Gradient Langevin dynamics and a variety of its variants have attracted increasing attention owing to their convergence towards the global optimal solution, initially in the unconstrained convex framework while recently even in convex constrained non-convex problems. In the present work, we extend those frameworks to non-convex problems on a non-convex feasible region with a global optimization algorithm built upon reflected gradient Langevin dynamics and derive its convergence rates. By effectively making use of its reflection at the boundary in combination with the probabilistic representation for the Poisson equation with the Neumann boundary condition, we present promising convergence rates, particularly faster than the existing one for convex constrained non-convex problems.
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In the field of Learning from Demonstration (LfD), Dynamical Systems (DSs) have gained significant attention due to their ability to generate real-time motions and reach predefined targets. However, the conventional convergence-centric behavior exhibited by DSs may fall short in safety-critical tasks, specifically, those requiring precise replication of demonstrated trajectories or strict adherence to constrained regions even in the presence of perturbations or human intervention. Moreover, existing DS research often assumes demonstrations solely in Euclidean space, overlooking the crucial aspect of orientation in various applications. To alleviate these shortcomings, we present an innovative approach geared toward ensuring the safe execution of learned orientation skills within constrained regions surrounding a reference trajectory. This involves learning a stable DS on SO(3), extracting time-varying conic constraints from the variability observed in expert demonstrations, and bounding the evolution of the DS with Conic Control Barrier Function (CCBF) to fulfill the constraints. We validated our approach through extensive evaluation in simulation and showcased its effectiveness for a cutting skill in the context of assisted teleoperation.
Contextualized embeddings are the preferred tool for modeling Lexical Semantic Change (LSC). Current evaluations typically focus on a specific task known as Graded Change Detection (GCD). However, performance comparison across work are often misleading due to their reliance on diverse settings. In this paper, we evaluate state-of-the-art models and approaches for GCD under equal conditions. We further break the LSC problem into Word-in-Context (WiC) and Word Sense Induction (WSI) tasks, and compare models across these different levels. Our evaluation is performed across different languages on eight available benchmarks for LSC, and shows that (i) APD outperforms other approaches for GCD; (ii) XL-LEXEME outperforms other contextualized models for WiC, WSI, and GCD, while being comparable to GPT-4; (iii) there is a clear need for improving the modeling of word meanings, as well as focus on how, when, and why these meanings change, rather than solely focusing on the extent of semantic change.
Open-domain question answering (ODQA) has emerged as a pivotal research spotlight in information systems. Existing methods follow two main paradigms to collect evidence: (1) The \textit{retrieve-then-read} paradigm retrieves pertinent documents from an external corpus; and (2) the \textit{generate-then-read} paradigm employs large language models (LLMs) to generate relevant documents. However, neither can fully address multifaceted requirements for evidence. To this end, we propose LLMQA, a generalized framework that formulates the ODQA process into three basic steps: query expansion, document selection, and answer generation, combining the superiority of both retrieval-based and generation-based evidence. Since LLMs exhibit their excellent capabilities to accomplish various tasks, we instruct LLMs to play multiple roles as generators, rerankers, and evaluators within our framework, integrating them to collaborate in the ODQA process. Furthermore, we introduce a novel prompt optimization algorithm to refine role-playing prompts and steer LLMs to produce higher-quality evidence and answers. Extensive experimental results on widely used benchmarks (NQ, WebQ, and TriviaQA) demonstrate that LLMQA achieves the best performance in terms of both answer accuracy and evidence quality, showcasing its potential for advancing ODQA research and applications.
Batch Normalization's (BN) unique property of depending on other samples in a batch is known to cause problems in several tasks, including sequence modeling. Yet, BN-related issues are hardly studied for long video understanding, despite the ubiquitous use of BN in CNNs (Convolutional Neural Networks) for feature extraction. Especially in surgical workflow analysis, where the lack of pretrained feature extractors has led to complex, multi-stage training pipelines, limited awareness of BN issues may have hidden the benefits of training CNNs and temporal models end to end. In this paper, we analyze pitfalls of BN in video learning, including issues specific to online tasks such as a 'cheating' effect in anticipation. We observe that BN's properties create major obstacles for end-to-end learning. However, using BN-free backbones, even simple CNN-LSTMs beat the state of the art {\color{\colorrevtwo}on three surgical workflow benchmarks} by utilizing adequate end-to-end training strategies which maximize temporal context. We conclude that awareness of BN's pitfalls is crucial for effective end-to-end learning in surgical tasks. By reproducing results on natural-video datasets, we hope our insights will benefit other areas of video learning as well. Code is available at: \url{//gitlab.com/nct_tso_public/pitfalls_bn}
A Fixed-Parameter Tractable Algorithm for Counting Markov Equivalence Classes with the same Skeleton
Causal DAGs (also known as Bayesian networks) are a popular tool for encoding conditional dependencies between random variables. In a causal DAG, the random variables are modeled as vertices in the DAG, and it is stipulated that every random variable is independent of its ancestors conditioned on its parents. It is possible, however, for two different causal DAGs on the same set of random variables to encode exactly the same set of conditional dependencies. Such causal DAGs are said to be Markov equivalent, and equivalence classes of Markov equivalent DAGs are known as Markov Equivalent Classes (MECs). Beautiful combinatorial characterizations of MECs have been developed in the past few decades, and it is known, in particular that all DAGs in the same MEC must have the same "skeleton" (underlying undirected graph) and v-structures (induced subgraph of the form $a\rightarrow b \leftarrow c$). These combinatorial characterizations also suggest several natural algorithmic questions. One of these is: given an undirected graph $G$ as input, how many distinct Markov equivalence classes have the skeleton $G$? Much work has been devoted in the last few years to this and other closely related problems. However, to the best of our knowledge, a polynomial time algorithm for the problem remains unknown. In this paper, we make progress towards this goal by giving a fixed parameter tractable algorithm for the above problem, with the parameters being the treewidth and the maximum degree of the input graph $G$. The main technical ingredient in our work is a construction we refer to as shadow, which lets us create a "local description" of long-range constraints imposed by the combinatorial characterizations of MECs.
