Is Solving Graph Neural Tangent Kernel Equivalent to Training Graph Neural Network?

A rising trend in theoretical deep learning is to understand why deep learning works through Neural Tangent Kernel (NTK) [jgh18], a kernel method that is equivalent to using gradient descent to train a multi-layer infinitely-wide neural network. NTK is a major step forward in the theoretical deep learning because it allows researchers to use traditional mathematical tools to analyze properties of deep neural networks and to explain various neural network techniques from a theoretical view. A natural extension of NTK on graph learning is \textit{Graph Neural Tangent Kernel (GNTK)}, and researchers have already provide GNTK formulation for graph-level regression and show empirically that this kernel method can achieve similar accuracy as GNNs on various bioinformatics datasets [dhs+19]. The remaining question now is whether solving GNTK regression is equivalent to training an infinite-wide multi-layer GNN using gradient descent. In this paper, we provide three new theoretical results. First, we formally prove this equivalence for graph-level regression. Second, we present the first GNTK formulation for node-level regression. Finally, we prove the equivalence for node-level regression

Query Complexity of Active Learning for Function Family With Nearly Orthogonal Basis

Many machine learning algorithms require large numbers of labeled data to deliver state-of-the-art results. In applications such as medical diagnosis and fraud detection, though there is an abundance of unlabeled data, it is costly to label the data by experts, experiments, or simulations. Active learning algorithms aim to reduce the number of required labeled data points while preserving performance. For many convex optimization problems such as linear regression and $p$-norm regression, there are theoretical bounds on the number of required labels to achieve a certain accuracy. We call this the query complexity of active learning. However, today's active learning algorithms require the underlying learned function to have an orthogonal basis. For example, when applying active learning to linear regression, the requirement is the target function is a linear composition of a set of orthogonal linear functions, and active learning can find the coefficients of these linear functions. We present a theoretical result to show that active learning does not need an orthogonal basis but rather only requires a nearly orthogonal basis. We provide the corresponding theoretical proofs for the function family of nearly orthogonal basis, and its applications associated with the algorithmically efficient active learning framework

Improved Reconstruction for Fourier-Sparse Signals

We revisit the classical problem of Fourier-sparse signal reconstruction -- a variant of the \emph{Set Query} problem -- which asks to efficiently reconstruct (a subset of) a $d$-dimensional Fourier-sparse signal ($\|\hat{x}(t)\|_0 \leq k$), from minimum \emph{noisy} samples of $x(t)$ in the time domain. We present a unified framework for this problem by developing a theory of sparse Fourier transforms (SFT) for frequencies lying on a \emph{lattice}, which can be viewed as a ``semi-continuous'' version of SFT in between discrete and continuous domains. Using this framework, we obtain the following results: $\bullet$ **Dimension-free Fourier sparse recovery** We present a sample-optimal discrete Fourier Set-Query algorithm with $O(k^{\omega+1})$ reconstruction time in one dimension, \emph{independent} of the signal's length ($n$) and $\ell_\infty$-norm. This complements the state-of-art algorithm of [Kapralov, STOC 2017], whose reconstruction time is $\tilde{O}(k \log^2 n \log R^*)$, where $R^* \approx \|\hat{x}\|_\infty$ is a signal-dependent parameter, and the algorithm is limited to low dimensions. By contrast, our algorithm works for arbitrary $d$ dimensions, mitigating the $\exp(d)$ blowup in decoding time to merely linear in $d$. A key component in our algorithm is fast spectral sparsification of the Fourier basis. $\bullet$ **High-accuracy Fourier interpolation** In one dimension, we design a poly-time $(3+ \sqrt{2} +\epsilon)$-approximation algorithm for continuous Fourier interpolation. This bypasses a barrier of all previous algorithms [Price and Song, FOCS 2015, Chen, Kane, Price and Song, FOCS 2016], which only achieve $c>100$ approximation for this basic problem. Our main contribution is a new analytic tool for hierarchical frequency decomposition based on \emph{noise cancellation}

Demographic strategies of a dominant tree species in response to logging in a degraded subtropical forest in Southeast China

