> the approaches were completely different, often not even ML based.
Oh, the horror! Some aproaches were not (gasp!) even ML-based. As someone who was been working all these years in image processing without recourse to much ML stuff, I find this attitude cute and endearing.
Do you have some pointers to interesting research of the kind you are doing? Btw, when we're talking about "non-ML" we meen no-learning, not just no-neural-nets, correct?
> Do you have some pointers to interesting research of the kind you are doing?
I don't think my research is particularly interesting for a general public as it is quite niche (low level image processing). Still, we consistently receive industrial funding so it is probably useful to some extent. Some nice journals where we publish our research: Journal of Mathematical Imaging and Vision, SIAM Journal on Imaging Sciences.
> when we're talking about "non-ML" we mean no-learning, not just no-neural-nets, correct?
Why do you say "just" ? Machine learning and neural networks are independent things. There's plenty of wonderful research about neural networks that has nothing to do with learning.
By "just" I meant to clarify the use of "ML". It's often used to mean "deep learning" and while I thought you didn't use it that way I wanted to make sure.
I normally think of neural nets as a primarily connectionist approach to machine learning (although not necessarily statistical: the first artificial neuron was propositional logic-based). I'm curious to read research that treats them in a different manner. Can you recommend some?
Look for example the article "Approximation Spaces of Deep Neural Networks" by Gribonval et al. It contains a nice review of the spaces of functions that are represented by neural networks. It's just about properties of neural networks and their computing power, depending on their depth, width, skip connections, and nonlinearity type. The weights are fixed constants, there's no training whatsoever.
They have a really easy to use library in Python called Transformers. Below is an example of how to use it.
>>> from transformers import pipeline
# Allocate a pipeline for sentiment-analysis
>>> classifier = pipeline('sentiment-analysis')
>>> classifier('We are very happy to introduce pipeline to the transformers repository.')
[{'label': 'POSITIVE', 'score': 0.9996980428695679}]
Huggingface is great! The only issue is the documentation which is rather lacking if you want to get more serious about writing custom models and solving more complex issues than what normally documented in the examples there.
Transformers gained popularity due to the scalable nature of the architecture and how well it can be parallelized on existing GPU/XLA hardware. Modeling is always conditioned on the hardware available at hand.
Transfomers lack inductive bias which make it generic building blocks unlike CNN/RNN like models and by injecting inductive bias like positional encoding, it can be well translated to various domains.
Are transformers competitive with (for example) CNNs on vision-related tasks when there's less data available? I'm not that familiar with "injecting inductive bias" via positional encodings, but it sounds really interesting. My crude understanding is that the positional encodings were used in the original Transformer architecture to encode the ordering of words for NLP. Are they more flexible then that? For example, can they be used to replicate the image-related inductive bias of CNNs and match CNN performance on small datasets (1000 - 10,000)?
If not, then to me, it seems like only industries where it's possible to get access to a large amount of representative data (i.e. greater than a million?) benefit from transformers. In industries where there are bottlenecks to data generation, there's a clear benefit in leveraging the inductive bias in other architectures, such as the various ways CNNs have biases towards image recognition.
I'm in an industry (building energy consumption prediction) where we can only generate around 10,000 to 100,000 datapoints (from simulation engines) for DL. Are transformers ever used with that scale of data?
> Are transformers competitive with (for example) CNNs on vision-related tasks when there's less data available?
They can be, there's current research into the tradeoffs between local inductive bias (information from local receptive fields: CNNs have strong local inductive bias) and global inductive bias (large receptive fields: i.e. attention). There's plenty of works that combine CNNs and Attention/Transformers. A handful of them focus on smaller datasets, but the majority are more interested in ImageNet. There's also work being done to change the receptive fields within attention mechanisms as a means to balance this.
> Are transformers ever used with that scale of data?
So there's a yes and no to your question. But definitely yes since people have done work on Flowers102 (6.5k training) and CIFAR10 (50k training). Keep in mind that not all these models are pure transformers. Some have early convolutions or intermediate ones. Some of these works even have a smaller number of parameters and better computational efficiency than CNNs.
But more importantly, I think the big question is about what type of data you have. If large receptive fields are helpful to your problem then transformers will work great. If you need local receptive fields then CNNs will tend to do better (or combinations of transformers and CNNs or reduced receptive fields on transformers). I doubt there will be a one size fits all architecture.
One thing to also keep in mind is that transformers typically like heavy amounts of augmentation. Not all data can be augmented significantly. There's also pre-training and knowledge transfer/distillation.
