Antifragility in complex dynamical systems

https://www.nature.com/articles/s44260-024-00014-y

by RafelMri • 2 years ago

173 113 2 years ago

bob10297• 2 years ago

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.

JackeJR• 2 years ago

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

bob10297• 2 years ago

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.

UniverseHacker13• 2 years ago

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.

bob10297• 2 years ago

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.

sethammons• 2 years ago

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.

authorfly• 2 years ago

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.

taylorius• 2 years ago

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! :-)

bob10297• 2 years ago

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.

seanhunter• 2 years ago

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

neom• 2 years ago

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!

bob10297• 2 years ago

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.

lo0dot0• 2 years ago

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

adiM• 2 years ago

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

marci2• 2 years ago

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

mike_ivanov• 2 years ago

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

nottorp2• 2 years ago

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?

delichon• 2 years ago

  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.

UniverseHacker13• 2 years ago

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

fsckboy• 2 years ago

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?

tinix• 2 years ago

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

jrsdav• 2 years ago

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.

diab0lic• 2 years ago

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.

morning-coffee• 2 years ago

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.

seventytwo• 2 years ago

Entropy always wins

lucyv• 2 years ago

decay exists as an extant form of life

AgentOrange12342• 2 years ago

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

UniverseHacker13• 2 years ago

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.

defrost3• 2 years ago

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.

theOGognf• 2 years ago

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

padolsey2• 2 years ago

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".

tokai• 2 years ago

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.

AgentOrange12342• 2 years ago

I’ve written academic papers.

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

I’ve come to prize simple writing.

UniverseHacker13• 2 years ago

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

Animats2• 2 years ago

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

dwattttt• 2 years ago

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)

UniverseHacker13• 2 years ago

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.

BOOSTERHIDROGEN• 2 years ago

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

UniverseHacker13• 2 years ago

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.

krick• 2 years ago

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.

nottorp2• 2 years ago

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

padolsey2• 2 years ago

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.

rramadass2• 2 years ago

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.

mo_422• 2 years ago

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.

agumonkey2• 2 years ago

Where did he described this? (Honest question)

mo_422• 2 years ago

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...

r_hanz• 2 years ago

I believe Nassim Taleb coined the term.

fasteo• 2 years ago

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.

Beretta_Vexee• 2 years ago

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

dmichulke• 2 years ago

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

Resilience is just "not getting weaker".

baq• 2 years ago

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.

0134340• 2 years ago

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.

moffkalast• 2 years ago

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

rramadass2• 2 years ago

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

cfcf14• 2 years ago

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.

lokimedes• 2 years ago

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

buggythebug• 2 years ago

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

brians• 2 years ago

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

Eddy_Viscosity2• 2 years ago

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.

Antifragility in complex dynamical systems

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