We extend the pseudorandomness of random walks on expander graphs using the sticky random walk. Building on prior works, it was recently shown that expander random walks can fool all symmetric functions in total variation distance (TVD) upto an $O(\lambda(\frac{p}{\min f})^{O(p)})$ error, where $\lambda$ is the second largest eigenvalue of the expander, $p$ is the size of the arbitrary alphabet used to label the vertices, and $\min f = \min_{b\in[p]} f_b$, where $f_b$ is the fraction of vertices labeled $b$ in the graph. Golowich and Vadhan conjecture that the dependency on the $(\frac{p}{\min f})^{O(p)}$ term is not tight. In this paper, we resolve the conjecture in the affirmative for a family of expanders. We present a generalization of the sticky random walk for which Golowich and Vadhan predict a TVD upper bound of $O(\lambda p^{O(p)})$ using a Fourier-analytic approach. For this family of graphs, we use a combinatorial approach involving the Krawtchouk functions to derive a strengthened TVD of $O(\lambda)$. Furthermore, we present equivalencies between the generalized sticky random walk, and, using linear-algebraic techniques, show that the generalized sticky random walk parameterizes an infinite family of expander graphs.
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The aim of this work is to improve musculoskeletal-based models of the upper-limb Wrench Feasible Set i.e. the set of achievable maximal wrenches at the hand for applications in collaborative robotics and computer aided ergonomics. In particular, a recent method performing wrench capacity evaluation called the Iterative Convex Hull Method is upgraded in order to integrate non dislocation and compression limitation constraints at the glenohumeral joint not taken into account in the available models. Their effects on the amplitude of the force capacities at the hand, glenohumeral joint reaction forces and upper-limb muscles coordination in comparison to the original iterative convex hull method are investigated in silico. The results highlight the glenohumeral potential dislocation for the majority of elements of the wrench feasible set with the original Iterative Convex Hull method and the fact that the modifications satisfy correctly stability constraints at the glenohumeral joint. Also, the induced muscles coordination pattern favors the action of stabilizing muscles, in particular the rotator-cuff muscles, and lowers that of known potential destabilizing ones according to the literature.
Autonomous Cyber Defence is required to respond to high-tempo cyber-attacks. To facilitate the research in this challenging area, we explore the utility of the autonomous cyber operation environments presented as part of the Cyber Autonomy Gym for Experimentation (CAGE) Challenges, with a specific focus on CAGE Challenge 2. CAGE Challenge 2 required a defensive Blue agent to defend a network from an attacking Red agent. We provide a detailed description of the this challenge and describe the approaches taken by challenge participants. From the submitted agents, we identify four classes of algorithms, namely, Single- Agent Deep Reinforcement Learning (DRL), Hierarchical DRL, Ensembles, and Non-DRL approaches. Of these classes, we found that the hierarchical DRL approach was the most capable of learning an effective cyber defensive strategy. Our analysis of the agent policies identified that different algorithms within the same class produced diverse strategies and that the strategy used by the defensive Blue agent varied depending on the strategy used by the offensive Red agent. We conclude that DRL algorithms are a suitable candidate for autonomous cyber defence applications.
Our focus is on robust recovery algorithms in statistical linear inverse problem. We consider two recovery routines - the much studied linear estimate originating from Kuks and Olman [42] and polyhedral estimate introduced in [37]. It was shown in [38] that risk of these estimates can be tightly upper-bounded for a wide range of a priori information about the model through solving a convex optimization problem, leading to a computationally efficient implementation of nearly optimal estimates of these types. The subject of the present paper is design and analysis of linear and polyhedral estimates which are robust with respect to the uncertainty in the observation matrix. We evaluate performance of robust estimates under stochastic and deterministic matrix uncertainty and show how the estimation risk can be bounded by the optimal value of efficiently solvable convex optimization problem; "presumably good" estimates of both types are then obtained through optimization of the risk bounds with respect to estimate parameters.
In this paper, we investigate the computational complexity of solutions to the Laplace and the diffusion equation. We show that for a certain class of initial-boundary value problems of the Laplace and the diffusion equation, the solution operator is $\# P_1/ \#P$-complete in the sense that it maps polynomial-time computable functions to the set of $\#P_1/ \#P$-complete functions. Consequently, there exists polynomial-time (Turing) computable input data such that the solution is not polynomial-time computable, unless $FP=\#P$ or $FP_1=\#P_1$. In this case, we can, in general, not simulate the solution of the Laplace or the diffusion equation on a digital computer without having a complexity blowup, i.e., the computation time for obtaining an approximation of the solution with up to a finite number of significant digits grows non-polynomially in the number of digits. This indicates that the computational complexity of the solution operator that models a physical phenomena is intrinsically high, independent of the numerical algorithm that is used to approximate a solution.
