光谱分析是一种强大的工具，将任何功能分解成更简单的部件。在机器学习中，Mercer的定理概括了这个想法，为任何内核和输入分布提供了增加频率的自然基础。最近，几种作品通过神经切线内核的框架将此分析扩展到深度神经网络。在这项工作中，我们分析了深度神经网络的层面频谱偏压，并将其与不同层的贡献相关联在给定的目标函数的泛化误差减少中的贡献。我们利用Hermite多项式和球面谐波的性质来证明初始层朝着单位球体上定义的高频函数呈现较大偏差。我们进一步提供了验证我们在深神经网络的高维数据集中的理论的实证结果。

我们研究了具有由完全连接的神经网络产生的密度场的固体各向同性物质惩罚（SIMP）方法，将坐标作为输入。在大的宽度限制中，我们表明DNN的使用导致滤波效果类似于SIMP的传统过滤技术，具有由神经切线内核（NTK）描述的过滤器。然而，这种过滤器在翻译下不是不变的，导致视觉伪像和非最佳形状。我们提出了两个输入坐标的嵌入，导致NTK和滤波器的空间不变性。我们经验证实了我们的理论观察和研究了过滤器大小如何受网络架构的影响。我们的解决方案可以很容易地应用于任何其他基于坐标的生成方法。

At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit (16; 4; 7; 13; 6), thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: during gradient descent on the parameters of an ANN, the network function f θ (which maps input vectors to output vectors) follows the kernel gradient of the functional cost (which is convex, in contrast to the parameter cost) w.r.t. a new kernel: the Neural Tangent Kernel (NTK). This kernel is central to describe the generalization features of ANNs. While the NTK is random at initialization and varies during training, in the infinite-width limit it converges to an explicit limiting kernel and it stays constant during training. This makes it possible to study the training of ANNs in function space instead of parameter space. Convergence of the training can then be related to the positive-definiteness of the limiting NTK. We prove the positive-definiteness of the limiting NTK when the data is supported on the sphere and the non-linearity is non-polynomial. We then focus on the setting of least-squares regression and show that in the infinitewidth limit, the network function f θ follows a linear differential equation during training. The convergence is fastest along the largest kernel principal components of the input data with respect to the NTK, hence suggesting a theoretical motivation for early stopping. Finally we study the NTK numerically, observe its behavior for wide networks, and compare it to the infinite-width limit.

We address the problem of unsupervised domain adaptation when the source domain differs from the target domain because of a shift in the distribution of a latent subgroup. When this subgroup confounds all observed data, neither covariate shift nor label shift assumptions apply. We show that the optimal target predictor can be non-parametrically identified with the help of concept and proxy variables available only in the source domain, and unlabeled data from the target. The identification results are constructive, immediately suggesting an algorithm for estimating the optimal predictor in the target. For continuous observations, when this algorithm becomes impractical, we propose a latent variable model specific to the data generation process at hand. We show how the approach degrades as the size of the shift changes, and verify that it outperforms both covariate and label shift adjustment.

We introduce the Conditional Independence Regression CovariancE (CIRCE), a measure of conditional independence for multivariate continuous-valued variables. CIRCE applies as a regularizer in settings where we wish to learn neural features $\varphi(X)$ of data $X$ to estimate a target $Y$, while being conditionally independent of a distractor $Z$ given $Y$. Both $Z$ and $Y$ are assumed to be continuous-valued but relatively low dimensional, whereas $X$ and its features may be complex and high dimensional. Relevant settings include domain-invariant learning, fairness, and causal learning. The procedure requires just a single ridge regression from $Y$ to kernelized features of $Z$, which can be done in advance. It is then only necessary to enforce independence of $\varphi(X)$ from residuals of this regression, which is possible with attractive estimation properties and consistency guarantees. By contrast, earlier measures of conditional feature dependence require multiple regressions for each step of feature learning, resulting in more severe bias and variance, and greater computational cost. When sufficiently rich features are used, we establish that CIRCE is zero if and only if $\varphi(X) \perp \!\!\! \perp Z \mid Y$. In experiments, we show superior performance to previous methods on challenging benchmarks, including learning conditionally invariant image features.

