Same basic idea, in many ways. Ratios and scale just don't hold as things grow.

Back on the cities and preparing for a hurricane, this is not that they are stronger because they were hit by a hurricane. By this logic, you couldn't have a new coastal town that can weather one. After all, they weren't made stronger by the first hit. I think we can agree that is silly logic? If you know what forces you will get hit by, you can build anticipating them.

This is too close to the phrasing that "what doesn't kill you makes you stronger." Which, frankly, is mostly nonsense. Many things can weaken you to the point that what didn't kill you this time let something else finish you off. Its cute, but largely presupposes growth between hits that has to happen.

"What doesn't kill you makes you stronger (for certain types of systems)" is the actual point.

Right, and I said that is cute, but mostly nonsense. There are no systems that can take arbitrary hits without ending. And as soon as you acknowledge that this only works by spurring growth after the hit, you are back to tolerances and growth.

I mean you can go and argue with the biologists and economists if you need to. I'm just delivering the meesage.

My argument here would be that this isn't that new, all told? And... I would be shocked to find a lot of disagreement there. Indeed, other threads are already pointing out that terms already existed that covered this general idea.

My problem with antifragile, as often offered, is that it is positioned as something that gets stronger from being damaged, full stop. But... there is literally nothing on earth that would withstand the sun going nova, so that there are obvious limits to the idea. And if you accept that it is something in limits, you are back to model ideas of feedback and growth. And as you get back to that, you cover a lot of the same ground as many other discussions.

It is a cute model, mind. And somewhat fun to play with. Also worth knowing that some systems will react violently to small changes. Think flashbacks in building fires. It just doesn't bring much new to the table, all told.

Edit: I meant to add "fair enough!" at the top of this. Is a valid point to make! :D

I guess it's important that the negative signal be relatively small compared to the affected system, like antivenom doses, but also it needs to be predictable/differentiable to some degree. If two different doses of venom never had the same molecular patterns then it would be impossible to immunize against it.

A one-time supernova event would destroy a solar system, but the universe itself is antifragile to supernovas, and actually has built emergent spatiotemporal structures which depend on supernovas as part of their lifecycle. New solar systems rise up from old supernovas.

Predictability/differentiability of internal and external states is key for building robust systems, negative signals alone are often just detrimental. You can't learn from chaos.

Right. If you have systems that can adapt to stimulus in ways to prepare for recurring stimulus, you can look like this antifragile system. If the answer is to just be bigger... It is not a compelling model.

So building your immunity by using low doses doesn't mean you are antifragile. It means you are trainable. And even then, you are within tolerance levels. And cannot ever withstand some poisons.

Indeed, training is largely rehearsing some specific stimulus to be ready for it in a non training environment. We don't think of athletes as antifragile, though. Do we?

I don't think it's very common to experience antifragility outside of abstract complex systems such as economic markets. My intuition is that physical systems which exhibit antifragility tend to be metasystems, and the antifragility is described in the context of achieving specific states of subsystems.

For example, with the universe in relation to supernovas, we can say that a supernova wipes out a solar system. But new solar systems then take their place, with a different metal distribution that may be more conducive to advanced intelligence. If advanced intelligence is the goal, we might say that the universe is antifragile to supernovas, or more generally to the effects of gravity.

However, it's definitely a matter of perspective given that supernovas themselves are entirely inconsequential to the universe as a whole, and are only relevant to subsystems at specific emergent layers within the universe.

We could also form similar conclusions about natural evolution in general.

We might even be able to generalize further and posit that there is a natural tendency for order to arise out of chaos, and so order itself is antifragile to chaos, given that order thrives under the right chaotic conditions[0] and isn't simply immunized against it. So antifragility may exist as a fundamental property of the foundation of stuff, but it's not automatically an inheritable property of subsystems.

It all becomes very abstract, but at least we can define some constraints, namely that antifragility should be described in terms of optimization goals and measurement of specific states, and are thus subjective to the observer and not an innate property of the universe or any other system.

