Recently, linear formulations and convex optimization methods have been proposed to predict diffusion-weighted Magnetic Resonance Imaging (dMRI) data given estimates of brain connections generated using tractography algorithms. The size of the linear models comprising such methods grows with both dMRI data and connectome resolution, and can become very large when applied to modern data. In this paper, we introduce a method to encode dMRI signals and large connectomes, i.e., those that range from hundreds of thousands to millions of fascicles (bundles of neuronal axons), by using a sparse tensor decomposition. We show that this tensor decomposition accurately approximates the Linear Fascicle Evaluation (LiFE) model, one of the recently developed linear models.

The encoder-decoder framework has achieved promising progress for many sequence generation tasks, including machine translation, text summarization, dialog system, image captioning, etc. Such a framework adopts an one-pass forward process while decoding and generating a sequence, but lacks the deliberation process: A generated sequence is directly used as final output without further polishing. However, deliberation is a common behavior in human's daily life like reading news and writing papers/articles/books. In this work, we introduce the deliberation process into the encoder-decoder framework and propose deliberation networks for sequence generation. A deliberation network has two levels of decoders, where the first-pass decoder generates a raw sequence and the second-pass decoder polishes and refines the raw sentence with deliberation. Since the second-pass deliberation decoder has global information about what the sequence to be generated might be, it has the potential to generate a better sequence by looking into future words in the raw sentence. Experiments on neural machine translation and text summarization demonstrate the effectiveness of the proposed deliberation networks. On the WMT 2014 English-to-French translation task, our model establishes a new state-of-the-art BLEU score of 41.5.

We consider the above CP decomposition model of tensors, as well as the Tucker decomposition.

Spectral methods of moments provide a powerful tool for learning the parameters of latent variable models. Despite their theoretical appeal, the applicability of these methods to real data is still limited due to a lack of robustness to model misspecification. In this paper we present a hierarchical approach to methods of moments to circumvent such limitations. Our method is based on replacing the tensor decomposition step used in previous algorithms with approximate joint diagonalization. Experiments on topic modeling show that our method outperforms previous tensor decomposition methods in terms of speed and model quality.

Neural Information Processing Systems http://nips.cc/

In recent years, stochastic gradient descent (SGD) based techniques has become the standard tools for training neural networks. However, formal theoretical understanding of why SGD can train neural networks in practice is largely missing. In this paper, we make progress on understanding this mystery by providing a convergence analysis for SGD on a rich subset of two-layer feedforward networks with ReLU activations. This subset is characterized by a special structure called "identity mapping". We prove that, if input follows from Gaussian distribution, with standard O(1/ d) initialization of the weights, SGD converges to the global minimum in polynomial number of steps.

Non-convex optimization with local search heuristics has been widely used in machine learning, achieving many state-of-art results. It becomes increasingly important to understand why they can work for these NP-hard problems on typical data. The landscape of many objective functions in learning has been conjectured to have the geometric property that "all local optima are (approximately) global optima", and thus they can be solved efficiently by local search algorithms. However, establishing such property can be very difficult. In this paper, we analyze the optimization landscape of the random over-complete tensor decomposition problem, which has many applications in unsupervised leaning, especially in learning latent variable models.

Neural Information Processing Systems http://nips.cc/

This paper presents a solution to the problem of optimal ground station selection for low-Earth orbiting (LEO) space missions that enables mission operators to precisely design their ground segment performance and costs. Space mission operators are increasingly turning to Ground-Station-as-a-Service (GSaaS) providers to supply the terrestrial communications segment to reduce costs and increase network size. However, this approach leads to a new challenge of selecting the optimal service providers and station locations for a given mission. We consider the problem of ground station selection as an optimization problem and present a general solution framework that allows mission designers to set their overall optimization objective and constrain key mission performance variables such as total data downlink, total mission cost, recurring operational cost, and maximum communications time-gap. We solve the problem using integer programming (IP). To address computational scaling challenges, we introduce a surrogate optimization approach where the optimal station selection is determined based on solving the problem over a reduced time domain. Two different IP formulations are evaluated using randomized selections of LEO satellites of varying constellation sizes. We consider the networks of the commercial GSaaS providers Atlas Space Operations, Amazon Web Services (AWS) Ground Station, Azure Orbital Ground Station, Kongsberg Satellite Services (KSAT), Leaf Space, and Viasat Real-Time Earth. We compare our results against standard operational practices of integrating with one or two primary ground station providers.

Recently, when dealing with high-resolution images, dominant LMMs usually divide them into multiple local images and one global image, which will lead to a large number of visual tokens. In this work, we introduce AVG-LLaVA, an LMM that can adaptively select the appropriate visual granularity based on the input image and instruction. This approach not only reduces the number of visual tokens and speeds up inference, but also improves the overall model performance. Specifically, we introduce the following modules based on LLaVA-NeXT: (a) a visual granularity scaler that includes multiple pooling layers to obtain visual tokens with different granularities; (b) a visual granularity router, which includes a Transformer layer, an MLP layer, and a voter layer, used to select the appropriate visual granularity based on the image and instruction. Furthermore, we propose RGLF, a novel training paradigm that aims at aligning the granularity predicted by the router with the preferences of the LMM, without the need for additional manually annotated data. Extensive experiments and analysis show that AVG-LLaVA achieves superior performance across 11 benchmarks, as well as significantly reduces the number of visual tokens and speeds up inference (e.g., an 85.3% reduction in visual tokens and a 2.53$\times$ increase in inference speed on the AI2D benchmark).