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Consistency models (CMs) are an emerging class of generative models that offer faster sampling than traditional diffusion models. CMs enforce that all points along a sampling trajectory are mapped to the same initial point. But this target leads to resource-intensive training: for example, as of 2024, training a SoTA CM on CIFAR-10 takes one week on 8 GPUs. In this work, we propose an alternative scheme for training CMs, vastly improving the efficiency of building such models. Specifically, by expressing CM trajectories via a particular differential equation, we argue that diffusion models can be viewed as a special case of CMs with a specific discretization. We can thus fine-tune a consistency model starting from a pre-trained diffusion model and progressively approximate the full consistency condition to stronger degrees over the training process. Our resulting method, which we term Easy Consistency Tuning (ECT), achieves vastly improved training times while indeed improving upon the quality of previous methods: for example, ECT achieves a 2-step FID of 2.73 on CIFAR10 within 1 hour on a single A100 GPU, matching Consistency Distillation trained of hundreds of GPU hours. Owing to this computational efficiency, we investigate the scaling law of CMs under ECT, showing that they seem to obey classic power law scaling, hinting at their ability to improve efficiency and performance at larger scales. Code (//github.com/locuslab/ect) is available.

The generation of equilibrium samples of molecular systems has been a long-standing problem in statistical physics. Boltzmann Generators are a generative machine learning method that addresses this issue by learning a transformation via a normalizing flow from a simple prior distribution to the target Boltzmann distribution of interest. Recently, flow matching has been employed to train Boltzmann Generators for small molecular systems in Cartesian coordinates. We extend this work and propose a first framework for Boltzmann Generators that are transferable across chemical space, such that they predict zero-shot Boltzmann distributions for test molecules without being retrained for these systems. These transferable Boltzmann Generators allow approximate sampling from the target distribution of unseen systems, as well as efficient reweighting to the target Boltzmann distribution. The transferability of the proposed framework is evaluated on dipeptides, where we show that it generalizes efficiently to unseen systems. Furthermore, we demonstrate that our proposed architecture enhances the efficiency of Boltzmann Generators trained on single molecular systems.

We propose a unified multinomial link model for analyzing categorical responses. It not only covers the existing multinomial logistic models and their extensions as special cases, but also includes new models that can incorporate the observations with NA or Unknown responses in the data analysis. We provide explicit formulae and detailed algorithms for finding the maximum likelihood estimates of the model parameters and computing the Fisher information matrix. Our algorithms solve the infeasibility issue of existing statistical software on estimating parameters of cumulative link models. The applications to real datasets show that the new models can fit the data significantly better, and the corresponding data analysis may correct the misleading conclusions due to missing responses.

Benchmarks for large multimodal language models (MLMs) now serve to simultaneously assess the general capabilities of models instead of evaluating for a specific capability. As a result, when a developer wants to identify which models to use for their application, they are overwhelmed by the number of benchmarks and remain uncertain about which benchmark's results are most reflective of their specific use case. This paper introduces Task-Me-Anything, a benchmark generation engine which produces a benchmark tailored to a user's needs. Task-Me-Anything maintains an extendable taxonomy of visual assets and can programmatically generate a vast number of task instances. Additionally, it algorithmically addresses user queries regarding MLM performance efficiently within a computational budget. It contains 113K images, 10K videos, 2K 3D object assets, over 365 object categories, 655 attributes, and 335 relationships. It can generate 750M image/video question-answering pairs, which focus on evaluating MLM perceptual capabilities. Task-Me-Anything reveals critical insights: open-source MLMs excel in object and attribute recognition but lack spatial and temporal understanding; each model exhibits unique strengths and weaknesses; larger models generally perform better, though exceptions exist; and GPT4o demonstrates challenges in recognizing rotating/moving objects and distinguishing colors.

We will show how to implement binary decision tree traversal in the language of matrix computation. Our main contribution is to propose some equivalent algorithms of binary tree traversal based on a novel matrix representation of the hierarchical structure of the decision tree. Our key idea is to travel the binary decision tree by maximum inner product search. We not only implement decision tree methods without the recursive traverse but also delve into the partitioning nature of tree-based methods.

Unclonable cryptography utilizes the principles of quantum mechanics to addresses cryptographic tasks that are impossible classically. We introduce a novel unclonable primitive in the context of secret sharing, called unclonable secret sharing (USS). In a USS scheme, there are $n$ shareholders, each holding a share of a classical secret represented as a quantum state. They can recover the secret once all parties (or at least $t$ parties) come together with their shares. Importantly, it should be infeasible to copy their own shares and send the copies to two non-communicating parties, enabling both of them to recover the secret. Our work initiates a formal investigation into the realm of unclonable secret sharing, shedding light on its implications, constructions, and inherent limitations. ** Connections: We explore the connections between USS and other quantum cryptographic primitives such as unclonable encryption and position verification, showing the difficulties to achieve USS in different scenarios. **Limited Entanglement: In the case where the adversarial shareholders do not share any entanglement or limited entanglement, we demonstrate information-theoretic constructions for USS. **Large Entanglement: If we allow the adversarial shareholders to have unbounded entanglement resources (and unbounded computation), we prove that unclonable secret sharing is impossible. On the other hand, in the quantum random oracle model where the adversary can only make a bounded polynomial number of queries, we show a construction secure even with unbounded entanglement. Furthermore, even when these adversaries possess only a polynomial amount of entanglement resources, we establish that any unclonable secret sharing scheme with a reconstruction function implementable using Cliffords and logarithmically many T-gates is also unattainable.

We consider an online decision-making problem with a reward function defined over graph-structured data. We formally formulate the problem as an instance of graph action bandit. We then propose \texttt{GNN-TS}, a Graph Neural Network (GNN) powered Thompson Sampling (TS) algorithm which employs a GNN approximator for estimating the mean reward function and the graph neural tangent features for uncertainty estimation. We prove that, under certain boundness assumptions on the reward function, GNN-TS achieves a state-of-the-art regret bound which is (1) sub-linear of order $\tilde{\mathcal{O}}((\tilde{d} T)^{1/2})$ in the number of interaction rounds, $T$, and a notion of effective dimension $\tilde{d}$, and (2) independent of the number of graph nodes. Empirical results validate that our proposed \texttt{GNN-TS} exhibits competitive performance and scales well on graph action bandit problems.

The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.

We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and word sequence information. Compared with word-based methods, lattice LSTM does not suffer from segmentation errors. Gated recurrent cells allow our model to choose the most relevant characters and words from a sentence for better NER results. Experiments on various datasets show that lattice LSTM outperforms both word-based and character-based LSTM baselines, achieving the best results.