This is an interesting paper that makes a fairly radical claim, and I haven't fully decided whether what they find is an interesting-but-rare corner case, or a more fundamental weakness in the design of neural nets. The claim is: neural nets prefer learning simple features, even if there exist complex features that are equally or more predictive, and even if that means learning a classifier with a smaller margin - where margin means "the distance between the decision boundary and the nearest-by data". A large-margin classifier is preferable in machine learning because the larger the margin, the larger the perturbation that would have to be made - by an adversary, or just by the random nature of the test set - to trigger misclassification. 

https://i.imgur.com/PJ6QB6h.png

This paper defines simplicity and complexity in a few ways. In their simulated datasets,  a feature is simpler when the decision boundary along that axis requires fewer piecewise linear segments to separate datapoints. (In the example above, note that having multiple alternating blocks still allows for linear separation, but with a higher piecewise linear requirement). In their datasets that concatenate MNIST and CIFAR images, the MNIST component represents the simple feature. 

The authors then test which models use which features by training a model with access to all of the features - simple and complex - and then testing examples where one set of features is sampled in alignment with the label, and one set of features is sampled randomly. If the features being sampled randomly are being used by the model, perturbing them like this should decrease the test performance of the model. For the simulated datasets, a fully connected network was used; for the MNIST/CIFAR concatenation, a variety of different image classification convolutional architectures were tried. 

The paper finds that neural networks will prefer to use the simpler feature to the complete exclusion of more complex features, even if the complex feature is slightly more predictive (can achieve 100 vs 95% separation). The authors go on to argue that what they call this Extreme Simplicity Bias, or Extreme SB, might actually explain some of the observed pathologies in neural nets, like relying on spurious features or being subject to adversarial perturbations. They claim that spurious features - like background color or texture - will tend to be simpler, and that their theory explains networks' reliance on them. Additionally, relying completely or predominantly on single features means that a perturbation along just that feature can substantially hurt performance, as opposed to a network using multiple features, all of which must be perturbed to hurt performance an equivalent amount. 

As I mentioned earlier, I feel like I'd need more evidence before I was strongly convinced by the claims made in this paper, but they are interestingly provocative. On a broader level, I think a lot of the difficulties in articulating why we expect simpler features to perform well come from an imprecision in thinking in language around the idea - we think of complex features as inherently brittle and high-dimensional, but this paper makes me wonder how well our existing definitions of simplicity actually match those intuitions.

Transformers - powered by self-attention mechanisms - have been a paradigm shift in NLP, and are now the standard choice for training large language models. However, while transformers do have many benefits in terms of computational constraints - most saliently, that attention between tokens can be computed in parallel, rather than needing to be evaluated sequentially like in a RNN - a major downside is their memory (and, secondarily, computational) requirements. The baseline form of self-attention works by having every token attend to every other token, where "attend" here means that a query from each token A will take an inner product with each other token -A, and then be elementwise-multiplied with the values of every other token -A. This implies a O(N^2) memory and computation requirement, where N is your sequence length. 

So, the question this paper asks is: how do you get the benefits, or most of the benefits, of a full-attention network, while reducing the number of other tokens each token attends to. 

The authors' solution - Big Bird - has three components. First, they approach the problem of approximating the global graph as a graph theory problem, where each token attending to every other is "fully connected," and the goal is to try to sparsify the graph in a way that keeps shortest path between any two nodes low. They use the fact that in an Erdos-Renyi graph - where very edge is simply chosen to be on or off with some fixed probability - the shortest path is known to be logN. In the context of aggregating information about a sequence, a short path between nodes means that the number of iterations, or layers, that it will take for information about any given node A to be part of the "receptive field" (so to speak) of node B, will be correspondingly short. Based on this, they propose having the foundation of their sparsified attention mechanism be simply a random graph, where each node attends to each other with probability k/N, where k is a tunable hyperparameter representing how many nodes each other node attends to on average. 