Good point. The fact there is no inductive bias inherent to transformers makes it difficult to train a decent model on small datasets from scratch. However, there are recent research directions that try to address this problem [1].
Also baking in some sort of domain specific inductive bias into model architecture itself can address this problem as well [2].
Maybe a naive question: is there no transfer learning with transformers? I've done a lot of work with CNN architectures on small datasets, and almost always start with something trained on imagenet, and fine tune, or do some kine of semi-supervised training to start. Can we do that with VIT et al as well? Or are they really usually trained from scratch?
Lots of people transfer learn with transformers. ViT[0] originally did CIFAR with it. Then DeiT[1] introduced some knowledge transfer (note: their student is larger than the teacher). ViT pretrained on both ImageNet21k and JFT-300m.
CCT ([1] from above) was focused on training from scratch.
There's two paradigms to be aware of. ImageNet and pre-training can often be beneficial but it doesn't always help. It really depends on the problem you're trying to tackle and if there are similar features within the target dataset and the pre-trained dataset. If there is low similarity you might as well train from scratch. Also, you might not want as large of models (like ViT and DeiT have, which ViT's has more parameters than CIFAR-10 has features).
Sure thing. Also if you're getting into transformers I'd recommend lucidrains's GitHub[0] since it has a large collection of them with links to papers. It's nice that things are consolidated.
> by injecting inductive bias like positional encoding
I don't think it's fair to just call positional encoding "inductive bias". The positional encoding is the only way the word order is communicated to the model. That would be like saying it is inductive bias to include color channels when working with images.
I have not given transformers enough attention... but my impression is that this is still storing entities in the weights of the neural network instead of in a database where the can be operated on with CRUD. What are the knowledge discovery researchers doing with respect to transformers? And the SAT solver researchers?
I wrote a short post on retrieval transformers that you might find interesting [0]. It’s a twist on transformers that allows scaling “world knowledge” independently in a database-like manner.
First transformer models still dealt only with the training set.
Eventually it was extended to work with an external data source that it queries. This is not a new thing, for example, image style transfer and some other image tasks that were attempted before the domination of NNs did the same thing (linear models would query the db for help and guided feature extraction).
The greatest effect in transformers is the attention mechanism combined with self-supervised learning. Investigations in self-supervised learning tasks (article illustrates one word gap, but there are others) can result in superior models that are sometimes even easier to train.
As for SAT, optimization, graph neural networks might end up being more effective (due to high structure of the inputs). I'm definitely awaiting for traveling salesman solver or similar, guided by NN, solving things faster and reaching optimality more frequently that optimized heuristic algos.
> I'm definitely awaiting for traveling salesman solver or similar, guided by NN, solving things faster and reaching optimality more frequently that optimized heuristic algos.
There was a competition for exactly this at Neurips 2021
> As for SAT, optimization, graph neural networks might end up being more effective
Learning from data is a different problem from optimization. For example, if facts about cities gave additional clues beyond their location about the optimal order, then learning could benefit in the travelling salesman problem. Or if the cost of paths is only known implicitly through data examples.
Compare to how NN:s can be used for data compression, for example upscaling images, by learning from photographs only the tiny the subset of all possible images that are meaningful to humans. But it is not useful for general data compression.
Optimization is also data, given a local state, can you identify the sequence of transformations that will get you to a better state. The reward is instantly measurable and the goal is minimizing the total cost.
AlphaGo is local search guided by a learned heuristic, which is trained in a simulator of the game. The heuristic learns an approximation of the value of moves and board states, and is analogous to the "compute_cost_of_tour()" routine in TSP algorithms.
In the basic TSP (for example) there is no other data to learn from than "distances" between vertices, and anything learned from a single instance of the problem amounts to overfitting. This might still be useful - for example learning efficient sub-paths on a fixed map, rather than searching for them every time.
Self-organized maps can be used as a neural approach to find TSP solutions; in these cases the network itself is the optimized solution. Think of it as ~gradient-descent~ optimization for TSP. Not sure if it is relevant in benchmarks. (I think it might amount to minimizing the sum squared distance between hops (or a bound on that), not the total length of tour. It favours many shorter hops over a few long hops.)
(If you want time-window constraints in LKH, IIRC, you can try adding the time-diff as penalties to your global cost function.)
LKH does support a lot of things mentioned, but for practical usages it would not work. It's nice to leave it running and see what can be accomplished but asking it to give you back something in 1 second, with a lot of constraints, gives back solutions that are not feasible.
In the basic TSP there is a lot of data.