We present a deep learning-based iterative approach to solve the discrete heterogeneous Helmholtz equation for high wavenumbers. Combining classical iterative multigrid solvers and convolutional neural networks (CNNs) via preconditioning, we obtain a learned neural solver that is faster and scales better than a standard multigrid solver. Our approach offers three main contributions over previous neural methods of this kind. First, we construct a multilevel U-Net-like encoder-solver CNN with an implicit layer on the coarsest grid of the U-Net, where convolution kernels are inverted. This alleviates the field of view problem in CNNs and allows better scalability. Second, we improve upon the previous CNN preconditioner in terms of the number of parameters, computation time, and convergence rates. Third, we propose a multiscale training approach that enables the network to scale to problems of previously unseen dimensions while still maintaining a reasonable training procedure. Our encoder-solver architecture can be used to generalize over different slowness models of various difficulties and is efficient at solving for many right-hand sides per slowness model. We demonstrate the benefits of our novel architecture with numerical experiments on a variety of heterogeneous two-dimensional problems at high wavenumbers.
Multitask Reinforcement Learning (MTRL) approaches have gained increasing attention for its wide applications in many important Reinforcement Learning (RL) tasks. However, while recent advancements in MTRL theory have focused on the improved statistical efficiency by assuming a shared structure across tasks, exploration--a crucial aspect of RL--has been largely overlooked. This paper addresses this gap by showing that when an agent is trained on a sufficiently diverse set of tasks, a generic policy-sharing algorithm with myopic exploration design like $\epsilon$-greedy that are inefficient in general can be sample-efficient for MTRL. To the best of our knowledge, this is the first theoretical demonstration of the "exploration benefits" of MTRL. It may also shed light on the enigmatic success of the wide applications of myopic exploration in practice. To validate the role of diversity, we conduct experiments on synthetic robotic control environments, where the diverse task set aligns with the task selection by automatic curriculum learning, which is empirically shown to improve sample-efficiency.
Large language models (LLMs) have significantly advanced the field of natural language processing (NLP), providing a highly useful, task-agnostic foundation for a wide range of applications. The great promise of LLMs as general task solvers motivated people to extend their functionality largely beyond just a ``chatbot'', and use it as an assistant or even replacement for domain experts and tools in specific domains such as healthcare, finance, and education. However, directly applying LLMs to solve sophisticated problems in specific domains meets many hurdles, caused by the heterogeneity of domain data, the sophistication of domain knowledge, the uniqueness of domain objectives, and the diversity of the constraints (e.g., various social norms, cultural conformity, religious beliefs, and ethical standards in the domain applications). To fill such a gap, explosively-increase research, and practices have been conducted in very recent years on the domain specialization of LLMs, which, however, calls for a comprehensive and systematic review to better summarizes and guide this promising domain. In this survey paper, first, we propose a systematic taxonomy that categorizes the LLM domain-specialization techniques based on the accessibility to LLMs and summarizes the framework for all the subcategories as well as their relations and differences to each other. We also present a comprehensive taxonomy of critical application domains that can benefit from specialized LLMs, discussing their practical significance and open challenges. Furthermore, we offer insights into the current research status and future trends in this area.
The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question answering or machine translation). However, it builds upon the assumption that the data distribution is stationary, ie. that the data is sampled from a fixed distribution both at training and test time. This way of training is inconsistent with how we as humans are able to learn from and operate within a constantly changing stream of information. Moreover, it is ill-adapted to real-world use cases where the data distribution is expected to shift over the course of a model's lifetime. The first goal of this thesis is to characterize the different forms this shift can take in the context of natural language processing, and propose benchmarks and evaluation metrics to measure its effect on current deep learning architectures. We then proceed to take steps to mitigate the effect of distributional shift on NLP models. To this end, we develop methods based on parametric reformulations of the distributionally robust optimization framework. Empirically, we demonstrate that these approaches yield more robust models as demonstrated on a selection of realistic problems. In the third and final part of this thesis, we explore ways of efficiently adapting existing models to new domains or tasks. Our contribution to this topic takes inspiration from information geometry to derive a new gradient update rule which alleviate catastrophic forgetting issues during adaptation.
Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism which has been demonstrated effective is the most fundamental part of GNNs. Although most of GNNs basically follow a message passing manner, litter effort has been made to discover and analyze their essential relations. In this paper, we establish a surprising connection between different propagation mechanisms with a unified optimization problem, showing that despite the proliferation of various GNNs, in fact, their proposed propagation mechanisms are the optimal solution optimizing a feature fitting function over a wide class of graph kernels with a graph regularization term. Our proposed unified optimization framework, summarizing the commonalities between several of the most representative GNNs, not only provides a macroscopic view on surveying the relations between different GNNs, but also further opens up new opportunities for flexibly designing new GNNs. With the proposed framework, we discover that existing works usually utilize naive graph convolutional kernels for feature fitting function, and we further develop two novel objective functions considering adjustable graph kernels showing low-pass or high-pass filtering capabilities respectively. Moreover, we provide the convergence proofs and expressive power comparisons for the proposed models. Extensive experiments on benchmark datasets clearly show that the proposed GNNs not only outperform the state-of-the-art methods but also have good ability to alleviate over-smoothing, and further verify the feasibility for designing GNNs with our unified optimization framework.
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