To supplement, the authors further note that sequence tasks of interest - particularly language - are very local in their information structure, and, while it's important to understand the global context of the full sequence, tokens close to a given token are most likely to be useful in constructing a representation of it. Given this, they propose supplementing their random-graph attention with a block diagonal attention, where each token attends to w/2 tokens prior to and subsequent to itself. (Where, again, w is a tunable hyperparameter) 

However, the authors find that these components aren't enough, and so they add a final component: having some small set of tokens that attend to all tokens, and are attended to by all tokens. This allows them to theoretically prove that Big Bird can approximate full sequences, and is a universal Turing machine, both of which are true for full Transformers. I didn't follow the details of the proof, but, intuitively, my reading of this is that having a small number of these global tokens basically acts as a shortcut way for information to get between tokens in the sequence - if information is globally valuable, it can be "written" to one of these global aggregator nodes, and then all tokens will be able to "read" it from there. 



The authors do note that while their sparse model approximates the full transformer well in many settings, there are some problems - like needing to find the token in the sequence that a given token is farthest from in vector space - that a full attention mechanism could solve easily (since it directly calculates all pairwise comparisons) but that a sparse attention mechanism would require many layers to calculate. 


Empirically, Big Bird ETC (a version which adds on additional tokens for the global aggregators, rather than making existing tokens serve thhttps://i.imgur.com/ks86OgJ.pnge purpose) performs the best on a big language model training objective, has comparable performance to existing models on questionhttps://i.imgur.com/x0BdamC.png answering, and pretty dramatic performance improvements in document summarization. It makes sense for summarization to be a place where this model in particular shines, because it's explicitly designed to be able to integrate information from very large contexts (albeit in a randomly sampled way), where full-attention architectures must, for reasons of memory limitation, do some variant of a sliding window approach.

This paper argues that, in semi-supervised learning, it's suboptimal to use the same weight for all examples (as happens implicitly, when the unsupervised component of the loss for each example is just added together directly. Instead, it tries to learn weights for each specific data example, through a meta-learning-esque process. 

The form of semi-supervised learning being discussed here is label-based consistency loss, where a labeled image is augmented and run through the current version of the model, and the model is optimized to try to induce the same loss for the augmented image as the unaugmented one. The premise of the authors argument for learning per-example weights is that, ideally, you would enforce consistency loss less on examples where a model was unconfident in its label prediction for an unlabeled example. 

As a way to solve this, the authors suggest learning a vector of parameters - one for each example in the dataset - where element i in the vector is a weight for element i of the dataset, in the summed-up unsupervised loss. They do this via a two-step process, where first they optimize the parameters of the network given the example weights, and then the optimize the example weights themselves. To optimize example weights, they calculate a gradient of those weights on the post-training validation loss, which requires backpropogating through the optimization process (to determine how different weights might have produced a different gradient, which might in turn have produced better validation loss). This requires calculating the inverse Hessian (second derivative matrix of the loss), which is, generally speaking, a quite costly operation for huge-parameter nets. To lessen this cost, they pretend that only the final layer of weights in the network are being optimized, and so only calculate the Hessian with respect to those weights. They also try to minimize cost by only updating the example weights for the examples that were used during the previous update step, since, presumably those were the only ones we have enough information to upweight or downweight. With this model, the authors achieve modest improvements - performance comparable to or within-error-bounds better than the current state of the art, FixMatch. 

Overall, I find this paper a little baffling. It's just a crazy amount of effort to throw into something that is a minor improvement. A few issues I have with the approach: 

- They don't seem to have benchmarked against the simpler baseline of some inverse of using Dropout-estimated uncertainty as the weight on examples, which would, presumably, more directly capture the property of "is my model unsure of its prediction on this unlabeled example"
- If the presumed need for this is the lack of certainty of the model, that's a non-stationary problem that's going to change throughout the course of training, and so I'd worry that you're basically taking steps in the direction of a moving target
- Despite using techniques rooted in meta-learning, it doesn't seem like this models learns anything generalizable - it's learning index-based weights on specific examples, which doesn't give it anything useful it can do with some new data point it finds that it wasn't specifically trained on

Given that, I think I'd need to see a much stronger case for dramatic performance benefits for something like this to seem like it was worth the increase in complexity (not to mention computation, even with the optimized Hessian scheme)

This is a nice little empirical paper that does some investigation into which features get learned during the course of neural network training. To look at this, it uses a notion of "decodability", defined as the accuracy to which you can train a linear model to predict a given conceptual feature on top of the activations/learned features at a particular layer. This idea captures the amount of information about a conceptual feature that can be extracted from a given set of activations. 

