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Problem ========= Brain MRI segmentation using adversarial training approach Dataset ====== 55 T1 weighted brain MR images (35 adults and 20 elders) with respective label maps. Contributions ========== 1. The authors suggest an adversarial loss in addition to the traditional loss. 2. The authors compare 2 Generator (Segmentor) models - Fully convolutional and dilated networks. https://i.imgur.com/orhWhoM.png Dilated network ------------------ Using conv layers, allows for larger receptive field with fewer trainable weights (compared to the FCN option). However, the authors claim the adversarial loss contributes more when applying the FCN model |
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Brendel et al. propose a decision-based black-box attacks against (deep convolutional) neural networks. Specifically, the so-called Boundary Attack starts with a random adversarial example (i.e. random noise that is not classified as the image to be attacked) and randomly perturbs this initialization to move closer to the target image while remaining misclassified. In pseudo code, the algorithm is described in Algorithm 1. Key component is the proposal distribution $P$ used to guide the adversarial perturbation in each step. In practice, they use a maximum-entropy distribution (e.g. uniform) with a couple of constraints: the perturbed sample is a valid image; the perturbation has a specified relative size, i.e. $\|\eta^k\|_2 = \delta d(o, \tilde{o}^{k-1})$; and the perturbation reduces the distance to the target image $o$: $d(o, \tilde{o}^{k-1}) – d(o,\tilde{o}^{k-1} + \eta^k)=\epsilon d(o, \tilde{o}^{k-1})$. This is approximated by sampling from a standard Gaussian, clipping and rescaling and projecting the perturbation onto the $\epsilon$-sphere around the image. In experiments, they show that this attack is competitive to white-box attacks and can attack real-world systems. https://i.imgur.com/BmzhiFP.png Algorithm 1: Minimal pseudo code version of the boundary attack. Also find this summary at [davidstutz.de](https://davidstutz.de/category/reading/). |
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Nayebi and Ganguli propose saturating neural networks as defense against adversarial examples. The main observation driving this paper can be stated as follows: Neural networks are essentially based on linear sums of neurons (e.g. fully connected layers, convolutiona layers) which are then activated; by injecting a small amount of noise per neuron it is possible to shift the final sum by large values, thereby propagating the noisy through the network and fooling the network into misclassifying an example. To prevent the impact of these adversarial examples, the network should be trained in a manner to drive many neurons into a saturated regime – noisy will, so the argument, have less impact then. The authors also give a biological motivation, which I won't go into detail here. Letting $\psi$ be the used activation function, e.g. sigmoid or ReLU, a regularizer is added to drive neurons into saturation. In particular, a penalty $\lambda \sum_l \sum_i \psi_c(h_i^l)$ is added to the loss. Here, $l$ indexes the layer and $i$ the unit in the layer; $h_i^l$ then describes the input to the non-linearity computed for unit $i$ in layer $l$. $\psi_c$ is the complementary function defined as $\psi_c(z) = \inf_{z': \psi'(z') = 0} |z – z'|$ It defines the distance of the point $z$ to the nearest saturated point $z'$ where $\psi'(z') = 0$. For ReLU activations, the complementary function is the ReLU function itself; for sigmoid activations, the complementary function is $\sigma_c(z) = |\sigma(z)(1 - \sigma(z))|$. In experiments, Nayebi and Ganguli show that training with the additional penalty yields networks with higher robustness against adversarial examples compared to adversarial training (i.e. training on adversarial examples). They also provide some insight, showing e.g. the activation and weight distribution of layers illustrating that neurons are indeed saturated in large parts. For details, see the paper. I also want to point to a comment on the paper written by Brendel and Bethge [1] questioning the effectiveness of the proposed defense strategy. They discuss a variant of the fast sign gradient method (FSGM) with stabilized gradients which is able to fool saturated networks. [1] W. Brendel, M. Behtge. Comment on “Biologically inspired protection of deep networks from adversarial attacks”, https://arxiv.org/abs/1704.01547. Also find this summary at [davidstutz.de](https://davidstutz.de/category/reading/). |
