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Diffusion MRI (dMRI) is a widely used imaging modality, but requires long scanning times to acquire high resolution datasets. By leveraging the unique geometry present within this domain, we present a novel approach to dMRI angular super-resolution that extends upon the parametric continuous convolution (PCConv) framework. We introduce several additions to the operation including a Fourier feature mapping, global coordinates, and domain specific context. Using this framework, we build a fully parametric continuous convolution network (PCCNN) and compare against existing models. We demonstrate the PCCNN performs competitively while using significantly less parameters. Moreover, we show that this formulation generalises well to clinically relevant downstream analyses such as fixel-based analysis, and neurite orientation dispersion and density imaging.

In this work we connect two notions: That of the nonparametric mode of a probability measure, defined by asymptotic small ball probabilities, and that of the Onsager-Machlup functional, a generalized density also defined via asymptotic small ball probabilities. We show that in a separable Hilbert space setting and under mild conditions on the likelihood, modes of a Bayesian posterior distribution based upon a Gaussian prior exist and agree with the minimizers of its Onsager-Machlup functional and thus also with weak posterior modes. We apply this result to inverse problems and derive conditions on the forward mapping under which this variational characterization of posterior modes holds. Our results show rigorously that in the limit case of infinite-dimensional data corrupted by additive Gaussian or Laplacian noise, nonparametric maximum a posteriori estimation is equivalent to Tikhonov-Phillips regularization. In comparison with the work of Dashti, Law, Stuart, and Voss (2013), the assumptions on the likelihood are relaxed so that they cover in particular the important case of white Gaussian process noise. We illustrate our results by applying them to a severely ill-posed linear problem with Laplacian noise, where we express the maximum a posteriori estimator analytically and study its rate of convergence in the small noise limit.

Understanding superfluidity remains a major goal of condensed matter physics. Here we tackle this challenge utilizing the recently developed Fermionic neural network (FermiNet) wave function Ansatz for variational Monte Carlo calculations. We study the unitary Fermi gas, a system with strong, short-range, two-body interactions known to possess a superfluid ground state but difficult to describe quantitatively. We demonstrate key limitations of the FermiNet Ansatz in studying the unitary Fermi gas and propose a simple modification that outperforms the original FermiNet significantly, giving highly accurate results. We prove mathematically that the new Ansatz, which only differs from the original Ansatz by the method of antisymmetrization, is a strict generalization of the original FermiNet architecture, despite the use of fewer parameters. Our approach shares several advantages with the FermiNet: the use of a neural network removes the need for an underlying basis set; and the flexibility of the network yields extremely accurate results within a variational quantum Monte Carlo framework that provides access to unbiased estimates of arbitrary ground-state expectation values. We discuss how the method can be extended to study other superfluids.

In recent years, by leveraging more data, computation, and diverse tasks, learned optimizers have achieved remarkable success in supervised learning, outperforming classical hand-designed optimizers. Reinforcement learning (RL) is essentially different from supervised learning and in practice these learned optimizers do not work well even in simple RL tasks. We investigate this phenomenon and identity three issues. First, the gradients of an RL agent vary across a wide range in logarithms while their absolute values are in a small range, making neural networks hard to obtain accurate parameter updates. Second, the agent-gradient distribution is non-independent and identically distributed, leading to inefficient meta-training. Finally, due to highly stochastic agent-environment interactions, the agent-gradients have high bias and variance, which increase the difficulty of learning an optimizer for RL. We propose gradient processing, pipeline training, and a novel optimizer structure with good inductive bias to address these issues. By applying these techniques, for the first time, we show that learning an optimizer for RL from scratch is possible. Although only trained in toy tasks, our learned optimizer can generalize to unseen complex tasks in Brax.

With the advent of novel quantum computing technologies, and the knowledge that such technology might be used to fundamentally change computing applications, a prime opportunity has presented itself to investigate the practical application quantum computing. The goal of this research is to consider one of the most basic forms of mechanical structure, namely a 2D system of truss elements, and find a method by which such a structure can be optimized using quantum annealing. The optimization will entail a discrete truss sizing problem - to select the best size for each truss member so as to minimize a stress-based objective function. To make this problem compatible with quantum annealing devices, it will be written in a QUBO format. This work is focused on exploring the feasibility of making this translation, and investigating the practicality of using a quantum annealer for structural optimization problems. Using the methods described, it is found that it is possible to translate this traditional engineering problem to a QUBO form and have it solved by a quantum annealer. However, scaling the method to larger truss systems faces some challenges that would require further research to address.