They work with two synthetic datasets. 

1. Trifeature: Generated images with a color, shape, and texture, which can be engineered to be either entirely uncorrelated or correlated with each other to varying degrees. 
2. Navon: Generated images that are letters on the level of shape, and are also composed of letters on the level of texture 

The first thing the authors investigate is: to what extent are the different properties of these images decodable from their representations, and how does that change during training? In general, decodability is highest in lower layers, and lowest in higher layers, which makes sense from the perspective of the Information Processing Inequality, since all the information is present in the pixels, and can only be lost in the course of training, not gained. They find that decodability of color is high, even in the later layers untrained networks, and that the decodability of texture and shape, while much less high, is still above chance. When the network is trained to predict one of the three features attached to an image, you see the decodability of that feature go up (as expected), but you also see the decodability of the other features go down, suggesting that training doesn't just involve amplifying predictive features, but also suppressing unpredictive ones. This effect is strongest in the Trifeature case when training for shape or color; when training for texture, the dampening effect on color is strong, but on shape is less pronounced. 

https://i.imgur.com/o45KHOM.png

The authors also performed some experiments on cases where features are engineered to be correlated to various degrees, to see which of the predictive features the network will represent more strongly. In the case where two features are perfectly correlated (and thus both perfectly predict the label), the network will focus decoding power on whichever feature had highest decodability in the untrained network, and, interestingly, will reduce decodability of the other feature (not just have it be lower than the chosen feature, but decrease it in the course of training), even though it is equally as predictive. 
https://i.imgur.com/NFx0h8b.png

Similarly, the network will choose the "easy" feature (the one more easily decodable at the beginning of training) even if there's another feature that is slightly *more* predictive available. This seems quite consistent with the results of another recent paper, Shah et al, on the Pitfalls of Simplicity Bias in neural networks. The overall message of both of these experiments is that networks generally 'put all their eggs in one basket,' so to speak, rather than splitting representational power across multiple features. 

There were a few other experiments in the paper, and I'd recommend reading it in full - it's quite well written - but I think those convey most of the key insights for me.

In the past year or so, contrastive learning has experienced widespread success, and has risen to be a dominant problem framing within self-supervised learning. The basic idea of contrastive learning is that, instead of needing human-generated labels to generate a supervised task, you instead assume that there exists some automated operation you can perform to a data element to generate another data element that, while different, should be considered still fundamentally the same, or at least more strongly related, and that you can contrast these related pairs against pairs constructed with the rest of the dataset, with which any given frame would not by default have this assumed relationship of sameness or quasi-similarity. 

One fairly central way that "different but still effectively similar" has been historically defined - at least within the realm of image-based models - is through the use of data augmentations: image transformations such as cropping, color jitter, or Gaussian blur, which are used on an image to create the counterpart in its related pair. Fundamentally, what we're doing when we define these particular augmentations is saying: these transformations don't cause a meaningful change in what the image is, and so we want the representations we get with and without the transformations to be close to one another (or at least to contain enough information to predict one another). Another way you can say this is that we're defining properties of the image that we want our representation to be invariant to. 

