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Our work focuses on the development of a learnable neural representation of human pose for advanced AI assisted animation tooling. Specifically, we tackle the problem of constructing a full static human pose based on sparse and variable user inputs (e.g. locations and/or orientations of a subset of body joints). To solve this problem, we propose a novel neural architecture that combines residual connections with prototype encoding of a partially specified pose to create a new complete pose from the learned latent space. We show that our architecture outperforms a baseline based on Transformer, both in terms of accuracy and computational efficiency. Additionally, we develop a user interface to integrate our neural model in Unity, a real-time 3D development platform. Furthermore, we introduce two new datasets representing the static human pose modeling problem, based on high-quality human motion capture data, which will be released publicly along with model code.

We study population protocols, a model of distributed computing appropriate for modeling well-mixed chemical reaction networks and other physical systems where agents exchange information in pairwise interactions, but have no control over their schedule of interaction partners. The well-studied *majority* problem is that of determining in an initial population of $n$ agents, each with one of two opinions $A$ or $B$, whether there are more $A$, more $B$, or a tie. A *stable* protocol solves this problem with probability 1 by eventually entering a configuration in which all agents agree on a correct consensus decision of $\mathsf{A}$, $\mathsf{B}$, or $\mathsf{T}$, from which the consensus cannot change. We describe a protocol that solves this problem using $O(\log n)$ states ($\log \log n + O(1)$ bits of memory) and optimal expected time $O(\log n)$. The number of states $O(\log n)$ is known to be optimal for the class of polylogarithmic time stable protocols that are "output dominant" and "monotone". These are two natural constraints satisfied by our protocol, making it simultaneously time- and state-optimal for that class. We introduce a key technique called a "fixed resolution clock" to achieve partial synchronization. Our protocol is *nonuniform*: the transition function has the value $\left \lceil {\log n} \right \rceil$ encoded in it. We show that the protocol can be modified to be uniform, while increasing the state complexity to $\Theta(\log n \log \log n)$.

Molecular dynamics (MD) simulation, a computationally intensive method that provides invaluable insights into the behavior of biomolecules, typically requires large-scale parallelization. Implementation of fast parallel MD simulation demands both high bandwidth and low latency for inter-node communication, but in current semiconductor technology, neither of these properties is scaling as quickly as intra-node computational capacity. This disparity in scaling necessitates architectural innovations to maximize the utilization of computational units. For Anton 3, the latest in a family of highly successful special-purpose supercomputers designed for MD simulations, we thus designed and built a completely new specialized network as part of our ASIC. Tightly integrating this network with specialized computation pipelines enables Anton 3 to perform simulations orders of magnitude faster than any general-purpose supercomputer, and to outperform its predecessor, Anton 2 (the state of the art prior to Anton 3), by an order of magnitude. In this paper, we present the three key features of the network that contribute to the high performance of Anton 3. First, through architectural optimizations, the network achieves very low end-to-end inter-node communication latency for fine-grained messages, allowing for better overlap of computation and communication. Second, novel application-specific compression techniques reduce the size of most messages sent between nodes, thereby increasing effective inter-node bandwidth. Lastly, a new hardware synchronization primitive, called a network fence, supports fast fine-grained synchronization tailored to the data flow within a parallel MD application. These application-driven specializations to the network are critical for Anton 3's MD simulation performance advantage over all other machines.

We study the allocative challenges that governmental and nonprofit organizations face when tasked with equitable and efficient rationing of a social good among agents whose needs (demands) realize sequentially and are possibly correlated. To better achieve their dual aims of equity and efficiency, social planners intend to maximize the minimum fill rate across agents, where each agent's fill rate is determined by a one-time allocation that must be irrevocably decided upon its arrival. For an arbitrarily correlated sequence of demands, we establish upper bounds on both the expected minimum fill rate (ex-post fairness) and the minimum expected fill rate (ex-ante fairness) achievable by any policy. Our bounds are parameterized by the number of agents and the expected demand-to-supply ratio. Further, we show that for any set of parameters, a simple adaptive policy of projected proportional allocation achieves the best possible fairness guarantee, ex post as well as ex ante. We obtain the performance guarantees of our proposed adaptive policy by inductively designing lower-bound functions on its corresponding value-to-go. Our policy is transparent and easy to implement, as it does not rely on distributional information beyond the first conditional moments. Despite our policy's simplicity, we demonstrate that it provides significant improvement over the class of non-adaptive target-fill-rate policies by characterizing the performance of the optimal such policy. We complement our theoretical developments with a numerical study motivated by the rationing of COVID-19 medical supplies based on a standard SEIR model approach that is commonly used to forecast pandemic trajectories. In such a setting, our simple adaptive policy significantly outperforms its theoretical guarantee as well as the optimal target-fill-rate policy.

