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We develop a vector space semantics for Lambek Calculus with Soft Subexponentials, apply the calculus to construct compositional vector interpretations for parasitic gap noun phrases and discourse units with anaphora and ellipsis, and experiment with the constructions in a distributional sentence similarity task. As opposed to previous work, which used Lambek Calculus with a Relevant Modality the calculus used in this paper uses a bounded version of the modality and is decidable. The vector space semantics of this new modality allows us to meaningfully define contraction as projection and provide a linear theory behind what we could previously only achieve via nonlinear maps.

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We introduce a new approach to prediction in graphical models with latent-shift adaptation, i.e., where source and target environments differ in the distribution of an unobserved confounding latent variable. Previous work has shown that as long as "concept" and "proxy" variables with appropriate dependence are observed in the source environment, the latent-associated distributional changes can be identified, and target predictions adapted accurately. However, practical estimation methods do not scale well when the observations are complex and high-dimensional, even if the confounding latent is categorical. Here we build upon a recently proposed probabilistic unsupervised learning framework, the recognition-parametrised model (RPM), to recover low-dimensional, discrete latents from image observations. Applied to the problem of latent shifts, our novel form of RPM identifies causal latent structure in the source environment, and adapts properly to predict in the target. We demonstrate results in settings where predictor and proxy are high-dimensional images, a context to which previous methods fail to scale.

We focus on decentralized stochastic non-convex optimization, where $n$ agents work together to optimize a composite objective function which is a sum of a smooth term and a non-smooth convex term. To solve this problem, we propose two single-time scale algorithms: Prox-DASA and Prox-DASA-GT. These algorithms can find $\epsilon$-stationary points in $\mathcal{O}(n^{-1}\epsilon^{-2})$ iterations using constant batch sizes (i.e., $\mathcal{O}(1)$). Unlike prior work, our algorithms achieve comparable complexity without requiring large batch sizes, more complex per-iteration operations (such as double loops), or stronger assumptions. Our theoretical findings are supported by extensive numerical experiments, which demonstrate the superiority of our algorithms over previous approaches. Our code is available at //github.com/xuxingc/ProxDASA.

Reinforcement learning often needs to deal with the exponential growth of states and actions when exploring optimal control in high-dimensional spaces (often known as the curse of dimensionality). In this work, we address this issue by learning the inherent structure of action-wise similar MDP to appropriately balance the performance degradation versus sample/computational complexity. In particular, we partition the action spaces into multiple groups based on the similarity in transition distribution and reward function, and build a linear decomposition model to capture the difference between the intra-group transition kernel and the intra-group rewards. Both our theoretical analysis and experiments reveal a \emph{surprising and counter-intuitive result}: while a more refined grouping strategy can reduce the approximation error caused by treating actions in the same group as identical, it also leads to increased estimation error when the size of samples or the computation resources is limited. This finding highlights the grouping strategy as a new degree of freedom that can be optimized to minimize the overall performance loss. To address this issue, we formulate a general optimization problem for determining the optimal grouping strategy, which strikes a balance between performance loss and sample/computational complexity. We further propose a computationally efficient method for selecting a nearly-optimal grouping strategy, which maintains its computational complexity independent of the size of the action space.

Understanding and manipulating articulated objects, such as doors and drawers, is crucial for robots operating in human environments. We wish to develop a system that can learn to articulate novel objects with no prior interaction, after training on other articulated objects. Previous approaches for articulated object manipulation rely on either modular methods which are brittle or end-to-end methods, which lack generalizability. This paper presents FlowBot++, a deep 3D vision-based robotic system that predicts dense per-point motion and dense articulation parameters of articulated objects to assist in downstream manipulation tasks. FlowBot++ introduces a novel per-point representation of the articulated motion and articulation parameters that are combined to produce a more accurate estimate than either method on their own. Simulated experiments on the PartNet-Mobility dataset validate the performance of our system in articulating a wide range of objects, while real-world experiments on real objects' point clouds and a Sawyer robot demonstrate the generalizability and feasibility of our system in real-world scenarios.

The optimal branch number of MDS matrices makes them a preferred choice for designing diffusion layers in many block ciphers and hash functions. Consequently, various methods have been proposed for designing MDS matrices, including search and direct methods. While exhaustive search is suitable for small order MDS matrices, direct constructions are preferred for larger orders due to the vast search space involved. In the literature, there has been extensive research on the direct construction of MDS matrices using both recursive and nonrecursive methods. On the other hand, in lightweight cryptography, Near-MDS (NMDS) matrices with sub-optimal branch numbers offer a better balance between security and efficiency as a diffusion layer compared to MDS matrices. However, no direct construction method is available in the literature for constructing recursive NMDS matrices. This paper introduces some direct constructions of NMDS matrices in both nonrecursive and recursive settings. Additionally, it presents some direct constructions of nonrecursive MDS matrices from the generalized Vandermonde matrices. We propose a method for constructing involutory MDS and NMDS matrices using generalized Vandermonde matrices. Furthermore, we prove some folklore results that are used in the literature related to the NMDS code.