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This paper from 2016 introduced a new k-mer based method to estimate isoform abundance from RNA-Seq data called kallisto. The method provided a significant improvement in speed and memory usage compared to the previously used methods while yielding similar accuracy. In fact, kallisto is able to quantify expression in a matter of minutes instead of hours. The standard (previous) methods for quantifying expression rely on mapping, i.e. on the alignment of a transcriptome sequenced reads to a genome of reference. Reads are assigned to a position in the genome and the gene or isoform expression values are derived by counting the number of reads overlapping the features of interest. The idea behind kallisto is to rely on a pseudoalignment which does not attempt to identify the positions of the reads in the transcripts, only the potential transcripts of origin. Thus, it avoids doing an alignment of each read to a reference genome. In fact, kallisto only uses the transcriptome sequences (not the whole genome) in its first step which is the generation of the kallisto index. Kallisto builds a colored de Bruijn graph (T-DBG) from all the k-mers found in the transcriptome. Each node of the graph corresponds to a k-mer (a short sequence of k nucleotides) and retains the information about the transcripts in which they can be found in the form of a color. Linear stretches having the same coloring in the graph correspond to transcripts. Once the T-DBG is built, kallisto stores a hash table mapping each k-mer to its transcript(s) of origin along with the position within the transcript(s). This step is done only once and is dependent on a provided annotation file (containing the sequences of all the transcripts in the transcriptome). Then for a given sequenced sample, kallisto decomposes each read into its k-mers and uses those k-mers to find a path covering in the T-DBG. This path covering of the transcriptome graph, where a path corresponds to a transcript, generates k-compatibility classes for each k-mer, i.e. sets of potential transcripts of origin on the nodes. The potential transcripts of origin for a read can be obtained using the intersection of its k-mers k-compatibility classes. To make the pseudoalignment faster, kallisto removes redundant k-mers since neighboring k-mers often belong to the same transcripts. Figure1, from the paper, summarizes these different steps. https://i.imgur.com/eNH2kuO.png **Figure1**. Overview of kallisto. The input consists of a reference transcriptome and reads from an RNA-seq experiment. (a) An example of a read (in black) and three overlapping transcripts with exonic regions as shown. (b) An index is constructed by creating the transcriptome de Bruijn Graph (T-DBG) where nodes (v1, v2, v3, ... ) are k-mers, each transcript corresponds to a colored path as shown and the path cover of the transcriptome induces a k-compatibility class for each k-mer. (c) Conceptually, the k-mers of a read are hashed (black nodes) to find the k-compatibility class of a read. (d) Skipping (black dashed lines) uses the information stored in the T-DBG to skip k-mers that are redundant because they have the same k-compatibility class. (e) The k-compatibility class of the read is determined by taking the intersection of the k-compatibility classes of its constituent k-mers.[From Bray et al. Near-optimal probabilistic RNA-seq quantification, Nature Biotechnology, 2016.] Then, kallisto optimizes the following RNA-Seq likelihood function using the expectation-maximization (EM) algorithm. $$L(\alpha) \propto \prod_{f \in F} \sum_{t \in T} y_{f,t} \frac{\alpha_t}{l_t} = \prod_{e \in E}\left( \sum_{t \in e} \frac{\alpha_t}{l_t} \right )^{c_e}$$ In this function, $F$ is the set of fragments (or reads), $T$ is the set of transcripts, $l_t$ is the (effective) length of transcript $t$ and **y**$_{f,t}$ is a compatibility matrix defined as 1 if fragment $f$ is compatible with $t$ and 0 otherwise. The parameters $α_t$ are the probabilities of selecting reads from a transcript $t$. These $α_t$ are the parameters of interest since they represent the isoforms abundances or relative expressions. To make things faster, the compatibility matrix is collapsed (factorized) into equivalence classes. An equivalent class consists of all the reads compatible with the same subsets of transcripts. The EM algorithm is applied to equivalence classes (not to reads). Each $α_t$ will be optimized to maximise the likelihood of transcript abundances given observations of the equivalence classes. The speed of the method makes it possible to evaluate the uncertainty of the abundance estimates for each RNA-Seq sample using a bootstrap technique. For a given sample containing $N$ reads, a bootstrap sample is generated from the sampling of $N$ counts from a multinomial distribution over the equivalence classes derived from the original sample. The EM algorithm is applied on those sampled equivalence class counts to estimate transcript abundances. The bootstrap information is then used in downstream analyses such as determining which genes are differentially expressed. Practically, we can illustrate the different steps involved in kallisto