The authors of this paper make the point that, when aggressive cropping is part of your toolkit of augmentations, the crops of the image can actually contain meaningfully different content than the uncropped image. If you remove a few pixels around the edges of an image, it still fundamentally contains the same things. However, if you zoom in dramatically, you may get crops that contain different objects. From an image classification standpoint, you would expect that coding in an invariance to cropping in our representations would, in some cases, also mean coding in an invariance to object type, which would presumably be detrimental to the task of classifying objects. To explain the extent of the success that aggressive-cropping methods have had so far, they argue that ImageNet has the particular property that its images are curated to be primarily and centrally containing a single object at a time, such that, even if you zoom in, you're getting a part of the central object, rather than another object entirely. They argue that this dataset bias might explain why you haven't seen as much of this object-invariance be a problem in earlier augmentation-based contrastive work. To try to test this, they train different contrastive (MoCo v2) models on the MSCOCO dataset, which consists of pictures of rooms, and thus no longer has the property of being centrally of one object. They tried one setting where they performed contrastive loss on the images as a whole, and another where the input to the augmentation pipeline were images from the same dataset, but pre-cropped to only contain one image at a time. This was meant, as far as I can tell, to isolate the effect of "object-centric vs not" while holding other dataset factors constant. They then test how well these different models do on an object-centric classification task (Pascal Cropped Boxes). They find that the contrastive model that trains cropped versions of the dataset gets about 3.5 points higher mean accuracy (71.9 vs 75.3) compared to the contrastive loss done on the multi-object versions of images. 

They also explicitly try to measure different forms of invariance, through a scheme where they binarize the elements of the representation vector, and calculate what proportion of them fire on average with and without a given set of transformations. They find that the main form of invariances that contrastive learning does well at is invariance to occlusion (part of the image not being visible), where both contrastive methods give ~84 percent co-firing, and supervised pre-training only gets about 80.9. However, on other important measures of invariance - viewpoint, illumination direction, and instance (that is, specific instance within a class) - contrastive representations perform notably worse than supervised pretraining. 

https://i.imgur.com/7Ghbv5A.png

To try to solve these two problems, they propose a method that learns from video, and that uses temporally separated frames (which are then augmented) as pairs. They call this Frame Temporal Invariance, and argue, reasonably, that by pushing the representations of adjacent frames which track a (presumably consistent, or at least slowly-evolving) scene closer together, you should expect better invariance to viewpoint change and image deformation, since those things naturally happen when an object is moving through the world. They also suggest using an off-the-shelf object bounding box model to find particular objects, and track them throughout the video, and to use contrastive learning specifically on the bounding boxes that the algorithm thinks track a consistent object. 

https://i.imgur.com/2GfCTog.png

Overall, my take on this paper is that the analysis they do - of different kinds of invariances contrastive vs supervised loss does well on, and of the extent to which contrastive loss results might be biased by datasets - is quite interesting and a valuable contribution to our understanding of these very currently-hypey algorithms. However, I'm a bit less impressed by the novelty of their proposed solution. Temporal forms of contrastive learning have been around before - in reinforcement learning, and even in the original Contrastive Predictive Coding paper, where the related pairs were related by dint of temporal closeness. So, while using it in video is certainly a good idea, it doesn't really feel strongly novel to me. I also feel a little confused by their choice of using an off-the-shelf object detection model as a pre-requisite for a self-supervised task, since my impression was that a central goal of self-supervision was building techniques that could scale to situations where it was infeasible to get large amounts of labels, and any method that relies on a pre-existing trained object bounding box model is pretty inherently limited in that regard.

When humans classify images, we tend to use high-level information about the shape and position of the object. However, when convolutional neural networks classify images,, they tend to use low-level, or textural, information more than high-level shape information. This paper tries to understand what factors lead to higher shape bias or texture bias. 

To investigate this, the authors look at three datasets with disagreeing shape and texture labels. The first is GST, or Geirhos Style Transfer. In this dataset, style transfer is used to render the content of one class in the style of another (for example, a cat shape in the texture of an elephant). In the Navon dataset, a large-scale letter is rendered by tiling smaller letters. And, in the ImageNet-C dataset, a given class is rendered with a particular kind of distortion; here the distortion is considered to be the "texture label". In the rest of the paper, "shape bias" refers to the extent to which a model trained on normal images will predict the shape label rather than the texture label associated with a GST image. The other datasets are used in experiments where a model explicitly tries to learn either shape or texture. 