Vector embeddings have become ubiquitous tools for many language-related tasks. A leading embedding model is OpenAI's text-ada-002 which can embed approximately 6,000 words into a 1,536-dimensional vector. While powerful, text-ada-002 is not open source and is only available via API. We trained a simple neural network to convert open-source 768-dimensional MPNet embeddings into text-ada-002 embeddings. We compiled a subset of 50,000 online food reviews. We calculated MPNet and text-ada-002 embeddings for each review and trained a simple neural network to for 75 epochs. The neural network was designed to predict the corresponding text-ada-002 embedding for a given MPNET embedding. Our model achieved an average cosine similarity of 0.932 on 10,000 unseen reviews in our held-out test dataset. We manually assessed the quality of our predicted embeddings for vector search over text-ada-002-embedded reviews. While not as good as real text-ada-002 embeddings, predicted embeddings were able to retrieve highly relevant reviews. Our final model, Vec2Vec, is lightweight (<80 MB) and fast. Future steps include training a neural network with a more sophisticated architecture and a larger dataset of paired embeddings to achieve greater performance. The ability to convert between and align embedding spaces may be helpful for interoperability, limiting dependence on proprietary models, protecting data privacy, reducing costs, and offline operations.

Music similarity is an essential aspect of music retrieval, recommendation systems, and music analysis. Moreover, similarity is of vital interest for music experts, as it allows studying analogies and influences among composers and historical periods. Current approaches to musical similarity rely mainly on symbolic content, which can be expensive to produce and is not always readily available. Conversely, approaches using audio signals typically fail to provide any insight about the reasons behind the observed similarity. This research addresses the limitations of current approaches by focusing on the study of musical similarity using both symbolic and audio content. The aim of this research is to develop a fully explainable and interpretable system that can provide end-users with more control and understanding of music similarity and classification systems.

Staging of liver fibrosis is important in the diagnosis and treatment planning of patients suffering from liver diseases. Current deep learning-based methods using abdominal magnetic resonance imaging (MRI) usually take a sub-region of the liver as an input, which nevertheless could miss critical information. To explore richer representations, we formulate this task as a multi-view learning problem and employ multiple sub-regions of the liver. Previously, features or predictions are usually combined in an implicit manner, and uncertainty-aware methods have been proposed. However, these methods could be challenged to capture cross-view representations, which can be important in the accurate prediction of staging. Therefore, we propose a reliable multi-view learning method with interpretable combination rules, which can model global representations to improve the accuracy of predictions. Specifically, the proposed method estimates uncertainties based on subjective logic to improve reliability, and an explicit combination rule is applied based on Dempster-Shafer's evidence theory with good power of interpretability. Moreover, a data-efficient transformer is introduced to capture representations in the global view. Results evaluated on enhanced MRI data show that our method delivers superior performance over existing multi-view learning methods.

A fundamental goal of scientific research is to learn about causal relationships. However, despite its critical role in the life and social sciences, causality has not had the same importance in Natural Language Processing (NLP), which has traditionally placed more emphasis on predictive tasks. This distinction is beginning to fade, with an emerging area of interdisciplinary research at the convergence of causal inference and language processing. Still, research on causality in NLP remains scattered across domains without unified definitions, benchmark datasets and clear articulations of the remaining challenges. In this survey, we consolidate research across academic areas and situate it in the broader NLP landscape. We introduce the statistical challenge of estimating causal effects, encompassing settings where text is used as an outcome, treatment, or as a means to address confounding. In addition, we explore potential uses of causal inference to improve the performance, robustness, fairness, and interpretability of NLP models. We thus provide a unified overview of causal inference for the computational linguistics community.

Search in social networks such as Facebook poses different challenges than in classical web search: besides the query text, it is important to take into account the searcher's context to provide relevant results. Their social graph is an integral part of this context and is a unique aspect of Facebook search. While embedding-based retrieval (EBR) has been applied in eb search engines for years, Facebook search was still mainly based on a Boolean matching model. In this paper, we discuss the techniques for applying EBR to a Facebook Search system. We introduce the unified embedding framework developed to model semantic embeddings for personalized search, and the system to serve embedding-based retrieval in a typical search system based on an inverted index. We discuss various tricks and experiences on end-to-end optimization of the whole system, including ANN parameter tuning and full-stack optimization. Finally, we present our progress on two selected advanced topics about modeling. We evaluated EBR on verticals for Facebook Search with significant metrics gains observed in online A/B experiments. We believe this paper will provide useful insights and experiences to help people on developing embedding-based retrieval systems in search engines.

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