The detection and prevention of illegal fishing is critical to maintaining a healthy and functional ecosystem. Recent research on ship detection in satellite imagery has focused exclusively on performance improvements, disregarding detection efficiency. However, the speed and compute cost of vessel detection are essential for a timely intervention to prevent illegal fishing. Therefore, we investigated optimization methods that lower detection time and cost with minimal performance loss. We trained an object detection model based on a convolutional neural network (CNN) using a dataset of satellite images. Then, we designed two efficiency optimizations that can be applied to the base CNN or any other base model. The optimizations consist of a fast, cheap classification model and a statistical algorithm. The integration of the optimizations with the object detection model leads to a trade-off between speed and performance. We studied the trade-off using metrics that give different weight to execution time and performance. We show that by using a classification model the average precision of the detection model can be approximated to 99.5% in 44% of the time or to 92.7% in 25% of the time.

Quantifying the deviation of a probability distribution is challenging when the target distribution is defined by a density with an intractable normalizing constant. The kernel Stein discrepancy (KSD) was proposed to address this problem and has been applied to various tasks including diagnosing approximate MCMC samplers and goodness-of-fit testing for unnormalized statistical models. This article investigates a convergence control property of the diffusion kernel Stein discrepancy (DKSD), an instance of the KSD proposed by Barp et al. (2019). We extend the result of Gorham and Mackey (2017), which showed that the KSD controls the bounded-Lipschitz metric, to functions of polynomial growth. Specifically, we prove that the DKSD controls the integral probability metric defined by a class of pseudo-Lipschitz functions, a polynomial generalization of Lipschitz functions. We also provide practical sufficient conditions on the reproducing kernel for the stated property to hold. In particular, we show that the DKSD detects non-convergence in moments with an appropriate kernel.

Can continuous diffusion models bring the same performance breakthrough on natural language they did for image generation? To circumvent the discrete nature of text data, we can simply project tokens in a continuous space of embeddings, as is standard in language modeling. We propose Self-conditioned Embedding Diffusion, a continuous diffusion mechanism that operates on token embeddings and allows to learn flexible and scalable diffusion models for both conditional and unconditional text generation. Through qualitative and quantitative evaluation, we show that our text diffusion models generate samples comparable with those produced by standard autoregressive language models - while being in theory more efficient on accelerator hardware at inference time. Our work paves the way for scaling up diffusion models for text, similarly to autoregressive models, and for improving performance with recent refinements to continuous diffusion.

当歌曲创作或演奏时，歌手/词曲作者通常会出现通过它表达感受或情感的意图。对于人类而言，将音乐作品或表演中的情感与观众的主观感知相匹配可能会非常具有挑战性。幸运的是，此问题的机器学习方法更简单。通常，它需要一个数据集，从该数据集中提取音频功能以将此信息呈现给数据驱动的模型，从而又将训练以预测给定歌曲与目标情绪匹配的概率是什么。在本文中，我们研究了最近出版物中最常见的功能和模型来解决此问题，揭示了哪些最适合在无伴奏歌曲中识别情感。

机器人的感知目前处于在有效的潜在空间中运行的现代方法与数学建立的经典方法之间的跨道路，并提供了可解释的，可信赖的结果。在本文中，我们引入了卷积的贝叶斯内核推理（Convbki）层，该层在可分离的卷积层中明确执行贝叶斯推断，以同时提高效率，同时保持可靠性。我们将层应用于3D语义映射的任务，在该任务中，我们可以实时学习激光雷达传感器信息的语义几何概率分布。我们根据KITTI数据集的最新语义映射算法评估我们的网络，并通过类似的语义结果证明了延迟的提高。