In the two years since it’s been introduced, the Transformer architecture, which uses multi-headed self-attention in lieu of recurrent models to consolidate information about input and output sequences, has more or less taken the world of language processing and understanding by storm. It has become the default choice for language for problems like translation and questioning answering, and was the foundation of OpenAI’s massive language-model-trained GPT. In this context, I really appreciate this paper’s work to try to build our collective intuitions about the structure, specifically by trying to understand how the multiple heads that make up the aforementioned multi-head attention divide up importance and specialize function. 

As a quick orientation, attention works by projecting each value in the sequence into query, key, and value vectors. Then, each element in the sequence creates its next-layer value by calculating a function of query and key (typically dot product) and putting that in a softmax against the query results with every other element. This weighting distribution is then used as the weights of a weighted average, combining the values together. By default this is a single operation, with a single set of projection matrices, but in the Transformer approach, they use multi-headed attention, which simply means that they learn independent parameters for multiple independent attention “filters”, each of which can then notionally specialize to pull in and prioritize a certain kind of information. 
https://i.imgur.com/yuC91Ja.png

The high level theses of this paper are: 
- Among attention heads, there’s a core of the most crucial and important ones, and then a long tail of heads that can be pruned (or, have their weight in the concatenation of all attention heads brought to nearly zero) and have a small effect on performance 
- It’s possible and useful to divide up the heads according to the kinds of other tokens that it is most consistently pulling information from. The authors identify three: positional, syntactic, and rare.  Positional heads consistently (>90% of the time) put their maximum attention weight on the same position relative to the query word. Syntactic heads are those that recurringly in the same grammatical relation to the query, the subject to its verb, or the adjective to its noun, for example. Rare words is not a frequently used head pattern, but it is a very valuable head within the first layer, and will consistently put its highest weight on the lowest-frequency word in a given sentence. 

An interesting side note here is that the authors tried at multiple stages in pruning to retrain a network using only the connections between unpruned heads, and restarting from scratch. However, in a effect reminiscent of the Lottery Ticket Thesis, retraining from scratch cannot get quite the same performance. 

The authors analyse in the very well written paper the relation between Fisher $F(\theta) = \sum_n \mathbb{E}_{p_{\theta}(y \vert x)}[\nabla_{\theta} \log(p_{\theta}(y \vert x_n))\nabla_{\theta} \log(p_{\theta}(y \vert x_n))^T] $ and empirical Fisher $\bar{F}(\theta) = \sum_n [\nabla_{\theta} \log(p_{\theta}(y_n \vert x_n))\nabla_{\theta} \log(p_{\theta}(y_n \vert x_n))^T] $, which has recently seen a surge in interest. . The definitions differ in that $y_n$ is a training label instead of a sample of the model $p_{\theta}(y \vert x_n)$, thus even so the name suggests otherwise $\bar{F}$ is not a empirical, for example Monte Carlo, estimate of the Fisher. The authors rebuff common arguments used to justify the use of the empirical fisher by an amendment to the generalized Gauss-Newton, give conditions when the empirical Fisher does indeed approach the Fisher and give an argument why the empirical fisher might work in practice nonetheless.   

The Fisher, capturing the curvature of the parameter space, provides information about the geometry of the parameters pace, the empirical Fisher might however fail so capture the curvature as the striking plot from the paper shows:
https://i.imgur.com/c5iCqXW.png

The authors rebuff the two major justifications for the use of empirical Fisher:
1. "the empirical Fisher matches the construction of a generalized Gauss-Newton"
 * for the log-likelihood $log(p(y \vert f) = \log \exp(-\frac{1}{2}(y-f)^2))$ the generalized Gauss-Newton intuition that small residuals $f(x_n, \theta) - y_n$ lead to a good approximation of the Hessian is not satisfied. Whereas the Fisher approaches the Hessian, the empirical Fisher approaches 0
2. "the empirical Fisher converges to the true Fisher when the model is a good fit for the data"
 * the authors sharpen the argument to "the empirical Fisher converges at the minimum to the Fisher as the number of samples grows", which is unlikely to be satisfied in practice. 

The authors provide an alternative perspective on why the empirical Fisher might be successful, namely to adapt the gradient to the gradient noise in stochastic optimization. The empirical Fisher coincides with the second moment of the stochastic gradient estimate and encodes as such covariance information about the gradient noise. This allows to reduce the effects of gradient noise by scaling back the updates in high variance aka noise directions. 

Bechtle et al. propose meta learning via learned loss ($ML^3$) and derive and empirically evaluate the framework on classification, regression, model-based and model-free reinforcement learning tasks. 

The problem is formalized as learning parameters $\Phi$ of a meta loss function $M_\phi$ that computes loss values $L_{learned} = M_{\Phi}(y, f_{\theta}(x))$. Following the outer-inner loop meta algorithm design the learned loss $L_{learned}$ is used to update the parameters of the learner in the inner loop via gradient descent:
$\theta_{new} = \theta - \alpha \nabla_{\theta}L_{learned} $. The key contribution of the paper is the way to construct a differentiable learning signal for the loss parameters $\Phi$.