[0] https://en.wikipedia.org/wiki/Edge_of_chaos

My intuition is that antifragile is often mistaken for controlled/directed growth. In that it works well in examples where things are able to die off and to be regrown. Muscles, in that regard, are able to withstand tears and are able to grow back. They will do so largely where they were torn.

That said, loving this exploration of it! Thanks!

There are limits. It's not about arbitrary negative stmuli and the entire idea only applies to certain kinds of systems. These criteria are covered in Taleb's books. The limits are well known in biology.

I read his books. Will try them again sometime.

My gut is my main gripe is with many of the examples used. They often ignore that they are all on things that are in a healthy state of growth and that what is largely happening is that growth is refocused based on stimuli. More, there is no guarantee that you can refocus growth based on feedback in a way that will be ideal for future stimuli.

Which, I confess is silly for me to really get upset about. Luckily, I'm confident I'm sounding far more upset on this message board than I am on it. :D

Resilience is the ability of not having a (catastrophic? depends on who is defining) failure when the situation changes.

Resistance is the ability of not requiring any adjustment to avoid a failure when the situation changes.

That antifragility term, that yeah, is the same as hormesis is the ability of increasing your fitness when the situation changes (in unpredictable ways).

A machine that has very thick parts is resistant. A machine with redundant parts that you can fix is resilient. A machine whose builder is always learning from failure and improving is antifragil.

Ok I looked it up. It is to withstand or recover quickly, or the ability to spring back into shape; elasticity. (Oxford American)

Or even getting weaker slower than others

It is something that Taleb proposed and given a name for - given 'fragility', 'antifragility' makes sense, since it isn't resilience (he discusses that).

https://en.wikipedia.org/wiki/Antifragility contains a mathematical heuristic of the term applied to some function.

That's what immediately came to mind when reading OP's comment. He's basically describing the action of perturbing a system just enough with a weak force that it 'innoculates', for lack of a better word, itself against similar but stronger forces.

So in a nutshell, making sure our robots are vaccinated against errors.

This presentation by Todd Becker titled How Hormesis Works: The Biology of Beneficial Adaptation to Stress is a great introduction to the subject with some practical advice - https://www.youtube.com/watch?v=NDm_guQfESA

Also see his Desirable Difficulties: Using Hormesis to Learn More Effectively - https://www.youtube.com/watch?v=Zc0PZe08Ues

  Systems or organisms can be defined as antifragile if they derive benefit from systemic variability, volatility, randomness, or disorder.

If that's a riddle, death fits. Those things are characteristic of the pestilence, famine, war, etc. that feed death. The decay surrounding death is complex and dynamical. And death is more sustainable than any living system.

but death isn't a system or organism...

>but death isn't a system

death is entropy. do you know of a system without entropy?

>or organism...

boy are you going to be surprised when you answer that knock on the door, eh?

Isn’t it definitely not an organism? If death is the inevitable process from order to disorder, isn’t it deeply a-systemic at its core? If it were a system, it would also eventually have to end.

Arguably it does, the heat death of the universe option would spell the end of entropy, and the end of death (unless you believe in a conformal cyclic universe)

Actually yeah fair enough; I’ll grant that death may be a system.

A complex dynamic system has a large number of working parts, and responds in specific ways to inputs and stressors. It just doesn't make sense to think of death itself as a "complex system." They are certainly related- I think death could be seen as an event that irreversibly dismantles a complex system in some way, such that the parts no longer function together as a system.

I was thinking of systems more as just processes that have low-entropy behavior, i.e. those that are predictable in some meaningful way. If one takes the process of death, which is really a behavior of any low-entropy system, to be its own object, I do think that object would be a system under my definition. I agree that yours does not come to the same conclusion, and perhaps my definition of system is too broad.