https://i.imgur.com/aw1MThL.png

To start off, the authors try to understand whether CNNs are inherently more capable of learning texture information rather than shape information. To do this, they train models on either the shape or the textural label on each of the three aforementioned datasets. On GST and Navon, shape labels can be learned faster and more efficiently than texture ones. On ImageNet-C (i.e. distorted ImageNet), it seems to be easier to learn texture than texture, but recall here that texture corresponds to the type of noise, and I imagine that the cardinality of noise types is far smaller than that of ImageNet images, so I'm not sure how informative this comparison is. Overall, this experiment suggests that CNNs are able to learn from shape alone without low-level texture as a clue, in cases where the two sources of information disagree 

The paper moves on to try to understand what factors about a normal ImageNet model give it higher or lower shape bias - that is, a higher or lower likelihood of classifying a GST image according to its shape rather than texture. Predictably, data augmentations have an effect here. When data is augmented with aggressive random cropping, this increases texture bias relative to shape bias, presumably because when large chunks of an object are cropped away, its overall shape becomes a less useful feature. Center cropping is better for shape bias, probably because objects are likely to be at the center of the image, so center cropping has less of a chance of distorting them. On the other hand, more "naturalistic" augmentations like adding Gaussian noise or distorting colors lead to a higher shape bias in the resulting networks, up to 60% with all the modifications. However, the authors also find that pushing the shape bias up has the result of dropping final test accuracy. 

https://i.imgur.com/Lb6RMJy.png

Interestingly, while the techniques that increase shape bias seem to also harm performance, the authors also find that higher-performing models tend to have higher shape bias (though with texture bias still outweighing shape) suggesting that stronger models learn how to use shape more effectively, but also that handicapping models' ability to use texture in order to incentivize them to use shape tends to hurt performance overall. 

Overall, my take from this paper is that texture-level data is actually statistically informative and useful for classification - even in terms of generalization - even if is too high-resolution to be useful as a visual feature for humans. CNNs don't seem inherently incapable of learning from shape, but removing their ability to rely on texture seems to lead to a notable drop in accuracy, suggesting there was real signal there that we're losing out on.

This paper focuses on an effort by a Deepmind team to train an agent that can play the game Diplomacy - a complex, multiplayer game where players play as countries controlling units, trying to take over the map of Europe. Some relevant factors of this game, for the purposes of this paper, are: 

1) All players move at the same time, which means you need to model your opponent's current move, and play a move that succeeds in expectation over that predicted move distribution. This also means that, in order to succeed, your policy can't be easily predictable, since, if it is, you're much easier to exploit, since your opponents can more easily optimize their response to what they predict you'll do 

2) The action space is huge, even compared to something like Chess 

3) The game has significant multiagent complexity: rather than being straightforwardly zero-sum in its reward structure, like Chess or Go, it's designed to require alliances between players in order to succeed 

Prior work - DipNet -  had been able to outperform other hand-coded models through a deep network that imitated human actions, but the authors hadn't been able to get RL to successfully learn on top of that imitation baseline. 

The basic approach this model takes is one that will probably feel familiar if you've read Deepmind's prior work on Chess or Go: an interplay between a fast-to-evaluate neural net component, and a slower, more explicit, strategically designed component. The slower "expert" component uses the fast network component as part of its evaluation of different moves' consequences, and then, once the slow expert has generated a series of decisions, the neural net policy learns to imitate those decisions. 

In this case, the slower expert tries to explicitly calculate a Best Response strategy, given some belief about what your opponents will do at the state you're in. Since the action space is so large, it isn't possible to calculate a full best response (that is, your best *possible* action given the actions you expect your opponents to take), so this paper instead lays out a Sampled Best Response algorithm. It takes as input a state, as well as an opponent policy, a candidate policy, and a value network. (More on how those come to be layer). In the simplest case, the SBR algorithm works by: 

1. Sampling some number (B) of actions from the opponent policy given the state. These represent a sample distribution of what moves you think your opponents are likely to play
2. Sampling some number (C) of candidate actions from your candidate policy. 
3. For each candidate action, evaluating - for each opponent action - the state you'd reach if you took the candidate action and the opponent took the opponent action, according to your value network. 
4. This gives you an estimated Q value for each of your candidate actions; if you pick the action with the highest Q value, this approximates your best response action to the opponent policy distribution you pass in 

Once you have this SBR procedure, you can use it to bootstrap a better policy and a value network by starting with a policy and value learned from pure human-imitation, and then using SBR - with your current policy as both the opponent and candidate policy - to generate a dataset of trajectories (where each action in the trajectory is chosen according to the SBR procedure). With that trajectory dataset, you can train your policy and value networks to be able to better approximate the actions that SBR would have taken. 