While multilinear algebra appears natural for studying the multiway interactions modeled by hypergraphs, tensor methods for general hypergraphs have been stymied by theoretical and practical barriers. A recently proposed adjacency tensor is applicable to nonuniform hypergraphs, but is prohibitively costly to form and analyze in practice. We develop tensor times same vector (TTSV) algorithms for this tensor which improve complexity from $O(n^r)$ to a low-degree polynomial in $r$, where $n$ is the number of vertices and $r$ is the maximum hyperedge size. Our algorithms are implicit, avoiding formation of the order $r$ adjacency tensor. We demonstrate the flexibility and utility of our approach in practice by developing tensor-based hypergraph centrality and clustering algorithms. We also show these tensor measures offer complementary information to analogous graph-reduction approaches on data, and are also able to detect higher-order structure that many existing matrix-based approaches provably cannot.

Robust feature selection is vital for creating reliable and interpretable Machine Learning (ML) models. When designing statistical prediction models in cases where domain knowledge is limited and underlying interactions are unknown, choosing the optimal set of features is often difficult. To mitigate this issue, we introduce a Multidata (M) causal feature selection approach that simultaneously processes an ensemble of time series datasets and produces a single set of causal drivers. This approach uses the causal discovery algorithms PC1 or PCMCI that are implemented in the Tigramite Python package. These algorithms utilize conditional independence tests to infer parts of the causal graph. Our causal feature selection approach filters out causally-spurious links before passing the remaining causal features as inputs to ML models (Multiple linear regression, Random Forest) that predict the targets. We apply our framework to the statistical intensity prediction of Western Pacific Tropical Cyclones (TC), for which it is often difficult to accurately choose drivers and their dimensionality reduction (time lags, vertical levels, and area-averaging). Using more stringent significance thresholds in the conditional independence tests helps eliminate spurious causal relationships, thus helping the ML model generalize better to unseen TC cases. M-PC1 with a reduced number of features outperforms M-PCMCI, non-causal ML, and other feature selection methods (lagged correlation, random), even slightly outperforming feature selection based on eXplainable Artificial Intelligence. The optimal causal drivers obtained from our causal feature selection help improve our understanding of underlying relationships and suggest new potential drivers of TC intensification.

Parallel software codes in high performance computing (HPC) continue to grow in complexity and scale as we enter the exascale era. A diverse set of emerging hardware and programming paradigms make developing, optimizing, and maintaining parallel software burdensome for developers. One way to alleviate some of these burdens is with automated development and analysis tools. Such tools can perform complex and/or remedial tasks for developers that increase their productivity and decrease the chance for error. So far, such tools for code development and performance analysis have been limited in the complexity of tasks they can perform. However, with recent advancements in language modeling, and the wealth of code related data that is now available online, these tools have started to utilize predictive language models to automate more complex tasks. In this paper, we show how large language models (LLMs) can be applied to tasks specific to high performance and scientific codes. We train LLMs using code and performance data that is specific to parallel codes. We compare several recent LLMs on HPC related tasks and introduce a new model, HPC-Coder, trained on parallel code. In our experiments we show that this model can auto-complete HPC functions where general models cannot, decorate for loops with OpenMP pragmas, and model performance changes in two scientific application repositories.

Instruction tuning is an effective technique to align large language models (LLMs) with human intents. In this work, we investigate how an adversary can exploit instruction tuning by injecting specific instruction-following examples into the training data that intentionally changes the model's behavior. For example, an adversary can achieve content injection by injecting training examples that mention target content and eliciting such behavior from downstream models. To achieve this goal, we propose \textit{AutoPoison}, an automated data poisoning pipeline. It naturally and coherently incorporates versatile attack goals into poisoned data with the help of an oracle LLM. We showcase two example attacks: content injection and over-refusal attacks, each aiming to induce a specific exploitable behavior. We quantify and benchmark the strength and the stealthiness of our data poisoning scheme. Our results show that AutoPoison allows an adversary to change a model's behavior by poisoning only a small fraction of data while maintaining a high level of stealthiness in the poisoned examples. We hope our work sheds light on how data quality affects the behavior of instruction-tuned models and raises awareness of the importance of data quality for responsible deployments of LLMs. Code is available at \url{//github.com/azshue/AutoPoison}.