I didn't say that complex systems can't die, I said death itself is not a complex system. Antifragility is specifically a property or behavior of a complex system. "Death" can't anymore be antifragile than the color red can be.

you are an organism that is continually dying.

https://en.m.wikipedia.org/wiki/Autophagy

https://en.m.wikipedia.org/wiki/Secondary_succession

https://en.m.wikipedia.org/wiki/Restructuring

https://en.m.wikipedia.org/wiki/Code_refactoring

https://en.m.wikipedia.org/wiki/Shiva

https://en.m.wikipedia.org/wiki/Tandava

it's all the same shit

That entirely misses my point. Antifragility is a property complex systems can exhibit. Concept systems can also 'die' but the concept of death isn't itself an example of a complex system.

So life as a system benefits from the randomness — but inevitableness — of death, is how I interpret that. Benefits as in, key to its continual perpetuation.

The whole conversation is very scope dependent. A species can be antifragile specifically because the constituent organisms are fragile. The species evolves not in spite of death and mutation (variation) of the organisms but because of it.

At the same time organisms themselves can be antifragile at a different scope. My body gets stronger when I stress the muscles, and gets weaker when I do not.

Edit to add… it is also very dose dependent. Zero muscle stress and I get weaker. Some and I get strong. Too much and I get rhabdomyolysis — an absorbing barrier.

Same goes for the species. No death means no evolution. Some means evolution. Extinction level deaths are an absorbing barrier.

What's the benefit derived from death? I'd suggest death is simply the terminal state that most systems find themselves in after a sufficiently long period of time has elapsed or they've experienced a set of inputs outside the range they were designed to handle and keep operating.

Entropy always wins

decay exists as an extant form of life

I wish folks would write more plainly. “Antifragility characterizes the benefit of a dynamical system derived from the variability in environmental perturbations.” Geish.

Well it is in a journal called "complexity." But I agree, that sentence is awful, I'm surprised they decided to lead with it, and nobody proof reading the paper objected.

The leading three authors are from Germany, Mexico, and Switzerland resptfully.

The sentence they want should capture the notion of being robust when poked with a stick.

A pencil on it's tip is a fragile system, one burp and it falls to the table, far from the intial state. Marbles in fruit bowls are anti-fragile, given a good shake (up to a threshold) and they remain in the bowl and return to the low centre.

Reading further, they want more; that repeated perturbations should deliver benefit, that systems in an warped egg carton configuration can be annealed to reveal an optimal point by vigorous shaking slowly reduced in degree.

Having now read the whole paper it doesn't seem novel wrt to the state of dynamic system discussions in the mid 1980s other than the insertion of "antifragility" as nomenclature into the mix.

> A pencil on it's tip is a fragile system, one burp and it falls to the table, far from the intial state. Marbles in fruit bowls are anti-fragile, given a good shake (up to a threshold) and they remain in the bowl and return to the low centre.

I believe what you're describing is a stable vs unstable system, not fragile vs antifragile.

You can perturb a bowl with a marble, and the marble will still end up in the middle because it will return to stable equilibrium point (an "attractor"). Yours is an illustration of a stable system. Whereas a marble placed in an upside down bowl (with no ridges, just a half sphere), when perturbed, will fall off. This is an unstable system. These are classic examples used in (Lyapunov) stability theory.

Fragility and antifragility aren't about stability (returning to equilibria), but gains or losses after perturbation, which is related to convexity/concavity.

When you perturb an anti-fragile (or convex) system, it doesn't return to equilibrium but in fact improves. Conversely, when you perturb a fragile system, it degrades. The analysis is usually done with Jensen's inequality rather than Lyapunov.

EDIT: not sure why the downvotes. I'm pointing out a fact. The examples do not demonstrate antifragility, but stability, which is not the same concept.

You appear to have replied the first draft of my comment as I was expanding it. Thank you for the response.

No, I replied to your full post. Just wanted to point out that your examples showed stability, not antifragility.

My initial motivation was to point out the authors likely weren't native in English.