International audienceAbstractKey messageThe demography of pioneer tree species (Pinus massonianaLamb.) is significantly affected by logging in Southeast China. Logging negatively affects the population growth rate ofP. massoniana, which facilitates the growth of individual trees but has no effect on reproduction probability. The survival and growth of seedlings contribute the most to population growth.ContextSubtropical forest degradation caused by unreasonable disturbances is closely related to anthropogenic activities in Southeast China, and the frequent small-scale logging activity by local people was the dominated disturbance regime in forests in this region over the past several decades.AimsThe objective of this study is to evaluate the demographic consequences of logging on Pinus massoniana, a pioneer tree species, at individual level (survival, growth, and fecundity) and population level (the population growth rate and size distribution) over short-term period.MethodsThe size of tree individuals was combined with vital rates using various modeling approaches based on demographic data from three annual censuses. The integral projection model (IPM) was constructed and used to conduct comparative demographic analyses.ResultsLogging negatively affected the population growth rate: from a slight expansion before logging to a moderate decline after logging. This study found a significant reduction in seedling recruitment after logging, and plant growth and mortality were slightly enhanced. The survival of seedlings greatly contributes to population growth rate compared to other life stages for both periods (before and after logging) while its relative importance decreases after logging. Seedling growth is also important to population growth, and its relative importance increased after logging. Shrinkage and fecundity have a minimal contribution effect on the population growth rate.ConclusionGrowing plants in a nursery with a similar demography to P. massoniana could be beneficial for pioneer species regeneration in that this will improve the survival rate and growth of small individuals after logging

Molybdenum disulfide nanoflowers mediated anti-inflammation macrophage modulation for spinal cord injury treatment

Spinal cord injury (SCI) can cause locomotor dysfunctions and sensory deficits. Evidence shows that functional nanodrugs can regulate macrophage polarization and promote anti-inflammatory cytokine expression, which is feasible in SCI immunotherapeutic treatments. Molybdenum disulfide (MoS2) nanomaterials have garnered great attention as potential carriers for therapeutic payload. Herein, we synthesize MoS2@PEG (MoS2 = molybdenum disulfide, PEG = poly (ethylene glycol)) nanoflowers as an effective carrier for loading etanercept (ET) to treat SCI. We characterize drug loading and release properties of MoS2@PEG in vitro and demonstrate that ET-loading MoS2@PEG obviously inhibits the expression of M1-related pro-inflammatory markers (TNF-α, CD86 and iNOS), while promoting M2-related anti-inflammatory markers (Agr1, CD206 and IL-10) levels. In vivo, the mouse model of SCI shows that long-circulating ET-MoS2@PEG nanodrugs can effectively extravasate into the injured spinal cord up to 96 h after SCI, and promote macrophages towards M2 type polarization. As a result, the ET-loading MoS2@PEG administration in mice can protect survival motor neurons, thus, reducing injured areas at central lesion sites, and significantly improving locomotor recovery. This study demonstrates the anti-inflammatory and neuroprotective activities of ET-MoS2@PEG and promising utility of MoS2 nanomaterial-mediated drug delivery

Connection of the proto-Yangtze River to the East China Sea traced by sediment magnetic properties

The evolution of the Yangtze River, and specifically how and when it connected to the East China Sea, has been hotly debated with regard to possible linkages with the so-called ‘Cenozoic Topographic Reversal’ (tectonic tilting of continental east China in the Cenozoic) and particularly the relationship to the uplift history of the Tibetan Plateau. Resolving this key question would shed light on the development of large Asian rivers and related changes in landforms and monsoon climate during this interval. Here, we use the magnetic properties of both Plio-Quaternary sediments in the Yangtze delta and of surficial river sediments to identify a key mid-late Quaternary switch in sediment source-sink relationships. Our results reveal a fundamental shift in sediment magnetic properties at this time; the upper 145 m of sediment has magnetic mineral concentrations 5 to 10 times higher than those of the underlying late Pliocene/early Quaternary sediments. We show that the distinctive magnetic properties of the upper core sediments closely match those of surficial river sediments of the upper Yangtze basin, where the large-scale E'mei Basalt block (2.5 × 105 km2) is the dominant magnetic mineral source. This switch in sediment magnetic properties occurred at around the Jaramillo event (~ 1.2–1.0 Ma), which indicates that both the westward extension of the proto-Yangtze River into the upper basin and completion of the connection to the East China Sea occurred no later than at that age

Enhancement of Vaccinia Virus Based Oncolysis with Histone Deacetylase Inhibitors

Histone deacetylase inhibitors (HDI) dampen cellular innate immune response by decreasing interferon production and have been shown to increase the growth of vesicular stomatitis virus and HSV. As attenuated tumour-selective oncolytic vaccinia viruses (VV) are already undergoing clinical evaluation, the goal of this study is to determine whether HDI can also enhance the potency of these poxviruses in infection-resistant cancer cell lines. Multiple HDIs were tested and Trichostatin A (TSA) was found to potently enhance the spread and replication of a tumour selective vaccinia virus in several infection-resistant cancer cell lines. TSA significantly decreased the number of lung metastases in a syngeneic B16F10LacZ lung metastasis model yet did not increase the replication of vaccinia in normal tissues. The combination of TSA and VV increased survival of mice harbouring human HCT116 colon tumour xenografts as compared to mice treated with either agent alone. We conclude that TSA can selectively and effectively enhance the replication and spread of oncolytic vaccinia virus in cancer cells