One of the dominant narratives of the deep learning renaissance has been the value of well-designed inductive bias - structural choices that shape what a model learns. The biggest example of this can be found in convolutional networks, where models achieve a dramatic parameter reduction by having features maps learn local patterns, which can then be re-used across the whole image. This is based on the prior belief that patterns in local images are generally locally contiguous, and so having feature maps that focus only on small (and gradually larger) local areas is a good fit for that prior. This paper operates in a similar spirit, except its input data isn’t in the form of an image, but a graph: the social graph of multiple agents operating within a Multi Agent RL Setting. In some sense, a graph is just a more general form of a pixel image: where a pixel within an image has a fixed number of neighbors, which have fixed discrete relationships to it (up, down, left, right), nodes within graphs have an arbitrary number of nodes, which can have arbitrary numbers and types of attributes attached to that relationship. 

The authors of this paper use graph networks as a sort of auxiliary information processing system alongside a more typical policy learning framework, on tasks that require group coordination and knowledge sharing to complete successfully. For example, each agent might be rewarded based on the aggregate reward of all agents together, and, in the stag hunt, it might require collaborative effort by multiple agents to successfully “capture” a reward. Because of this, you might imagine that it would be valuable to be able to predict what other agents within the game are going to do under certain circumstances, so that you can shape your strategy accordingly. 

The graph network used in this model represents both agents and objects in the environment as nodes, which have attributes including their position, whether they’re available or not (for capture-able objects), and what their last action was. As best I can tell, all agents start out with directed connections going both ways to all other agents, and to all objects in the environment, with the only edge attribute being whether the players are on the same team, for competitive environments. Given this setup, the graph network works through a sort of “diffusion” of information, analogous to a message passing algorithm. At each iteration (analogous to a layer), the edge features pull in information from their past value and sender and receiver nodes, as well as from a “global feature”. Then, all of the nodes pull in information from their edges, and their own past value. Finally, this “global attribute” gets updated based on summations over the newly-updated node and edge information. (If you were predicting attributes that were graph-level attributes, this global attribute might be where you’d do that prediction. However, in this case, we’re just interested in predicting agent-level actions). 

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

All of this has the effect of explicitly modeling agents as entities that both have information, and have connections to other entities. One benefit the authors claim of this structure is that it allows them more interpretability: when they “play out” the values of their graph network, which they call a Relational Forward Model or RFM, they observe edge values for two agents go up if those agents are about to collaborate on an action, and observe edge values for an agent and an object go up before that object is captured. Because this information is carefully shaped and structured, it makes it easier for humans to understand, and, in the tests the authors ran, appears to also help agents do better in collaborative games.

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

While I find graph networks quite interesting, and multi-agent learning quite interesting, I’m a little more uncertain about the inherent “graphiness” of this problem, since there aren’t really meaningful inherent edges between agents.  One thing I am curious about here is how methods like these would work in situations of sparser graphs, or, places where the connectivity level between a node’s neighbors, and the average other node in the graph is more distinct. Here, every node is connected to every other node, so the explicit information localization function of graph networks is less pronounced. I might naively think that - to whatever extent the graph is designed in a way that captures information meaningful to the task - explicit graph methods would have an even greater comparative advantage in this setting. 

The goal of this paper is to learn a model that embeds 2D keypoints(the locations of specific key body parts in 2D space) representing a particular pose into a vector embedding where nearby points in embedding space are also nearby in 3D space. This sort of model is useful because the same 3D pose can generate a wide variety of 2D pose projections, and it can be useful to learn which apparently-distinct representations actually map to the same 3D pose. 

To do this, the basic approach used by the authors (with has a few variants), is

- Take a dataset of 3D poses, and corresponding 2D projections
- Define a notion of "matching" 3D poses, based on a parameter kappa, which designates the maximum average per-joint distance at which two 3D poses can be considered the same
- Construct triplets composed of an anchor pose, a "positive" pose (a different 2D pose with a matching 3D pose), and a "negative" pose (some other 2D pose sampled from the dataset using a strategy that explicitly seeks out hard negative examples)
- Calculate a triplet loss, that pushes positive examples closer together, and pulls negative examples farther apart. This is specifically done by defining a probabilistic representation of p(match | z1, z2), or, the probability of a match in 3D space given the embeddings of the two 2D poses. This is parametrized using a sigmoid with trainable parameters, as shown below

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

- They they calculate a distance kernel as the negative log of that probability, and calculate the basic triplet loss, which tries to maximize the diff between the the distance between negative examples, and the distance between positive examples.
- They also add an additional loss further incentivizing the match probability to be higher on the positive pair (in addition to just pushing the positive and negative pair further apart)
- The final loss is a Gaussian prior loss, incentivizing the learned embeddings z to be in the shape of a Gaussian

https://i.imgur.com/SxvcvJG.png
This represents the central shape of the method. Some additional ablations include: 

- Camera Augmentation: Creational additional triplets by taking existing 3D poses and generating artificial pairs of 2D poses at different camera views
- Temporal Pose Embedding -  Embedding multiple temporally connected pose, rather than just a single one
- Keypoint Dropout - To simulate situations where some keypoints are occluded, the authors tried training with some keypoints dropped out, either keypoints selected at random, or selected jointly and non-independently based on a model of which keypoints are likely to be occluded together

The authors found that their method was generally quite a bit stronger that prior approaches for the task of querying similar 3D poses given a 2D pose input, including some alternate methods that do direct 3D estimation.

Rozsa et al. describe an adersarial attack against OpenMax [1] by directly targeting the logits. Specifically, they assume a network using OpenMax instead of a SoftMax layer to compute the final class probabilities. OpenMax allows “open-set” networks by also allowing to reject input samples. By directly targeting the logits of the trained network, i.e. iteratively pushing the logits in a target direction, it does not matter whether SoftMax or OpenMax layers are used on top, the network can be fooled in both cases.

Also find this summary at [davidstutz.de](https://davidstutz.de/category/reading/).

Sharif et al. study the effectiveness of $L_p$ norms for creating adversarial perturbations. In this context, their main discussion revolves around whether $L_p$ norms are sufficient and/or necessary for perceptual similarity. Their main conclusion is that $L_p$ norms are neither necessary nor sufficient to ensure perceptual similarity. For example, an adversarial example might be within a specific $L_p$ bal, but humans might still identify it as not similar enough to the originally attacked sample; on the other hand, there are also some imperceptible perturbations that usually extend beyond a reasonable $L_p$ ball. Such transformatons might for example include small rotations or translation. These findings are interesting because it indicates that our current model, or approximation, or perceptual similarity is not meaningful in all cases.

Also find this summary at [davidstutz.de](https://davidstutz.de/category/reading/).

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?)