The problem of robust hypothesis testing is studied, where under the null and the alternative hypotheses, the data-generating distributions are assumed to be in some uncertainty sets, and the goal is to design a test that performs well under the worst-case distributions over the uncertainty sets. In this paper, uncertainty sets are constructed in a data-driven manner using kernel method, i.e., they are centered around empirical distributions of training samples from the null and alternative hypotheses, respectively; and are constrained via the distance between kernel mean embeddings of distributions in the reproducing kernel Hilbert space, i.e., maximum mean discrepancy (MMD). The Bayesian setting and the Neyman-Pearson setting are investigated. For the Bayesian setting where the goal is to minimize the worst-case error probability, an optimal test is firstly obtained when the alphabet is finite. When the alphabet is infinite, a tractable approximation is proposed to quantify the worst-case average error probability, and a kernel smoothing method is further applied to design test that generalizes to unseen samples. A direct robust kernel test is also proposed and proved to be exponentially consistent. For the Neyman-Pearson setting, where the goal is to minimize the worst-case probability of miss detection subject to a constraint on the worst-case probability of false alarm, an efficient robust kernel test is proposed and is shown to be asymptotically optimal. Numerical results are provided to demonstrate the performance of the proposed robust tests.
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Place bisimilarity is a behavioral equivalence for finite Petri nets, proposed in \cite{ABS91} and proved decidable in \cite{Gor21}. In this paper we propose an extension to finite Petri nets with silent moves of the place bisimulation idea, yielding {\em branching} place bisimilarity $\approx_p$, following the intuition of branching bisimilarity \cite{vGW96} on labeled transition systems. We also propose a slightly coarser variant, called branching {\em d-place} bisimilarity $\approx_d$, following the intuition of d-place bisimilarity in \cite{Gor21}. We prove that $\approx_p$ and $\approx_d$ are decidable equivalence relations. Moreover, we prove that $\approx_d$ is strictly finer than branching fully-concurrent bisimilarity \cite{Pin93,Gor20c}, essentially because $\approx_d$ does not consider as unobservable those $\tau$-labeled net transitions with pre-set size larger than one, i.e., those resulting from (multi-party) interaction.
To exploit the expressivity of being able to refer to the type of types, such as for large elimination, dependent type systems will either employ a universe hierarchy or else contend with an inconsistent type-in-type rule. However, these are not be the only possible options. Taking inspiration from Stratified System F, we introduce Stratified Type Theory (StraTT), where rather than stratifying universes by levels, we stratify typing judgements and restrict the domain of dependent function types to some fixed level strictly lower than that of the overall type. Even in the presence of type-in-type, this restriction suffices to enforce consistency of the system. We explore the expressivity of several extensions atop this design. First, the subsystem subStraTT employs McBride's crude-but-effective stratification (also known as displacement) as a simple form of level polymorphism where top-level definitions can be displaced uniformly to any higher level as needed, which is valid due to level cumulativity and plays well with stratified judgements. Second, to recover some expressivity lost due to the restriction on dependent function domains, the full StraTT system includes a separate nondependent function type with floating domains, whose level instead matches that of the overall type. Finally, we have implemented a prototype type checker for StraTT extended with datatypes along with a small type checked core library. While it's possible to show that the subsystem is consistent, showing consistency for the full system with floating nondependent functions remains open. Nevertheless, we believe that the full system is also consistent and have mechanized a syntactic proof of subject reduction. Furthermore, we use our implementation to investigate various well-known type-theoretic type-in-type paradoxes. These examples all fail to type check in expected ways as evidence towards consistency.