The basic version of this procedure is called IBR - Iterated Best Response. This is because, at each stage, SBR will return a policy that tries to perform well against the current version of the opponent policy. This kind of behavior is potentially troublesome, since you can theoretically have it lead to cycles, like those in Rock Paper Scissors where paper beats rock, scissors beat paper, and then rock beats scissors again. At each stage, you find the best response to what your opponent is doing right now, but you don't actually make transitive progress. A common way of improving along the axis of this particular failure mode is to learn via a "fictitious play" rather than "self play". Putting aside the name - which I don't find very usefully descriptive - this translates to simulating playing against, not the current version of your opponent, but a distribution made up of past versions of the opponent. This helps prevent cycling, because choosing a strategy that only defeats the current version but would lose to a prior version is no longer a rewarding option. 

The Fictitious Play-based approach this paper proposes - FPPI2 - tries to resolve this problem. Instead of sampling actions in step (1) from only your current opponent policy, it uses a sampling procedure where, for each opponent action, it first samples a point in history, and then samples the opponent policy vector at that point in history (so the multiple opponent moves collectively represent a coherent point in strategy space). Given this action profile, the final version of the algorithm continues to use the most recent/updated timestep of the policy and value network for the candidate policy and value network used in SBR, so that you're (hopefully) sampling high quality actions, and making accurate assessments of states, even while you use the distribution of (presumably worse) policies to construct the opponent action distribution that you evaluate your candidate actions against. 

https://i.imgur.com/jrQAAQW.png

The authors don't evaluate against human players, but do show that their FPPI2 approach consistently outperforms the prior DipNet state of the art, and performed the best overall, though Iterated Best Response performs better than they say they expected.

Some other thoughts: 

- This system is still fairly exploitable, and doesn't become meaningfully less so during training, though it does become more difficult to exploit quickly
- This does seem like a problem overall where you do a lot of modeling of what you expect your opponents strategies to be, and it seems hard to be robust, especially to collusion of your opponents
- I was a bit disappointed that the initial framing of the paper put a lot of emphasis on the alliance-focused nature of the game, but then neither suggested mechanisms targeting that aspect of the game, nor seemed to do any specific analysis of
- I would have expected this game to benefit from some explicit modeling of different agents having different policies; possibly this just isn't something they could have had be the case under their evaluation scheme, which played against copies of a given policy?

Overall, my sense is that this is still a pretty early-stage checkpoint in the effort of playing Diplomacy, and that we've still got a ways to go, but it is interesting early work, and I'm curious where it leads.

This was a really cool-to-me paper that asked whether contrastive losses, of the kind that have found widespread success in semi-supervised domains, can add value in a supervised setting as well. In a semi-supervised context, contrastive loss works by pushing together the representations of an "anchor" data example with an augmented version of itself (which is taken as a positive or target, because the image is understood to not be substantively changed by being augmented), and pushing the representation of that example away from other examples in the batch, which are negatives in the sense that they are assumed to not be related to the anchor image. 