I meandered onwards to waffle about the nature of what they were describing, which to my mind at least begins with a notion of stability, in pursuit of a better succint opening line (which I don't have).

You've said:

    Fragility and antifragility aren't about stability (returning to equilibria), but gains or losses after perturbation, which is related to convexity/concavity.

I've said:

    Reading further, they want more; that repeated perturbations should deliver benefit, that systems in an warped egg carton configuration can be annealed to reveal an optimal point by vigorous shaking slowly reduced in degree.

We likely both agree that an anti-fragile system should not spiral out of control. I assume when you refer to "convexity/concavity" you mean at a scale greater than local, at the scale of the warp in an egg carton as I made reference.

My principal gripe with such discussion, as I said, was I don't see much that is new other than language over what was discussed in the mid 1980s .. but perhaps I've not read enough.

The downvoting of your comment is poor form.

Thanks for engaging. You're right in that the ideas are not new, but I feel the language and the framing somewhat is.

I'm not sure if you've come across N. N. Taleb's work -- he's the guy who coined the term "antifragility" = things things that benefit from perturbation. In it he argues that the antifragility is a property of systems that satisfy Jensen's inequality [1]. If the system's function f is convex, then:

  E[f(X)] > f(E[X])

X is a random variable representing perturbations to the system, and f(.) is the system's response. If Jensen's inequality is satisfied (which is only true if f is convex), the inequality tells us that the average response to variable inputs (E[f(X)]) is greater than the response to the average input f(E[X]). This means that the system benefits more from variability in the input than it would from a constant, average input.

Antifragile systems, in that sense, are not conventionally "stable". Taleb describes a spectrum: Fragile -> Robust -> Antifragile

Stable systems often fall into the robust category -- they can withstand stress without breaking, but they don't necessarily improve from it.

It's a really subtle nuance.

An example from life: the young person who takes no risks, has a stable job, does well enough but isn't really interested in moving or taking on new opportunities. They'll never make it big. This is stability.

But the young person who starts a startup and keeps taking risks, iterating and pivoting. If they win, they win big. If they lose, they only lose a few years of their early life. This is antifragility, and it is actually a departure from stability.

[1] https://en.wikipedia.org/wiki/Jensen%27s_inequality

> You're right in that the ideas are not new

It's not just an old scientific idea, but a popular idea discussed at length by the ancient greeks: Talebs whole thing is taking ideas from ancient philosophy, especially stoicism and translating them into rigorous math concepts for modern applications and audience. He's also obsessed with "The Lindy Effect" which implies that older ideas are generally also likely to be more valuable and lastingly useful.

Thanks for this- lots of people on here are misunderstanding the concept of anti-fragility as the same as robustness, e.g. in a control system. They are not at all the same- anti-fragility is a system progressively improving in a lasting way in response to an appropriate stressor, e.g. like a weight lifter getting stronger from weight training, or getting weaker from skipping training. It is not robustiness but literally a negative fragility: a system whose function is impaired by lack of stress (e.g. fragile to lack of stress), and improved by stressors.

The sentence captures the notion clearly, it just sounds a little awkward, especially for an opening sentence in an abstract, which is usually carefully crafted. I think you're probably correct that this is because the authors aren't native English speakers.

Ironically, that sentence is pretty plain for a dynamics and control paper lol

Yeh agree. Seems like someone's been drinking ivory tower soda-pop too long!

FWIW, I tend to think of it like this: Antifragility is a property of something that benefits from a bit of hammering. Like young tree saplings tend to do better in older life when they've been whipped around by the wind a bit. It's basically "whatever doesn't kill you makes you stronger".

That sentence is completely fine, and not even close to being difficult. If that is not plainly enough for you, scholarly communication is not going to be possible.

I’ve written academic papers.

I’ve worked with amazing folks who aren’t native English speakers.

I’ve come to prize simple writing.

I'd like to point out that Norbert Wiener was the first to discover the concept of antifragility (under a different term though).