For example, the reason why minimum spanning tree works is because the algorithm makes use of the relationship between vertices. Similar techniques use alpha-nearness, Steiner trees and direct modifications of distance matrix to create relaxations of the TSP and improve the performance of local search (I believe most are implemented in LKH).
I am obviously not expecting NNs to be capable of doing something like that currently but I'm hoping they might be able to discover interesting instance patterns for something more constrained.
> But these do not stay they same between problem instances; anything you learn from solving one problem is not helpful when solving the next problem.
But nothing in ML stays the same between instances. The reason why ML works is because there are redundancies in the training set. I am pretty sure that distribution wise, set of TSP instances still has a lot of redundancies.
You would want your model to learn to execute something like MST or to approximate alpha-nearness or to remap the instance into a relaxation that when solved by a simpler algorithm results in a solution that, when remapped back to original, is feasible and optimal.
> I'm definitely awaiting for traveling salesman solver or similar, guided by NN, solving things faster and reaching optimality more frequently that optimized heuristic algos.
Just in case we are not being clear, let's be clear. Bluntly in nearly every practical sense, the traveling salesman problem (TSP) is NOT very difficult. Instead we have had good approaches for decades.
I got into the TSP writing software to schedule the fleet for FedEx. A famous, highly accomplished mathematician asked me what I was doing at FedEx, and as soon as I mentioned scheduling the fleet he waved his hand and concluded I was only wasting time, that the TSP was too hard. He was wrong, badly wrong.
Once I was talking with some people in a startup to design the backbone of the Internet. They were convinced that the TSP was really difficult. In one word, WRONG. Big mistake. Expensive mistake. Hype over reality.
I mentioned that my most recent encounter with combinatorial optimization was solving a problem with 600,000 0-1 variables and 40,000 constraints. They immediately, about 15 of them, concluded I was lying. I was telling the full, exact truth.
So, what is difficult about the TSP? Okay, we would like an algorithm for some software that would solve TSP problems (1) to exact optimality, (2) in worst cases, (3) in time that grows no faster than some polynomial in the size of the input data to the problem. So, for (1) being provably within 0.025% of exact optimality is not enough. And for (2) exact optimality in polynomial time for 99 44/100% of real problems is not enough.
In the problem I attacked with 600,000 0-1 variables and 40,000 constraints, a real world case of allocation of marketing resources, I came within the 0.025% of optimality. I know I was this close due to some bounding from some nonlinear duality -- easy math.
So, in your
> reaching optimality more frequently that optimized heuristic algos.
heuristics may not be, in nearly all of reality probably are not, reaching "optimality" in the sense of (2).
The hype around the TSP has been to claim that the TSP is really difficult. Soooo, given some project that is to cost $100 million, an optimal solution might save $15 million, and some software based on what has long been known (e.g., from G. Nemhauser) can save all but $1500 is not of interest. Bummer. Wasted nearly all of $15 million.
For this, see the cartoon early in Garey and Johnson where they confess they can't solve the problem (optimal network design at Bell Labs) but neither can a long line of other people. WRONG. SCAM. The stockholders of AT&T didn't care about the last $1500 and would be thoroughly pleased by the $15 million without the $1500. Still that book wanted to say the network design problem could not yet be solved -- that statement was true only in the sense of exact optimality in polynomial time on worst case problems, a goal of essentially no interest to the stockholders of AT&T.
For neural networks (NN), I don't expect (A) much progress in any sense over what has been known (e.g., Nemhauser et al.) for decades. And, (B) the progress NNs might make promise to be in performance aspects other than getting to exact optimality.
Yes, there are some reasons for taking the TSP and the issue of P versus NP seriously, but optimality on real world optimization problems is not one of the main reasons.
Here my goal is to get us back to reality and set aside some of the hype about how difficult the real world TSP is.
When TSP is mentioned today, unlike 50 years ago when LK heuristic got published, I assume all of the popular & practical variants, like time window constraints, pickup and delivery, capacity constraints, max drop time requirement after pickup, flexible route start, adding location independent breaks (break can happen anytime in the sequence or in a particular time window of day) etc. Some of the subproblems are so constrained that you cannot even move around that effectively as you can with raw TSP.
Some of the subproblems have O(n) or O(n log n) evaluations of best local moves, generic solvers are even worse at handling that (Concorde LP optimizations cannot cover that efficiently). When no moves are possible, you have to see what moves brings you back to a feasible solution and how many local changes you need to do to accomplish this.
For example, just adding time windows complicates or makes most well known TSP heuristics useless. Now imagine if we add a requirement between pairs of locations that they need to be at most X time apart (picking up and then delivering perishable goods), that the route can start at an arbitrary moment etc.