Emerging from the monolithic pairwise attention mechanism in conventional Transformer models, there is a growing interest in leveraging sparse interactions that align more closely with biological principles. Approaches including the Set Transformer and the Perceiver employ cross-attention consolidated with a latent space that forms an attention bottleneck with limited capacity. Building upon recent neuroscience studies of Global Workspace Theory and associative memory, we propose the Associative Transformer (AiT). AiT induces low-rank explicit memory that serves as both priors to guide bottleneck attention in the shared workspace and attractors within associative memory of a Hopfield network. Through joint end-to-end training, these priors naturally develop module specialization, each contributing a distinct inductive bias to form attention bottlenecks. A bottleneck can foster competition among inputs for writing information into the memory. We show that AiT is a sparse representation learner, learning distinct priors through the bottlenecks that are complexity-invariant to input quantities and dimensions. AiT demonstrates its superiority over methods such as the Set Transformer, Vision Transformer, and Coordination in various vision tasks.
A key theme in the past decade has been that when large neural networks and large datasets combine they can produce remarkable results. In deep reinforcement learning (RL), this paradigm is commonly made possible through experience replay, whereby a dataset of past experiences is used to train a policy or value function. However, unlike in supervised or self-supervised learning, an RL agent has to collect its own data, which is often limited. Thus, it is challenging to reap the benefits of deep learning, and even small neural networks can overfit at the start of training. In this work, we leverage the tremendous recent progress in generative modeling and propose Synthetic Experience Replay (SynthER), a diffusion-based approach to flexibly upsample an agent's collected experience. We show that SynthER is an effective method for training RL agents across offline and online settings, in both proprioceptive and pixel-based environments. In offline settings, we observe drastic improvements when upsampling small offline datasets and see that additional synthetic data also allows us to effectively train larger networks. Furthermore, SynthER enables online agents to train with a much higher update-to-data ratio than before, leading to a significant increase in sample efficiency, without any algorithmic changes. We believe that synthetic training data could open the door to realizing the full potential of deep learning for replay-based RL algorithms from limited data. Finally, we open-source our code at //github.com/conglu1997/SynthER.
Virtual element methods (VEMs) without extrinsic stabilization in arbitrary degree of polynomial are developed for second order elliptic problems, including a nonconforming VEM and a conforming VEM in arbitrary dimension. The key is to construct local $H(\textrm{div})$-conforming macro finite element spaces such that the associated $L^2$ projection of the gradient of virtual element functions is computable, and the $L^2$ projector has a uniform lower bound on the gradient of virtual element function spaces in $L^2$ norm. Optimal error estimates are derived for these VEMs. Numerical experiments are provided to test the VEMs without extrinsic stabilization.
Interactive Natural Language Processing (iNLP) has emerged as a novel paradigm within the field of NLP, aimed at addressing limitations in existing frameworks while aligning with the ultimate goals of artificial intelligence. This paradigm considers language models as agents capable of observing, acting, and receiving feedback iteratively from external entities. Specifically, language models in this context can: (1) interact with humans for better understanding and addressing user needs, personalizing responses, aligning with human values, and improving the overall user experience; (2) interact with knowledge bases for enriching language representations with factual knowledge, enhancing the contextual relevance of responses, and dynamically leveraging external information to generate more accurate and informed responses; (3) interact with models and tools for effectively decomposing and addressing complex tasks, leveraging specialized expertise for specific subtasks, and fostering the simulation of social behaviors; and (4) interact with environments for learning grounded representations of language, and effectively tackling embodied tasks such as reasoning, planning, and decision-making in response to environmental observations. This paper offers a comprehensive survey of iNLP, starting by proposing a unified definition and framework of the concept. We then provide a systematic classification of iNLP, dissecting its various components, including interactive objects, interaction interfaces, and interaction methods. We proceed to delve into the evaluation methodologies used in the field, explore its diverse applications, scrutinize its ethical and safety issues, and discuss prospective research directions. This survey serves as an entry point for researchers who are interested in this rapidly evolving area and offers a broad view of the current landscape and future trajectory of iNLP.
Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.
The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.
We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and word sequence information. Compared with word-based methods, lattice LSTM does not suffer from segmentation errors. Gated recurrent cells allow our model to choose the most relevant characters and words from a sentence for better NER results. Experiments on various datasets show that lattice LSTM outperforms both word-based and character-based LSTM baselines, achieving the best results.
The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.
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