Natural language relies on a finite lexicon to express an unbounded set of emerging ideas. One result of this tension is the formation of new compositions, such that existing linguistic units can be combined with emerging items into novel expressions
. We develop a framework that exploits the cognitive mechanisms of chaining and multimodal knowledge to predict emergent compositional expressions through time. We present the syntactic frame extension model (SFEM) that draws on the theory of chaining and knowledge from percept, concept, and language to infer how verbs extend their frames to form new compositions with existing and novel nouns. We evaluate SFEM rigorously on the 1) modalities of knowledge and 2) categorization models of chaining, in a syntactically parsed English corpus over the past 150 years. We show that multimodal SFEM predicts newly emerged verb syntax and arguments substantially better than competing models using purely linguistic or unimodal knowledge. We find support for an exemplar view of chaining as opposed to a prototype view and reveal how the joint approach of multimodal chaining may be fundamental to the creation of literal and figurative language uses including metaphor and metonymy.
Few-shot learning aims to recognize new categories using very few labeled samples. Although few-shot learning has witnessed promising development in recent years, most existing methods adopt an average operation to calculate prototypes, thus limited
by the outlier samples. In this work, we propose a simple yet effective framework for few-shot classification, which can learn to generate preferable prototypes from few support data, with the help of an episodic prototype generator module. The generated prototype is meant to be close to a certain textit{targetproto{}} and is less influenced by outlier samples. Extensive experiments demonstrate the effectiveness of this module, and our approach gets a significant raise over baseline models, and get a competitive result compared to previous methods on textit{mini}ImageNet, textit{tiered}ImageNet, and cross-domain (textit{mini}ImageNet $rightarrow$ CUB-200-2011) datasets.
In this paper, we prove that for the doubly symmetric binary distribution, the lower increasing envelope and the upper envelope of the minimum-relative-entropy region are respectively convex and concave. We also prove that another function induced th
e minimum-relative-entropy region is concave. These two envelopes and this function were previously used to characterize the optimal exponents in strong small-set expansion problems and strong Brascamp--Lieb inequalities. The results in this paper, combined with the strong small-set expansion theorem derived by Yu, Anantharam, and Chen (2021), and the strong Brascamp--Lieb inequality derived by Yu (2021), confirm positively Ordentlich--Polyanskiy--Shayevitzs conjecture on the strong small-set expansion (2019) and Polyanskiys conjecture on the strong Brascamp--Lieb inequality (2016). The proofs in this paper are based on the equivalence between the convexity of a function and the convexity of the set of minimizers of its Lagrangian dual.
Observations of Interplanetary Scintillation (IPS) are an efficient remote-sensing method to study the solar wind and inner heliosphere. From 2016 to 2018, some distinctive observations of IPS sources like 3C 286 and 3C 279 were accomplished with the
Five-hundred-meter Aperture Spherical radio Telescope (FAST), the largest single-dish telescope in the world. Due to the 270-1620 MHz wide frequency coverage of the Ultra-Wideband (UWB) receiver, one can use both single-frequency and dual-frequency analyses to determine the projected velocity of the solar wind. Moreover, based on the extraordinary sensitivity owing to the large collecting surface area of FAST, we can observe weak IPS signals. With the advantages of both the wider frequency coverage and high sensitivity, also with our radio frequency interference (RFI) mitigation strategy and an optimized model-fitting method developed, in this paper, we analyze the fitting confidence intervals of the solar wind velocity, and present some preliminary results achieved using FAST, which points to the current FAST system being highly capable of carrying out observations of IPS
Let $mathbf{X}$ be a random variable uniformly distributed on the discrete cube $left{ -1,1right} ^{n}$, and let $T_{rho}$ be the noise operator acting on Boolean functions $f:left{ -1,1right} ^{n}toleft{ 0,1right} $, where $rhoin[0,1]$ is the noise
parameter, representing the correlation coefficient between each coordination of $mathbf{X}$ and its noise-corrupted version. Given a convex function $Phi$ and the mean $mathbb{E}f(mathbf{X})=ain[0,1]$, which Boolean function $f$ maximizes the $Phi$-stability $mathbb{E}left[Phileft(T_{rho}f(mathbf{X})right)right]$ of $f$? Special cases of this problem include the (symmetric and asymmetric) $alpha$-stability problems and the Most Informative Boolean Function problem. In this paper, we provide several upper bounds for the maximal $Phi$-stability. Considering specific $Phi$s, we partially resolve Mossel and ODonnells conjecture on $alpha$-stability with $alpha>2$, Li and Medards conjecture on $alpha$-stability with $1<alpha<2$, and Courtade and Kumars conjecture on the Most Informative Boolean Function which corresponds to a conjecture on $alpha$-stability with $alpha=1$. Our proofs are based on discrete Fourier analysis, optimization theory, and improvements of the Friedgut--Kalai--Naor (FKN) theorem. Our improvements of the FKN Theorem are sharp or asymptotically sharp for certain cases.