I personally spent quite a lot of time working on these algorithms and I'd say the biggest issue is instance representation (is it enough to have a sequence of location ids ?). For example, one of my recent experiments was using zero suppressed binary decision diagrams to easily traverse some of these constrained neighborhoods and maintain the invariants after doing local changes. Still too slow for some instances I handle (real world is 5000 locations, 100 salesmen and an insane amount of location/salesmen constraints).
Amazing. Of course I've heard of Kernighan long ago, but this is the first I've heard of LKH.
I did a lot in optimization, in my Ph.D. studies and in my career, but I dropped it, decades ago -- my decision was made for me by my customers, essentially there weren't any or at least not nearly enough that I could find.
Actually, my summary view is that for applications of math in the US, the main customer is US national security. Now there are big bucks to apply algorithms and software to some big data, and maybe, maybe, there is some interest in math. But the call I got from Google didn't care at all about my math, optimization, statistics, or stochastic processes background. Instead they asked what was my favorite programming language, and my answer, PL/I, was the end of the interview. I'm sure the correct answer was C++. I still think PL/I is a better language than C++.
Early in my career, I was doing really well with applied math and computing, but that was all for US national security and within 50 miles of the Washington Monument.
Now? I'm doing a startup. There is some math in it, but it is just a small part, an advantage, maybe crucial, but still small.
There's quite a resurgence of need for optimization.
There's a lot of companies that want to provide an Uber/Lyft-like service of their own product. So you have a bunch of smaller problems that you want to solve as best as possible in ~1 second.
A lot of small companies with their delivery fleets want to optimize (pest control, christmas tree delivery, cleaning, technical service, construction (coordinating teams that construct multiple things at multiple locations at the same time) etc.).
On the other hand, not related to TSP, the whole energy market in the US is very LP/ILP optimizable and has a lot of customers (charging home batteries, car batteries, discharging when price is high, etc.).
I would admit that the scientific field of discrete optimization is littered with genetic algorithms, ant colonies and other "no free lunch" optimization algorithms that make very little sense from progress perspective, so it does feel like the golden era was from the 70s to early 90s. I do not have a PhD but somehow ended up doing machine learning and discrete optimization most of my career.
Improvements to ant colonies or genetic algorithms are not pushing the field forward. It becomes a benchmark game and has been that for the last 20 years (which many abuse, you can start from a previous best solution and leave your computer running for days and just claim that your new algorithm improvement found the new best solution, it's also quite common to never release your code).
If you look at the roots of discrete optimization, all of the approaches used in a solver like Concorde (developed in the open), there's no where near the amount of development and paradigm shifts happening in ant colonies, genetic algorithms, genetic programming, tabu search, annealing and similar.
E.g., finding an efficient representation of time-windows+pickup-and-delivery+breaks+flexible-start-time that allows you to efficiently update the solution and get an answer if the solution is feasible after the change and what the new cost is, is more progress than changing some recombination patterns in your genetic algorithm that will result in improvement on the instance set you are optimizing for (basically overfitting to data).
Here's an example of a paper that lists various update/feasibility/cost diff algorithms and their time complexity for a bunch of subproblems on a list-of-location-ids representation. Any genetic algorithm that wants to be fast will need to deal with that too.
That's why I think that graph NNs might allow us to find a way to remap our simple representation to something more efficient that is easier to work with and that can apply local changes without much effort.
For example, what if you can apply a transformation to TSP problem with time windows by adding new vertices or changing the distance matrix to eliminate time windows completely but still keep applying very efficient local changes that bring you close to optimum fast (do the same for pickup-and-delivery, flexible start time, etc.). Similar thing, an integer linear programming solver is used but the way the constraints of your instance are defined is hard to work with, there is a local pattern you are not seeing that allows simplification.
There have been attempts to learn exploration strategies of ILP solvers with ML but none made leaps forward (unlike AlphaFold, AlphaZero, AlphaGo, or even AlphaCode - competitive programming code generation). The biggest reason for that is that the current principled algorithms (60-30 years old) are insanely good on fundamental problems.
I remember reading about a new set of constraints, nurse rostering (nurse scheduling), and once researchers applied the principled methods, all of the instances of interest got solved to proved optimality. The amount of genetic algorithms, ant colonies and who knows what that was applied to these instances in the meanwhile was ridiculous and unnecessary.
Python-MIP is a great library that provides an interface to many different algorithms like this. It's practical for using in scientific programming where appropriate, and if you read through the docs you can find the names of specific algorithms that it uses with pointers to where to learn more.