using a small example. Starting from a tiny genome with 3 transcripts, assume that the RNA-Seq experiment produced 4 reads as depicted in the image below. https://i.imgur.com/5JDpQO8.png The first step is to build the T-DBG graph and the kallisto index. All transcript sequences are decomposed into k-mers (here k=5) to construct the colored de Bruijn graph. Not all nodes are represented in the following drawing. The idea is that each different transcript will lead to a different path in the graph. The strand is not taken into account, kallisto is strand-agnostic. https://i.imgur.com/4oW72z0.png Once the index is built, the four reads of the sequenced sample can be analysed. They are decomposed into k-mers (k=5 here too) and the pre-built index is used to determine the k-compatibility class of each k-mer. Then, the k-compatibility class of each read is computed. For example, for read 1, the intersection of all the k-compatibility classes of its k-mers suggests that it might come from transcript 1 or transcript 2. https://i.imgur.com/woektCH.png This is done for the four reads enabling the construction of the compatibility matrix **y**$_{f,t}$ which is part of the RNA-Seq likelihood function. In this equation, the $α_t$ are the parameters that we want to estimate. https://i.imgur.com/Hp5QJvH.png The EM algorithm being too slow to be applied on millions of reads, the compatibility matrix **y**$_{f,t}$ is factorized into equivalence classes and a count is computed for each class (how many reads are represented by this equivalence class). The EM algorithm uses this collapsed information to maximize the new equivalent RNA-Seq likelihood function and optimize the $α_t$. https://i.imgur.com/qzsEq8A.png The EM algorithm stops when for every transcript $t$, $α_tN$ > 0.01 changes less than 1%, where $N$ is the total number of reads. |
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The regulation of filopodia plays a crucial role during neuronal development and synaptogenesis. Axonal filopodia, which are known to originate presynaptic specializations, are regulated in response to neurotrophic factors. The structural components of filopodia are actin filaments, whose dynamics and organization are controlled by ensembles of actin-binding proteins. How neurotrophic factors regulate these latter proteins remains, however, poorly defined. Here, using a combination of mouse genetic, biochemical, and cell biological assays, we show that genetic removal of Eps8, an actin-binding and regulatory protein enriched in the growth cones and developing processes of neurons, significantly augments the number and density of vasodilator-stimulated phosphoprotein (VASP)-dependent axonal filopodia. The reintroduction of Eps8 wild type (WT), but not an Eps8 capping-defective mutant, into primary hippocampal neurons restored axonal filopodia to WT levels. We further show that the actin barbed-end capping activity of Eps8 is inhibited by brain-derived neurotrophic factor (BDNF) treatment through MAPK-dependent phosphorylation of Eps8 residues S624 and T628. Additionally, an Eps8 mutant, impaired in the MAPK target sites (S624A/T628A), displays increased association to actin-rich structures, is resistant to BDNF-mediated release from microfilaments, and inhibits BDNF-induced filopodia. The opposite is observed for a phosphomimetic Eps8 (S624E/T628E) mutant. Thus, collectively, our data identify Eps8 as a critical capping protein in the regulation of axonal filopodia and delineate a molecular pathway by which BDNF, through MAPK-dependent phosphorylation of Eps8, stimulates axonal filopodia formation, a process with crucial impacts on neuronal development and synapse formation. Neurons communicate with each other via specialized cell-cell junctions called synapses. The proper formation of synapses ("synaptogenesis") is crucial to the development of the nervous system, but the molecular pathways that regulate this process are not fully understood. External cues, such as brain-derived neurotrophic factor (BDNF), trigger synaptogenesis by promoting the formation of axonal filopodia, thin extensions projecting outward from a growing axon. Filopodia are formed by elongation of actin filaments, a process that is regulated by a complex set of actin-binding proteins. Here, we reveal a novel molecular circuit underlying BDNF-stimulated filopodia formation through the regulated inhibition of actin-capping factor activity. We show that the actin-capping protein Eps8 down-regulates axonal filopodia formation in neurons in the absence of neurotrophic factors. In contrast, in the presence of BDNF, the kinase MAPK becomes activated and phosphorylates Eps8, leading to inhibition of its actin-capping function and stimulation of filopodia formation. Our study, therefore, identifies actin-capping factor inhibition as a critical step in axonal filopodia formation and likely in new synapse formation. |