Non-Fermi liquid behavior and pseudogap formation are among the most well-known examples of exotic spectral features observed in several strongly correlated materials such as the hole-doped cuprates, nickelates, iridates, ruthenates, ferropnictides,
doped Mott organics, transition metal dichalcogenides, heavy fermions, d- and f- electron metals, etc. We demonstrate that these features are inevitable consequences when fermions couple to an unconventional Bose metal [1] mean field consisting of lower-dimensional coherence. Not only do we find both exotic phenomena, but also a host of other features that have been observed e.g. in the cuprates including nodal anti-nodal dichotomy and pseudogap asymmetry(symmetry) in momentum(real) space. Obtaining these exotic and heretofore mysterious phenomena via a mean field offers a simple, universal, and therefore widely applicable explanation for their ubiquitous empirical appearance. [1] A. Hegg, J. Hou, and W. Ku, Bose metal via failed insulator: A novel phase of quantum matter, arXiv preprint arXiv:2101.06264 (2021).
In this paper, we derive sharp nonlinear dimension-free Brascamp-Lieb inequalities (including hypercontractivity inequalities) for distributions on Polish spaces, which strengthen the classic Brascamp-Lieb inequalities. Applications include the exten
sion of Mr. and Mrs. Gerbers lemmas to the cases of Renyi divergences and distributions on Polish spaces, the strengthening of small-set expansion theorems, and the characterization of the exponent of $q$-stability of Boolean functions. Our proofs in this paper are based on information-theoretic and coupling techniques.
In this paper, we study the emph{type graph}, namely a bipartite graph induced by a joint type. We investigate the maximum edge density of induced bipartite subgraphs of this graph having a number of vertices on each side on an exponential scale. Thi
s can be seen as an isoperimetric problem. We provide asymptotically sharp bounds for the exponent of the maximum edge density as the blocklength goes to infinity. We also study the biclique rate region of the type graph, which is defined as the set of $left(R_{1},R_{2}right)$ such that there exists a biclique of the type graph which has respectively $e^{nR_{1}}$ and $e^{nR_{2}}$ vertices on two sides. We provide asymptotically sharp bounds for the biclique rate region as well. We then apply our results and proof ideas to noninteractive simulation problems. We completely characterize the exponents of maximum and minimum joint probabilities when the marginal probabilities vanish exponentially fast with given exponents. These results can be seen as strong small-set expansion theorems. We extend the noninteractive simulation problem by replacing Boolean functions with arbitrary nonnegative functions, and obtain new hypercontractivity inequalities which are stronger than the common hypercontractivity inequalities. Furthermore, as an application of our results, a new outer bound for the zero-error capacity region of the binary adder channel is provided, which improves the previously best known bound, due to Austrin, Kaski, Koivisto, and Nederlof. Our proofs in this paper are based on the method of types, linear algebra, and coupling techniques.
Exploration under sparse reward is a long-standing challenge of model-free reinforcement learning. The state-of-the-art methods address this challenge by introducing intrinsic rewards to encourage exploration in novel states or uncertain environment
dynamics. Unfortunately, methods based on intrinsic rewards often fall short in procedurally-generated environments, where a different environment is generated in each episode so that the agent is not likely to visit the same state more than once. Motivated by how humans distinguish good exploration behaviors by looking into the entire episode, we introduce RAPID, a simple yet effective episode-level exploration method for procedurally-generated environments. RAPID regards each episode as a whole and gives an episodic exploration score from both per-episode and long-term views. Those highly scored episodes are treated as good exploration behaviors and are stored in a small ranking buffer. The agent then imitates the episodes in the buffer to reproduce the past good exploration behaviors. We demonstrate our method on several procedurally-generated MiniGrid environments, a first-person-view 3D Maze navigation task from MiniWorld, and several sparse MuJoCo tasks. The results show that RAPID significantly outperforms the state-of-the-art intrinsic reward strategies in terms of sample efficiency and final performance. The code is available at https://github.com/daochenzha/rapid
The design of high-resolution and cross-term (CT) free time-frequency distributions (TFDs) has been an open problem. Classical kernel based methods are limited by the trade-off between TFD resolution and CT suppression, even under optimally derived p
arameters. To break the current limitation, we propose a data-driven kernel learning model directly based on Wigner-Ville distribution (WVD). The proposed kernel learning based TFD (KL-TFD) model includes several stacked multi-channel learning convolutional kernels. Specifically, a skipping operator is utilized to maintain correct information transmission, and a weighted block is employed to exploit spatial and channel dependencies. These two designs simultaneously achieve high TFD resolution and CT elimination. Numerical experiments on both synthetic and real-world data confirm the superiority of the proposed KL-TFD over traditional kernel function methods.