It's also worth checking out more of his works as he initiated the field of cybernetics.

Where did he described this? (Honest question)

To be correct, he maybe didn't coin the term. At least I didn't find it on quick search in his book Cybernetics. Seems like the term ultrastable actually comes from Ashby [1].

[1] https://users.sussex.ac.uk/~ezequiel/AS/lectures/AdaptiveSys...

Yeah, I'm more curious about his point of view than terminology. Thanks

I believe Nassim Taleb coined the term.

I love how Taleb managed to translate an ideal from stoic philosophy into a precisely defined mathematical concept

Some of this reads like rediscovering control theory, which is all about stability and robustness within defined limits. It's more popularization than innovation.

The person who first translated this idea into math was James Clerk Maxwell, in his paper, "On Governors", in 1868.[1] Maxwell was the first to get a mathematical handle on stability of feedback systems. He wrote: "If, by altering the adjustments of the machine, its governing power is continually increased, there is generally a lin1it at which the disturbance, instead of subsiding more rapidly, becomes an oscillating and jerking motion, increasing in violence till it reaches the limit of action of the governor. This takes place when the possible part of one of the impossible roots becomes positive. ... I have pointed out that, under certain conditions, the sudden disturbances of the machine do not act through the differential system on the governor, or vice versa. When these conditions are fulfilled, the equations of motion are not only simple, but the motion itself is not liable to disturbances depending on the mutual action of the machine and the governor." That, right there, is the beginning of the mathematics of antifragility. Today, we call this turning up the P term of a PID controller too high and getting outside the stable region. Maxwell was the first to formalize the role of delay and damping (he calls it "viscosity") in this.

There's "robust control", a useful theory of "antifragility" in industrial use for decades. Here's an excellent video on how this is done.[2] That's worth a watch. Note the emphasis on how the combination of delay and noise can cause instability in a system resistant to both delay and noise separately. This can be dealt with by moving the areas of instability around in the frequency domain.

(Modern control theory has become insanely complicated over the last few years. Until recent years, control theory was mostly linear control theory plus some self tuning. Now, control theorists are trying to figure out how to get the benefits of machine learning while still having predictable error bounds. This means getting into the innards of what neural nets are really doing. I still get IEEE Trans. on Control Systems Technology, but don't understand it any more. So I'm not sure how that's coming along.)

[1] https://archive.org/details/jstor-112510/mode/2up?view=theat...

[2] https://www.youtube.com/watch?v=A7wHSr6GRnc

I thought so too, and I thought "this is just robust control with different words", but after reading the abstract I don't think robust control actually describes deriving an improvement from perturbing an input.

On the other hand, "persistence of excitation" (a phrase I've heard of but never applied) suggests this too is well trodden ground (Wikipedia suggests end of 70s & 80s)

> I don't think robust control actually describes deriving an improvement from perturbing an input.

Not really. But using a step input to get info to tune a control system is well known. Eurotherm's auto-tuning system for temperature control was one of the first commercial products to self-tune PID loops that way. It started by setting the control value to 0 and listening to the sensors for a while to get data on sensor noise. Then it set the control value to some large value and watched the sensed value ramp up, being careful not to overshoot the goal. This provided enough data to tune the controller. Simple, but practical.

The paper is much more general, but doesn't cover how to do much. One of the references, the one on traffic control, is more interesting.[1] It's about traffic signal control in the presence of disruption. They only did some simulated experiments on one road setup, though. It's hard to tell if that actually works, but it's a reasonable idea with some data behind it.

[1] https://arxiv.org/pdf/2210.10460

I am not an expert on control theory, but I don't see how what you quoted is really the same concept as antifragility. A control system can compensate for disturbances, and may even perform better with some types of disturbances but that is just 'robustness' and isn't antifragility - where the system is progressively improved in a lasting way by stressors over time, like a person getting better at a sport by repeatedly training for it.

Interesting connection can you elaborate more about ideal stoic which part of the philosophy that translate to which math concept.

