A) vec ( B) (8) 14 Hence, identity 8 allows us to re-write the previous equation as follows: k ( g.x)=

A) vec ( B) (8) 14 Hence, identity 8 allows us to re-write the previous equation as follows: k ( g.x)=

We investigate the effects on authorship identification tasks of a fundamental shift in how to conceive the vectorial representations of documents that are given as input to a supervised learner. In ``classic'' authorship analysis a feature vector represents a document, the value of a feature represents (an increasing function of) the relative frequency of the feature in the document, and the class label represents the author of the document. We instead investigate the situation in which a feature vector represents an unordered pair of documents, the value of a feature represents the absolute difference in the relative frequencies (or increasing functions thereof) of the feature in the two documents, and the class label indicates whether the two documents are from the same author or not. This latter (learner-independent) type of representation has been occasionally used before, but has never been studied systematically. We argue that it is advantageous, and that in some cases (e.g., authorship verification) it provides a much larger quantity of information to the training process than the standard representation. The experiments that we carry out on several publicly available datasets (among which one that we here make available for the first time) show that feature vectors representing pairs of documents (that we here call Diff-Vectors) bring about systematic improvements in the effectiveness of authorship identification tasks, and especially so when training data are scarce (as it is often the case in real-life authorship identification scenarios). Our experiments tackle same-author verification, authorship verification, and closed-set authorship attribution; while DVs are naturally geared for solving the 1st, we also provide two novel methods for solving the 2nd and 3rd that use a solver for the 1st as a building block.

A recent line of work has established uncoupled learning dynamics such that, when employed by all players in a game, each player's \emph{regret} after $T$ repetitions grows polylogarithmically in $T$, an exponential improvement over the traditional guarantees within the no-regret framework. However, so far these results have only been limited to certain classes of games with structured strategy spaces -- such as normal-form and extensive-form games. The question as to whether $O(\text{polylog} T)$ regret bounds can be obtained for general convex and compact strategy sets -- which occur in many fundamental models in economics and multiagent systems -- while retaining efficient strategy updates is an important question. In this paper, we answer this in the positive by establishing the first uncoupled learning algorithm with $O(\log T)$ per-player regret in general \emph{convex games}, that is, games with concave utility functions supported on arbitrary convex and compact strategy sets. Our learning dynamics are based on an instantiation of optimistic follow-the-regularized-leader over an appropriately \emph{lifted} space using a \emph{self-concordant regularizer} that is, peculiarly, not a barrier for the feasible region. Further, our learning dynamics are efficiently implementable given access to a proximal oracle for the convex strategy set, leading to $O(\log\log T)$ per-iteration complexity; we also give extensions when access to only a \emph{linear} optimization oracle is assumed. Finally, we adapt our dynamics to guarantee $O(\sqrt{T})$ regret in the adversarial regime. Even in those special cases where prior results apply, our algorithm improves over the state-of-the-art regret bounds either in terms of the dependence on the number of iterations or on the dimension of the strategy sets.

We study the optimization problem associated with fitting two-layer ReLU neural networks with respect to the squared loss, where labels are generated by a target network. Use is made of the rich symmetry structure to develop a novel set of tools for studying the mechanism by which over-parameterization annihilates spurious minima. Sharp analytic estimates are obtained for the loss and the Hessian spectrum at different minima, and it is proved that adding neurons can turn symmetric spurious minima into saddles; minima of lesser symmetry require more neurons. Using Cauchy's interlacing theorem, we prove the existence of descent directions in certain subspaces arising from the symmetry structure of the loss function. This analytic approach uses techniques, new to the field, from algebraic geometry, representation theory and symmetry breaking, and confirms rigorously the effectiveness of over-parameterization in making the associated loss landscape accessible to gradient-based methods. For a fixed number of neurons and inputs, the spectral results remain true under symmetry breaking perturbation of the target.

In this paper, we present a method for learning from video demonstrations by using human feedback to construct a mapping between the standard representation of the agent and the visual representation of the demonstration. In this way, we leverage the advantages of both these representations, i.e., we learn the policy using standard state representations, but are able to specify the expected behavior using video demonstration. We train an autonomous agent using a single video demonstration and use human feedback (using numerical similarity rating) to map the standard representation to the visual representation with a neural network. We show the effectiveness of our method by teaching a hopper agent in the MuJoCo to perform a backflip using a single video demonstration generated in MuJoCo as well as from a real-world YouTube video of a person performing a backflip. Additionally, we show that our method can transfer to new tasks, such as hopping, with very little human feedback.

Many applications of machine learning require models that are human-aligned, i.e., that make decisions based on human-meaningful information about the input. We identify the pervasive brittleness of deep networks' learned representations as a fundamental barrier to attaining this goal. We then re-cast robust optimization as a tool for enforcing human priors on the features learned by deep neural networks. The resulting robust feature representations turn out to be significantly more aligned with human perception. We leverage these representations to perform input interpolation, feature manipulation, and sensitivity mapping, without any post-processing or human intervention after model training. Our code and models for reproducing these results is available at https://git.io/robust-reps.