The framework requires to specify a task loss $L_T$ during meta train time, which can be for example the mean squared error for regression tasks. After updating the model parameters to $\theta_{new}$ the task loss is used to measure how much learning progress has been made with loss parameters $\Phi$. The key insight is the decomposition via chain-rule of  $\nabla_{\Phi} L_T(y, f_{\theta_{new}})$:

$\nabla_{\Phi} L_T(y, f_{\theta_{new}}) = \nabla_f L_t \nabla_{\theta_{new}}f_{\theta_{new}} \nabla_{\Phi} \theta_{new} = \nabla_f L_t \nabla_{\theta_{new}}f_{\theta_{new}} [\theta - \alpha \nabla_{\theta} \mathbb{E}[M_{\Phi}(y, f_{\theta}(x))]]$.

This allows to update the loss parameters with gradient descent as: $\Phi_{new} = \Phi - \eta \nabla_{\Phi} L_T(y, f_{\theta_{new}})$. 

This update rules yield the following $ML^3$ algorithm for supervised learning tasks:

https://i.imgur.com/tSaTbg8.png

For reinforcement learning the task loss is the expected future reward of policies induced by the policy $\pi_{\theta}$, for model-based rl with respect to the approximate dynamics model and for the model free case a system independent surrogate: $L_T(\pi_{\theta_{new}}) = -\mathbb{E}_{\pi_{\theta_{new}}} \left[ R(\tau_{\theta_{new}})  \log \pi_{\theta_{new}}(\tau_{new})\right] $. 

The allows further to incorporate extra information via an additional loss term $L_{extra}$ and to consider the augmented task loss $\beta L_T + \gamma L_{extra} $, with weights $\beta, \gamma$ at train time. Possible extra loss terms are used to add physics priors, encouragement of exploratory behavior or to incorporate expert demonstrations. The experiments show that this, at test time unavailable information, is retained in the shape of the loss landscape. 

The paper is packed with insightful experiments and shows that the learned loss function:
- yields in regression and classification better accuracies at train and test tasks
- generalizes well and speeds up learning in model based rl tasks
- yields better generalization and faster learning in model free rl
- is agnostic across a bunch of evaluated architectures (2,3,4,5 layers)
- with incorporated extra knowledge yields better performance than without and is superior to alternative approaches like iLQR in a MountainCar task. 

The paper introduces a promising alternative, by learning the loss parameters, to MAML like approaches that learn the model parameters. It would be interesting to see if the learned loss function generalizes better than learned model parameters to a broader distribution of tasks like the meta-world tasks. 

Benchmarking Deep Learning Hardware and Frameworks: Qualitative Metrics 

Previous papers on benchmarking deep neural networks offer knowledge of deep learning hardware devices and software frameworks. This paper introduces benchmarking principles, surveys machine learning devices including GPUs, FPGAs, and ASICs, and reviews deep learning software frameworks. It also qualitatively compares these technologies with respect to benchmarking from the angles of our 7-metric approach to deep learning frameworks and 12-metric approach to machine learning hardware platforms. 

After reading the paper, the audience will understand seven benchmarking principles, generally know that differential characteristics of mainstream artificial intelligence devices,  qualitatively compare deep learning hardware through the 12-metric approach for benchmarking neural network hardware, and read benchmarking results of 16 deep learning frameworks via our 7-metric set for benchmarking  frameworks.

## General Framework
Extends T-REX (see [summary](https://www.shortscience.org/paper?bibtexKey=journals/corr/1904.06387&a=muntermulehitch)) so that preferences (rankings) over demonstrations are generated automatically (back to the common IL/IRL setting where we only have access to a set of unlabeled demonstrations). Also derives some theoretical requirements and guarantees for better-than-demonstrator performance. 

## Motivations
* Preferences over demonstrations may be difficult to obtain in practice. 
* There is no theoretical understanding of the requirements that lead to outperforming demonstrator. 

## Contributions
* Theoretical results (with linear reward function) on when better-than-demonstrator performance is possible: 1- the demonstrator must be suboptimal (room for improvement, obviously), 2- the learned reward must be close enough to the reward that the demonstrator is suboptimally optimizing for (be able to accurately capture the intent of the demonstrator), 3- the learned policy (optimal wrt the learned reward) must be close enough to the optimal policy (wrt to the ground truth reward). Obviously if we have 2- and a good enough RL algorithm we should have 3-, so it might be interesting to see if one can derive a requirement from only 1- and 2- (and possibly a good enough RL algo). 
* Theoretical results (with linear reward function) showing that pairwise preferences over demonstrations reduce the error and ambiguity of the reward learning. They show that without rankings two policies might have equal performance under a learned reward (that makes expert's demonstrations optimal) but very different performance under the true reward (that makes the expert optimal everywhere). Indeed, the expert's demonstration may reveal very little information about the reward of (suboptimal or not) unseen regions which may hurt very much the generalizations (even with RL as it would try to generalize to new states under a totally wrong reward). They also show that pairwise preferences over trajectories effectively give half-space constraints on the feasible reward function domain and thus may decrease exponentially the reward function ambiguity. 
* Propose a practical way to generate as many ranked demos as desired.

## Additional Assumption
Very mild, assumes that a Behavioral Cloning (BC) policy trained on the provided demonstrations is better than a uniform random policy. 

## Disturbance-based Reward Extrapolation (D-REX)

![](https://i.imgur.com/9g6tOrF.png)

![](https://i.imgur.com/zSRlDcr.png)

They also show that the more noise added to the BC policy the lower the performance of the generated trajs. 

## Results
Pretty much like T-REX.