We evaluate named entity representations of BERT-based NLP models by investigating their robustness to replacements from the same typed class in the input. We highlight that on several tasks while such perturbations are natural, state of the art trai
ned models are surprisingly brittle. The brittleness continues even with the recent entity-aware BERT models. We also try to discern the cause of this non-robustness, considering factors such as tokenization and frequency of occurrence. Then we provide a simple method that ensembles predictions from multiple replacements while jointly modeling the uncertainty of type annotations and label predictions. Experiments on three NLP tasks show that our method enhances robustness and increases accuracy on both natural and adversarial datasets.
This article contains a characterization of operator systems $cS$ with the property that every positive map $phi:cS rightarrow M_n$ is decomposable, as well as an alternate and a more direct proof of a characterization of decomposable maps due to E. Sto rmer.
Versions of well known function theoretic operator theory results of Szego and Widom are established for the Neil algebra. The Neil algebra is the subalgebra of the algebra of bounded analytic functions on the unit disc consisting of those functions whose derivative vanishes at the origin.
Subsets of the set of $g$-tuples of matrices that are closed with respect to direct sums and compact in the free topology are characterized. They are, in a dilation theoretic sense, contained in the hull of a single point.
In a recent work, Moslehian and Rajic have shown that the Gruss inequality holds for unital n-positive linear maps $phi:mathcal A rightarrow B(H)$, where $mathcal A$ is a unital C*-algebra and H is a Hilbert space, if $n ge 3$. They also demonstrate
that the inequality fails to hold, in general, if $n = 1$ and question whether the inequality holds if $n=2$. In this article, we provide an affirmative answer to this question.
The well known Douglas Lemma says that for operators $A,B$ on Hilbert space that $AA^*-BB^*succeq 0$ implies $B=AC$ for some contraction operator $C$. The result carries over directly to classical operator-valued Toeplitz operators by simply replacin
g operator by Toeplitz operator. Free functions generalize the notion of free polynomials and formal power series and trace back to the work of J. Taylor in the 1970s. They are of current interest, in part because of their connections with free probability and engineering systems theory. For free functions $a$ and $b$ on a free domain $cK$ defined free polynomial inequalities, a sufficient condition on the difference $aa^*-bb^*$ to imply the existence a free function $c$ taking contractive values on $cK$ such that $a=bc$ is established. The connection to recent work of Agler and McCarthy and their free Toeplitz Corona Theorem is exposited.
We obtain an extended Reich fixed point theorem for the setting of generalized cone rectangular metric spaces without assuming the normality of the underlying cone. Our work is a generalization of the main result in cite{AAB} and cite{JS}.
Let $Rx$ denote the ring of polynomials in $g$ freely non-commuting variables $x=(x_1,...,x_g)$. There is a natural involution * on $Rx$ determined by $x_j^*=x_j$ and $(pq)^*=q^* p^*$ and a free polynomial $pinRx$ is symmetric if it is invariant unde
r this involution. If $X=(X_1,...,X_g)$ is a $g$ tuple of symmetric $ntimes n$ matrices, then the evaluation $p(X)$ is naturally defined and further $p^*(X)=p(X)^*$. In particular, if $p$ is symmetric, then $p(X)^*=p(X)$. The main result of this article says if $p$ is symmetric, $p(0)=0$ and for each $n$ and each symmetric positive definite $ntimes n$ matrix $A$ the set ${X:A-p(X)succ 0}$ is convex, then $p$ has degree at most two and is itself convex, or $-p$ is a hermitian sum of squares.
We prove a Caratheodory-Fejer type interpolation theorem for certain matrix convex sets in $C^d$ using the Blecher-Ruan-Sinclair characterization of abstract operator algebras. Our results generalize the work of Dmitry S. Kalyuzhnyi-Verbovetzkii for the d-dimensional non-commutative polydisc.