Here is a quote from Marcus Aurelius which captures the same key concept as antifragility:

“The impediment to action advances action, what stands in the way becomes the way.”

What he is getting at here is that adapting to and overcoming challenges improves your skills, and opens up new ideas and possibilities. The stoics believe that if life goes smoothly and easily, it is actively harmful, and that hardship is required for personal growth.

The core idea of antifragility (which Taleb rigorously defines as a math/engineering principle in his papers) is also that a certain type of system that responds to a stressor in a specific way, can be progressively improved in a lasting way by experiencing that stressor, and conversely, harmed by not experiencing it. For example, an astronaut that spends time in zero gravity loses muscle mass and can lose the ability to walk, whereas a person doing heavy strength training on earth could train themselves strong enough to stand and walk while holding many times their bodyweight.

A more subtle aspect of this for the stoics would be where someone creatively turns a hardship into a unique opportunity. Think someone that loses their job because of a neurodevelopmental disorder, but then ends up studying ways to manage the disorder, and becomes a bestselling author sharing what they learned.

After reading the paper, I'm really unsure what the novel contribution is. It feels like they're attempting to rebrand well-understood concepts within various fields (control systems theory, etc). The provided mathematical definition of antifragility is somewhat unconvincing too: it's not that it's wrong, per say, but in the effort to find something sufficiently broad to apply to many different fields of applied dynamical theory they've had to adopt a definition which is a bit unintuitive, and overly general.

How odd that the word "Antifragility" has risen so fast. What's wrong with robust? Is it due to contemporary memes of personal fragility?

Title of a best seller by a respectable author, Nassim Taleb

It’s trying to highlight a different idea. A robust system can endure damage. An antifragile system grows stronger from damage.

I, along with several other commenters I see, also dislike "antifragility" as a word. However, Taleb in his book does discusses at length why a new word was needed and how its definition differs from existing words like 'robust', 'resilient', etc. which have a different meaning. He even talks even the process of choosing "antifragility" which in a nutshell was just the best he could come up with.

Seeing other comments, I think 'hormesis' might be a better word to start using instead of "antifragility" which, again, is a just an awkward word that feels kind of fake when you use it.

Is this just risk seeking behavior (in contrast to risk sensitive)

Now I wonder what a machine learning model with risk seeking behaviour would look like.

https://news.ycombinator.com/item?id=41231644

I had read this comment, but didn't read it under this lens. Thanks for (re)pointing me to it.

From the little I know about ML in general, you always want to introduce randomness so you don't get stuck in a local minimum/maximum. So they're all risk seeking?

There are now so many bullshit-terms derived from Taleb's bullshit books. Like how people still keep mentioning "black swans" as if it actually means something other (or something more) than "unexpected event". And for some unfathomable reason it keeps traction. Similarly how Mandelbrot "redefined" (i.e. distorted) the meaning of "Lindy effect", and it stuck (however, I didn't notice if it became popular to call a millenia-old banality by than name after Mandelbrot, or Taleb again). It probably should serve as an another example of that if you are arrogant enough, people will follow you just because of that.

However, I guess "antifragility" isn't the worst of these.

When I saw the title I thought it came out of one of those online bullshit generators...

I don't much mind the populurization of these terms or making people think in more novel ways. Even if it's seen as BS by those more informed, I'm glad such books are written and communicators like Taleb exist. Without him, I wouldn't have discovered a bunch of tangential things. I will admit, it gives my brain a satisfying itch too, as I realise that academia is often just the refined encoding of pretty mundane everyday truths, so when someone is able to come in and re-extract that and share it widely, even with a bit of gentle-re-branding, I think it's still net-positive.

Well said!

As you point out; "making people think in more novel ways" (or making them think at all given the amount of parroting in the education system) is the usp of Taleb's books. People need to stop focusing on the attributes of the author (arrogant etc.) but instead need to learn to focus on the content of their writings.

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