This paper investigates whether this same structure - of training representations of positives to be close relative to negatives - could be expanded to the supervised setting, where "positives" wouldn't just mean augmented versions of a single image, but augmented versions of other images belonging to the same class. This would ideally combine the advantages of self-supervised contrastive loss - that explicitly incentivizes invariance to augmentation-based changes - with the advantages of a supervised signal, which allows the representation to learn that it should also see instances of the same class as close to one another. 

https://i.imgur.com/pzKXEkQ.png

To evaluate the performance of this as a loss function, the authors first train the representation - either with their novel supervised contrastive loss SupCon, or with a control cross-entropy loss - and then train a linear regression with cross-entropy on top of that learned representation. (Just because, structurally, a contrastive loss doesn't lead to assigning probabilities to particular classes, even if it is supervised in the sense of capturing information relevant to classification in the representation) 

The authors investigate two versions of this contrastive loss, which differ, as shown below, in terms of the relative position of the sum and the log operation, and show that the L_out version dramatically outperforms (and I mean dramatically, with a top-one accuracy of 78.7 vs 67.4%). 

https://i.imgur.com/X5F1DDV.png

The authors suggest that the L_out version is superior in terms of training dynamics, and while I didn't fully follow their explanation, I believe it had to do with L_out version doing its normalization outside of the log, which meant it actually functioned as a multiplicative normalizer, as opposed to happening inside the log, where it would have just become an additive (or, really, subtractive) constant in the gradient term. Due to this stronger normalization, the authors positive the L_out loss was less noisy and more stable. 

Overall, the authors show that SupCon consistently (if not dramatically) outperforms cross-entropy when it comes to final accuracy. They also show that it is comparable in transfer performance to a self-supervised contrastive loss. One interesting extension to this work, which I'd enjoy seeing more explored in the future, is how the performance of this sort of loss scales with the number of different augmentations that performed of each element in the batch (this work uses two different augmentations, but there's no reason this number couldn't be higher, which would presumably give additional useful signal and robustness?)

A central problem in the domain of reinforcement learning is how to incentivize exploration and diversity of experience, since RL agents can typically only learn from states they go to, and it can often be the case that states with high reward don't have an obvious trail of high-reward states leading to them, meaning that algorithms that are naively optimizing for reward will be relatively unlikely to discover them. One potential way to promote exploration is to train an ensemble of agents, and have part of your loss that incentivizes diversity in the behavior of those agents. Intuitively, an incentive for diversity will push policies away from one another, which will force them to behave differently, and thus reach a wider range of different states. 

Current work in diversity tends to penalize, for each agent, the average pairwise distance between it and every other agent. The authors of this paper have two critiques with this approach:

1. Pure pairwise distance doesn't fully capture the notion of diversity we might want, since if you have policies that are clustered together into multiple clusters, average pairwise distance can be increased by moving the clusters farther apart, without having to break up the clusters themselves
2. Having the diversity term be calculated for each policy independently can lead to "cycling" behavior, where policies move in ways that increase distance at each step, but don't do so when each agent's independent steps are taken into account 

As an alternative, they propose calculating the pairwise Kernel function similarity between all policies (where each policy is represented as the average action probabilities it returns across a sample of states), and calculating the determinate of that matrix. The authors claim that this represents a better measure of full population diversity. I can't fully connect the dots on this intuitively, but what I think they're saying is: the determinant of the kernel matrix tells you  something about the effective dimensionality spanned by the different policies. In the same way that, if a matrix is low-rank, it tells you that some vectors within it can be nearly represented by linear combinations of others, a low value of the Kernel determinant means that some policies can be sufficiently represented by combinations of other policies, such that it isn't really adding diversity value to the ensemble. 

https://i.imgur.com/CmlGsNP.png

Another contribution of this paper is to propose an interesting bandit-based way of determining when to incentivize diversity vs focus on pure reward. The diversity term in the loss is governed by a lambda parameter, and the paper's model sets up Thompson sampling to determine what the value of the parameter should be at each training iteration. This bandit setup works by starting out uncertain over whether to include diversity in the loss, and building a model of whether reward tends to increase during steps where diversity is used. Over time, if diversity consistently doesn't produce benefits, the sampler will tend more towards excluding it from the loss. This is just a really odd, different idea, that I've never heard of before in the context of hyperparameter scheduling during training. I will say that I'm somewhat confused about the window of time that the bandit uses for calculating rewards. Is it a set of trajectories used in a single training batch, or longer than that? Questions aside, they do so fairly convincingly that the adaptive parameter schedule outperforms over a fixed schedule, though they don't test it against simpler forms of annealing, so I'm less clear on whether it would outperform those. 