We introduce DeepNash, an autonomous agent capable of learning to play the imperfect information game Stratego from scratch, up to a human expert level. Stratego is one of the few iconic board games that Artificial Intelligence (AI) has not yet mastered. This popular game has an enormous game tree on the order of $10^{535}$ nodes, i.e., $10^{175}$ times larger than that of Go. It has the additional complexity of requiring decision-making under imperfect information, similar to Texas hold'em poker, which has a significantly smaller game tree (on the order of $10^{164}$ nodes). Decisions in Stratego are made over a large number of discrete actions with no obvious link between action and outcome. Episodes are long, with often hundreds of moves before a player wins, and situations in Stratego can not easily be broken down into manageably-sized sub-problems as in poker. For these reasons, Stratego has been a grand challenge for the field of AI for decades, and existing AI methods barely reach an amateur level of play. DeepNash uses a game-theoretic, model-free deep reinforcement learning method, without search, that learns to master Stratego via self-play. The Regularised Nash Dynamics (R-NaD) algorithm, a key component of DeepNash, converges to an approximate Nash equilibrium, instead of 'cycling' around it, by directly modifying the underlying multi-agent learning dynamics. DeepNash beats existing state-of-the-art AI methods in Stratego and achieved a yearly (2022) and all-time top-3 rank on the Gravon games platform, competing with human expert players.
The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question answering or machine translation). However, it builds upon the assumption that the data distribution is stationary, ie. that the data is sampled from a fixed distribution both at training and test time. This way of training is inconsistent with how we as humans are able to learn from and operate within a constantly changing stream of information. Moreover, it is ill-adapted to real-world use cases where the data distribution is expected to shift over the course of a model's lifetime. The first goal of this thesis is to characterize the different forms this shift can take in the context of natural language processing, and propose benchmarks and evaluation metrics to measure its effect on current deep learning architectures. We then proceed to take steps to mitigate the effect of distributional shift on NLP models. To this end, we develop methods based on parametric reformulations of the distributionally robust optimization framework. Empirically, we demonstrate that these approaches yield more robust models as demonstrated on a selection of realistic problems. In the third and final part of this thesis, we explore ways of efficiently adapting existing models to new domains or tasks. Our contribution to this topic takes inspiration from information geometry to derive a new gradient update rule which alleviate catastrophic forgetting issues during adaptation.
AI is undergoing a paradigm shift with the rise of models (e.g., BERT, DALL-E, GPT-3) that are trained on broad data at scale and are adaptable to a wide range of downstream tasks. We call these models foundation models to underscore their critically central yet incomplete character. This report provides a thorough account of the opportunities and risks of foundation models, ranging from their capabilities (e.g., language, vision, robotics, reasoning, human interaction) and technical principles(e.g., model architectures, training procedures, data, systems, security, evaluation, theory) to their applications (e.g., law, healthcare, education) and societal impact (e.g., inequity, misuse, economic and environmental impact, legal and ethical considerations). Though foundation models are based on standard deep learning and transfer learning, their scale results in new emergent capabilities,and their effectiveness across so many tasks incentivizes homogenization. Homogenization provides powerful leverage but demands caution, as the defects of the foundation model are inherited by all the adapted models downstream. Despite the impending widespread deployment of foundation models, we currently lack a clear understanding of how they work, when they fail, and what they are even capable of due to their emergent properties. To tackle these questions, we believe much of the critical research on foundation models will require deep interdisciplinary collaboration commensurate with their fundamentally sociotechnical nature.
Predictions obtained by, e.g., artificial neural networks have a high accuracy but humans often perceive the models as black boxes. Insights about the decision making are mostly opaque for humans. Particularly understanding the decision making in highly sensitive areas such as healthcare or fifinance, is of paramount importance. The decision-making behind the black boxes requires it to be more transparent, accountable, and understandable for humans. This survey paper provides essential definitions, an overview of the different principles and methodologies of explainable Supervised Machine Learning (SML). We conduct a state-of-the-art survey that reviews past and recent explainable SML approaches and classifies them according to the introduced definitions. Finally, we illustrate principles by means of an explanatory case study and discuss important future directions.
BERT, a pre-trained Transformer model, has achieved ground-breaking performance on multiple NLP tasks. In this paper, we describe BERTSUM, a simple variant of BERT, for extractive summarization. Our system is the state of the art on the CNN/Dailymail dataset, outperforming the previous best-performed system by 1.65 on ROUGE-L. The codes to reproduce our results are available at //github.com/nlpyang/BertSum
Deep Convolutional Neural Networks (CNNs) are a special type of Neural Networks, which have shown state-of-the-art results on various competitive benchmarks. The powerful learning ability of deep CNN is largely achieved with the use of multiple non-linear feature extraction stages that can automatically learn hierarchical representation from the data. Availability of a large amount of data and improvements in the hardware processing units have accelerated the research in CNNs and recently very interesting deep CNN architectures are reported. The recent race in deep CNN architectures for achieving high performance on the challenging benchmarks has shown that the innovative architectural ideas, as well as parameter optimization, can improve the CNN performance on various vision-related tasks. In this regard, different ideas in the CNN design have been explored such as use of different activation and loss functions, parameter optimization, regularization, and restructuring of processing units. However, the major improvement in representational capacity is achieved by the restructuring of the processing units. Especially, the idea of using a block as a structural unit instead of a layer is gaining substantial appreciation. This survey thus focuses on the intrinsic taxonomy present in the recently reported CNN architectures and consequently, classifies the recent innovations in CNN architectures into seven different categories. These seven categories are based on spatial exploitation, depth, multi-path, width, feature map exploitation, channel boosting and attention. Additionally, it covers the elementary understanding of the CNN components and sheds light on the current challenges and applications of CNNs.
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