Efficient representation of text documents is an important building block in many NLP tasks. Research on long text categorization has shown that simple weighted averaging of word vectors for sentence representation often outperforms more sophisticated neural models. Recently proposed Sparse Composite Document Vector (SCDV) (Mekala et. al, 2017) extends this approach from sentences to documents…
Estimating depth from stereo vision cameras, i.e., “depth from stereo”, is critical to emerging intelligent applications deployed in energy- and performance-constrained devices, such as augmented reality headsets and mobile autonomous robots. While existing stereo vision systems make trade-offs between accuracy, performance and energy-efficiency, we describe ASV, an accelerated stereo vision system that simultaneously improves both…
We consider membership inference attacks, one of the main privacy issues in machine learning. These recently developed attacks have been proven successful in determining, with confidence better than a random guess, whether a given sample belongs to the dataset on which the attacked machine learning model was trained. Several approaches have been developed to mitigate…
In this paper we propose a new augmentation technique, called patch augmentation, that, in our experiments, improves model accuracy and makes networks more robust to adversarial attacks. In brief, this data-independent approach creates new image data based on image/label pairs, where a patch from one of the two images in the pair is superimposed on…
A fundamental barrier in extremal hypergraph theory is the presence of many near-extremal constructions with very different structure. Indeed, the notorious Tur\'{a}n problem for the complete triple system on four points most likely exhibits this phenomenon. We construct a finite family of triple systems $\mathcal{M}$, determine its Tur\'{a}n number, and prove that there are two…
The $2$-primary homotopy $\beta$-family, defined as the collection of Mahowald invariants of Mahowald invariants of $2^i$, $i \geq 1$, is an infinite collection of periodic elements in the stable homotopy groups of spheres. In this paper, we calculate $\mathit{tmf}$-based approximations to this family. Our calculations combine an analysis of the Atiyah-Hirzebruch spectral sequence for the…
We consider the task of estimating the entropy of $k$-ary distributions from samples in the streaming model, where space is limited. Our main contribution is an algorithm that requires $O\left(\frac{k \log (1/\varepsilon)^2}{\varepsilon^3}\right)$ samples and a constant $O(1)$ memory words of space and outputs a $\pm\varepsilon$ estimate of $H(p)$. Without space limitations, the sample complexity has…
Let $M_{\langle u,v,w\rangle}\in C^{uv}\otimes C^{vw}\otimes C^{wu}$ denote the matrix multiplication tensor (and write $M_n=M_{\langle n,n,n\rangle}$) and let $det_3\in ( C^9)^{\otimes 3}$ denote the determinant polynomial considered as a tensor. For a tensor $T$, let $\underline R(T)$ denote its border rank. We (i) give the first hand-checkable algebraic proof that $\underline R(M_2)=7$,(ii) prove $\underline R(M_{\langle 223\rangle})=10$,…
We consider a Bipartite Stochastic Block Model (BSBM) on vertex sets $V_1$ and $V_2$, and investigate asymptotic sufficient conditions of exact and almost full recovery for polynomial-time algorithms of clustering over $V_1$, in the regime where the cardinalities satisfy $|V_1|\ll|V_2|$. We improve upon the known conditions of almost full recovery for spectral clustering algorithms in…
The convex cone $SC_{\mathrm{SLip}}^1(\mathcal{X})$ of real-valued smooth semi-Lipschitz functions on a Finsler manifold $\mathcal{X}$ is an order-algebraic structure that captures both the differentiable and the quasi-metric feature of $\mathcal{X}$. In this work we show that the subset of smooth semi-Lipschitz functions of constant strictly less than $1$, denoted $SC_{1^{-}}^1(\mathcal{X})$, can be used to classify Finsler…