Overall, I still have some confusions about the method proposed by this paper, but it seems to be approaching the question of exploration from an interesting direction, and I'd enjoy trying to understand it further in future.

This is an interesting - and refreshing - paper, in that, instead of trying to go all-in on a particular theoretical point, the authors instead run a battery of empirical investigations, all centered around the question of how to explain what happens to make transfer learning work. The experiments don't all line up to support a single point, but they do illustrate different interesting facets of the transfer process. 

- An initial experiment tries to understand how much of the performance of fine-tuned models can be explained by (higher-level, and thus larger-scale) features, and how much is driven by lower level (and thus smaller-scale) image statistics.  To start with, the authors compare the transfer performance from ImageNet onto three different datasets - clip art, sketches, and real images. As expected, transfer performance is highest with real datasets, which are the most similar to training domain. However, there still *is* positive transfer in terms of final performance across all domains, as well as benefit in optimization speed.
- To try to further tease out the difference between the transfer benefits of high and low-level features, the authors run an experiment where blocks of pixels are shuffled around within the image on downstream tasks .  The larger the size of the blocks being shuffled, the more that large-scale features of the image are preserved. As predicted, accuracy drops dramatically when pixel block size is small, for both randomly initialized and pretrained models. In addition, the relative value added by pretraining drops, for all datasets except quickdraw (the dataset of sketches). This suggests that in most datasets, the value brought by fine-tuning was mostly concentrated in large-scale features. One interesting tangent of this experiment was the examination of optimization speed (in the form of mean training accuracy over initial epochs). Even at block sizes too small for pretraining to offer a benefit to final accuracy, it did still contribute to faster training. (See transparent bars in right-hand plot below)
https://i.imgur.com/Y8sO1da.png

- On a somewhat different front, the authors look into how similar pretrained + finetuned models are to one another, compared to models trained on the same dataset from random initializations. First, they look at a measure of feature similarity, and find that the features learned by two pretrained networks are more similar to each other than a pretrained network is to a randomly initalized network, and also more than two randomly initialized networks are to one another. Randomly initialized networks are closest to one another in their final-layer features, but this is still a multiple of 4 or 5 less than the similarity between the pretrained networks
- Looking at things from the perspective of optimization, the paper measures how much performance drops when you linearly interpolate between different solutions found by both randomly initialized and pretrained networks. For randomly initialized networks, interpolation requires traversing a region where test accuracy drops to 0%. However, for pretrained networks, this isn't the case, with test accuracy staying high throughout. This suggests that pretraining gets networks into a basin of the loss landscape, and that future training stays within that basin. There were also some experiments on module criticality that I believe were in a similar vein to these, but which I didn't fully follow
- Finally, the paper looks at the relationship between accuracy on the original pretraining task and both accuracy and optimization speed on the downstream task. They find that higher original-task accuracy moves in the same direction as higher downstream-task accuracy, though this is less true when the downstream task is less related (as with quickdraw). Perhaps more interestingly, they find that the benefits of transfer to optimization speed happen and plateau quite early in training. Clip Art and Real transfer tasks are much more similar in the optimization speed benefits they get form ImageNet training, where on the accuracy front, the real did dramatically better.
https://i.imgur.com/jBCJcLc.png

While there's a lot to dig into in these results overall, the things I think are most interesting are the reinforcing of the idea that even very random and noisy pretraining can be beneficial to optimization speed (this seems reminiscent of another paper I read from this year's NeurIPS, examining why pretraining on random labels can help downstream training), and the observation that pretraining deposits weights in a low-loss bucket, from which they can learn more efficiently (though, perhaps, if the task is too divergent from the pretraining task, this difficulty in leaving the basin becomes a disadvantage). This feels consistent with some work in the Lottery Ticket Hypothesis, which has recently suggested that, after a short duration of training, you can rewind a network to a checkpoint saved after that duration, and be successfully able to train to low loss again.