Can look at the now old work of G. Nemhauser. His work was for combinatorial optimization and not just for exactly the traveling salesman problem (TSP).
E.g., there is
George L. Nemhauser and
Laurence A. Wolsey,
Integer and Combinatorial Optimization,
ISBN 0-471-35943-2,
John Wiley & Sons, Inc.,
New York,
1999.
Some approaches involve set covering and set partitioning. Soooo, for the FedEx fleet, first just generate all single airplane feasible tours from the Memphis hub and back. Here can honor some really goofy constraints and complicated costing; can even handle some stochastic issues, i.e., the costs depend on the flight planning and that depends on the loads which are random, but it would be okay to work with just expectations -- we're talking complicated costing! Then with all those tours generated, pick ones that cover all the cities to be served, i.e., partition the cities. Have a good shot at using linear programming, tweaked a little to handle 0-1 constraints, to pick the tours.
Then more generally for a lot of practical problems can write linear programming problems with some of the variables integer. Then can tweak the simplex algorithm of linear programming to handle some of such constraints fairly naturally in the algorithm. E.g., of course, can proceed with now classic branch and bound.
The TSP taken narrowly can be regarded as more specialized.
So, net, there is a big bag of essentially tricks, some with some math and some just heuristics.
Part of the interest in the issue of P versus NP was to do away with the bag of tricks and have just some one grand, fantastic algorithm and computer program with guaranteed performance. Nice if doable. Alas, after all these years, so far not really "doable", not as just one grand, fantastic .... And the question of P versus NP has resisted so much for so long that it has even a philosophical flavor. And there are serious claims that a technically good algorithm would have some really astounding consequences.
Sure, I have some half baked ideas sitting around that I hope will show that P = NP -- doesn't everyone? But my point here was just simple: For several decades we have been able to do quite well on real problems. Oh, for the problem with 600,000 0-1 variables and 40,000 contraints, otherwise linear, I used nonlinear duality theory (which is simple) or, if you wish, Lagrangian relaxation -- it's one of the tricks.
Another old trick: For the actual TSP in any Euclidean space (sure, the plane but also 3 dimensions or 50 if you want), that is, with Euclidean distance, just find a minimum spanning tree (there are at least two good, that is, polynomial algorithms, for that) and then in a simple and fairly obvious way make a TSP tour out of that tree. That approach actually has some probabilistic bounds on how close it is to optimality, and it does better with more cities -- it's another tool in the kit.
My main conclusion about the TSP, combinatorial optimization, and optimization more generally is that there are way, Way, WAY too few good customers. Whether there is 15% of project cost to be saved or not, the people responsible for the projects just do NOT want to be bothered. In simple terms, in practice, it is essentially a dead field. My view is that suggesting that a young person devote some significant part of their career to optimization is, bluntly, in a word, irresponsible.
> The latest batch of language models can be much smaller yet achieve GPT-3 like performance by being able to query a database or search the web for information[0].
I think it’s relatively straightforward to serialize such a model into different representations, I completely understand that they keep the actual data inside pytorch state by default.
Out of curiosity, what tools are researchers generally using to explore neural networks? I’m just an armchair ML enthusiast myself, but NN always appear very much like black boxes.
What are the goals and methods for exploring neural network state nowadays?
Maybe. Transformers model associative memory in a way made precise by their connection to Hopfield networks. Individually, they're like look-up tables, but the queries can be ambiguous, even based on subtle higher-order patterns (which the network identifies on its own), and the returned values can be a mixture of stored information, weighted by statistically meaningful confidences.
I assume transformers will be replaced by something, just as transformers replaced other sequential models.
That said, transformers have already earned a place in the annals of ML, if for no other reason than they were the critical to the first technology to solve protein structure prediction.
After a long "training set", I have learned that when I see a headline that ends with a question mark, don't bother to read the article; the answer to the question is nearly always "No". E.g.,
"Will Expert Systems AI Replace Nearly All Knowledge Workers?"
No, they didn't. And I am fully confident they won't.
So, due to the question mark, just stop reading. Then I apply this training to
"Will Transformers Take over Artificial Intelligence?"
I think Transformers are a (good) tool in AI toolbox and they are already being used a conjunction with many other recent tools such as Normalizing Flows, Diffusion Models, Energy-Based Models, etc…
https://twitter.com/karpathy/status/1468370605229547522
And of course one of the early classic papers in the field, as a bonus:
https://papers.nips.cc/paper/2017/file/3f5ee243547dee91fbd05...
(The paper is mentioned in the article)