Data are often accommodated on centralized storage servers. This is the case, for instance, in remote sensing and astronomy, where projects produce several petabytes of data every year. While machine learning models are often trained on relatively small subsets of the data, the inference phase typically requires transferring significant amounts of data between the servers and the clients. In many cases, the bandwidth available per user is limited, which then renders the data transfer to be one of the major bottlenecks. In this work, we propose a framework that automatically selects the relevant parts of the input data for a given neural network. The model as well as the associated selection masks are trained simultaneously such that a good model performance is achieved while only a minimal amount of data is selected. During the inference phase, only those parts of the data have to be transferred between the server and the client. We propose both instance-independent and instance-dependent selection masks. The former ones are the same for all instances to be transferred, whereas the latter ones allow for variable transfer sizes per instance. Our experiments show that it is often possible to significantly reduce the amount of data needed to be transferred without affecting the model quality much.

Using rough path techniques, we provide a priori estimates for the output of Deep Residual Neural Networks in terms of both the input data and the (trained) network weights. As trained network weights are typically very rough when seen as functions of the layer, we propose to derive stability bounds in terms of the total $p$-variation of trained weights for any $p\in[1,3]$. Unlike the $C^1$-theory underlying the neural ODE literature, our estimates remain bounded even in the limiting case of weights behaving like Brownian motions, as suggested in [arXiv:2105.12245]. Mathematically, we interpret residual neural network as solutions to (rough) difference equations, and analyse them based on recent results of discrete time signatures and rough path theory.

The training of deep residual neural networks (ResNets) with backpropagation has a memory cost that increases linearly with respect to the depth of the network. A way to circumvent this issue is to use reversible architectures. In this paper, we propose to change the forward rule of a ResNet by adding a momentum term. The resulting networks, momentum residual neural networks (Momentum ResNets), are invertible. Unlike previous invertible architectures, they can be used as a drop-in replacement for any existing ResNet block. We show that Momentum ResNets can be interpreted in the infinitesimal step size regime as second-order ordinary differential equations (ODEs) and exactly characterize how adding momentum progressively increases the representation capabilities of Momentum ResNets. Our analysis reveals that Momentum ResNets can learn any linear mapping up to a multiplicative factor, while ResNets cannot. In a learning to optimize setting, where convergence to a fixed point is required, we show theoretically and empirically that our method succeeds while existing invertible architectures fail. We show on CIFAR and ImageNet that Momentum ResNets have the same accuracy as ResNets, while having a much smaller memory footprint, and show that pre-trained Momentum ResNets are promising for fine-tuning models.

In this work, we consider the distributed optimization of non-smooth convex functions using a network of computing units. We investigate this problem under two regularity assumptions: (1) the Lipschitz continuity of the global objective function, and (2) the Lipschitz continuity of local individual functions. Under the local regularity assumption, we provide the first optimal first-order decentralized algorithm called multi-step primal-dual (MSPD) and its corresponding optimal convergence rate. A notable aspect of this result is that, for non-smooth functions, while the dominant term of the error is in $O(1/\sqrt{t})$, the structure of the communication network only impacts a second-order term in $O(1/t)$, where $t$ is time. In other words, the error due to limits in communication resources decreases at a fast rate even in the case of non-strongly-convex objective functions. Under the global regularity assumption, we provide a simple yet efficient algorithm called distributed randomized smoothing (DRS) based on a local smoothing of the objective function, and show that DRS is within a $d^{1/4}$ multiplicative factor of the optimal convergence rate, where $d$ is the underlying dimension.

Recommender systems rely on large datasets of historical data and entail serious privacy risks. A server offering recommendations as a service to a client might leak more information than necessary regarding its recommendation model and training dataset. At the same time, the disclosure of the client's preferences to the server is also a matter of concern. Providing recommendations while preserving privacy in both senses is a difficult task, which often comes into conflict with the utility of the system in terms of its recommendation-accuracy and efficiency. Widely-purposed cryptographic primitives such as secure multi-party computation and homomorphic encryption offer strong security guarantees, but in conjunction with state-of-the-art recommender systems yield far-from-practical solutions. We precisely define the above notion of security and propose CryptoRec, a novel recommendations-as-a-service protocol, which encompasses a crypto-friendly recommender system. This model possesses two interesting properties: (1) It models user-item interactions in a user-free latent feature space in which it captures personalized user features by an aggregation of item features. This means that a server with a pre-trained model can provide recommendations for a client without having to re-train the model with the client's preferences. Nevertheless, re-training the model still improves accuracy. (2) It only uses addition and multiplication operations, making the model straightforwardly compatible with homomorphic encryption schemes.

In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.