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We introduce a new erasure decoder that applies to arbitrary quantum LDPC codes. Dubbed the cluster decoder, it generalizes the decomposition idea of Vertical-Horizontal (VH) decoding introduced by Connelly et al. in 2022. Like the VH decoder, the idea is to first run the peeling decoder and then post-process the resulting stopping set. The cluster decoder breaks the stopping set into a tree of clusters which can be solved sequentially via Gaussian Elimination (GE). By allowing clusters of unconstrained size, this decoder achieves maximum-likelihood (ML) performance with reduced complexity compared with full GE. When GE is applied only to clusters whose sizes are less than a constant, the performance is degraded but the complexity becomes linear in the block length. Our simulation results show that, for hypergraph product codes, the cluster decoder with constant cluster size achieves near-ML performance similar to VH decoding in the low-erasure-rate regime. For the general quantum LDPC codes we studied, the cluster decoder can be used to estimate the ML performance curve with reduced complexity over a wide range of erasure rates.

We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a commonly used model for the unknown parameter is a random field. We make use of the circulant embedding procedure for sampling from the aforementioned coefficient. To improve the computational complexity of the MLMC estimator in the case of highly oscillatory random fields, we devise and implement a smoothing technique integrated into the circulant embedding method. This allows to choose the coarsest mesh on the first level of MLMC independently of the correlation length of the covariance function of the random field, leading to considerable savings in computational cost. We illustrate this with numerical experiments, where we see a saving of factor 5-10 in computational cost for accuracies of practical interest.

We study the probability tail properties of Inverse Probability Weighting (IPW) estimators of the Average Treatment Effect (ATE) when there is limited overlap between the covariate distributions of the treatment and control groups. Under unconfoundedness of treatment assignment conditional on covariates, such limited overlap is manifested in the propensity score for certain units being very close (but not equal) to 0 or 1. This renders IPW estimators possibly heavy tailed, and with a slower than sqrt(n) rate of convergence. Trimming or truncation is ultimately based on the covariates, ignoring important information about the inverse probability weighted random variable Z that identifies ATE by E[Z]= ATE. We propose a tail-trimmed IPW estimator whose performance is robust to limited overlap. In terms of the propensity score, which is generally unknown, we plug-in its parametric estimator in the infeasible Z, and then negligibly trim the resulting feasible Z adaptively by its large values. Trimming leads to bias if Z has an asymmetric distribution and an infinite variance, hence we estimate and remove the bias using important improvements on existing theory and methods. Our estimator sidesteps dimensionality, bias and poor correspondence properties associated with trimming by the covariates or propensity score. Monte Carlo experiments demonstrate that trimming by the covariates or the propensity score requires the removal of a substantial portion of the sample to render a low bias and close to normal estimator, while our estimator has low bias and mean-squared error, and is close to normal, based on the removal of very few sample extremes.

We study consistent query answering via different graph representations. First, we introduce solution-conflict hypergraphs in which nodes represent facts and edges represent either conflicts or query solutions. Considering a monotonic query and a set of antimonotonic constraints, we present an explicit algorithm for counting the number of repairs satisfying the query based on a tree decomposition of the solution-conflict hypergraph. The algorithm not only provides fixed-parameter tractability results for data complexity over expressive query and constraint classes, but also introduces a novel and potentially implementable approach to repair counting. Second, we consider the Gaifman graphs arising from MSO descriptions of consistent query answering. Using a generalization of Courcelle's theorem, we then present fixed-parameter tractability results for combined complexity over expressive query and constraint classes.

We study Online Convex Optimization (OCO) with adversarial constraints, where an online algorithm must make repeated decisions to minimize both convex loss functions and cumulative constraint violations. We focus on a setting where the algorithm has access to predictions of the loss and constraint functions. Our results show that we can improve the current best bounds of $ O(\sqrt{T}) $ regret and $ \tilde{O}(\sqrt{T}) $ cumulative constraint violations to $ O(\sqrt{E_T(f)}) $ and $ \tilde{O}(\sqrt{E_T(g)}) $, respectively, where $ E_T(f) $ and $ E_T(g) $ represent the cumulative prediction errors of the loss and constraint functions. In the worst case, where $ E_T(f) = O(T) $ and $ E_T(g) = O(T) $ (assuming bounded loss and constraint functions), our rates match the prior $ O(\sqrt{T}) $ results. However, when the loss and constraint predictions are accurate, our approach yields significantly smaller regret and cumulative constraint violations. Notably, if the constraint function remains constant over time, we achieve $ \tilde{O}(1) $ cumulative constraint violation, aligning with prior results.

This survey presents an in-depth exploration of knowledge distillation (KD) techniques within the realm of Large Language Models (LLMs), spotlighting the pivotal role of KD in transferring sophisticated capabilities from proprietary giants such as GPT-4 to accessible, open-source models like LLaMA and Mistral. Amidst the evolving AI landscape, this work elucidates the critical disparities between proprietary and open-source LLMs, demonstrating how KD serves as an essential conduit for imbuing the latter with the former's advanced functionalities and nuanced understandings. Our survey is meticulously structured around three foundational pillars: algorithm, skill, and verticalization -- providing a comprehensive examination of KD mechanisms, the enhancement of specific cognitive abilities, and their practical implications across diverse fields. Crucially, the survey navigates the intricate interplay between data augmentation (DA) and KD, illustrating how DA emerges as a powerful paradigm within the KD framework to bolster LLMs' performance. By leveraging DA to generate context-rich, skill-specific training data, KD transcends traditional boundaries, enabling open-source models to approximate the contextual adeptness, ethical alignment, and deep semantic insights characteristic of their proprietary counterparts. This work aims to provide an insightful guide for researchers and practitioners, offering a detailed overview of current methodologies in knowledge distillation and proposing future research directions. By bridging the gap between proprietary and open-source LLMs, this survey underscores the potential for more accessible, efficient, and sustainable AI solutions, fostering a more inclusive and equitable landscape in AI advancements. An associated Github repository is available at //github.com/Tebmer/Awesome-Knowledge-Distillation-of-LLMs.

Emotion recognition in conversation (ERC) aims to detect the emotion label for each utterance. Motivated by recent studies which have proven that feeding training examples in a meaningful order rather than considering them randomly can boost the performance of models, we propose an ERC-oriented hybrid curriculum learning framework. Our framework consists of two curricula: (1) conversation-level curriculum (CC); and (2) utterance-level curriculum (UC). In CC, we construct a difficulty measurer based on "emotion shift" frequency within a conversation, then the conversations are scheduled in an "easy to hard" schema according to the difficulty score returned by the difficulty measurer. For UC, it is implemented from an emotion-similarity perspective, which progressively strengthens the model's ability in identifying the confusing emotions. With the proposed model-agnostic hybrid curriculum learning strategy, we observe significant performance boosts over a wide range of existing ERC models and we are able to achieve new state-of-the-art results on four public ERC datasets.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.

Named entity recognition (NER) is the task to identify text spans that mention named entities, and to classify them into predefined categories such as person, location, organization etc. NER serves as the basis for a variety of natural language applications such as question answering, text summarization, and machine translation. Although early NER systems are successful in producing decent recognition accuracy, they often require much human effort in carefully designing rules or features. In recent years, deep learning, empowered by continuous real-valued vector representations and semantic composition through nonlinear processing, has been employed in NER systems, yielding stat-of-the-art performance. In this paper, we provide a comprehensive review on existing deep learning techniques for NER. We first introduce NER resources, including tagged NER corpora and off-the-shelf NER tools. Then, we systematically categorize existing works based on a taxonomy along three axes: distributed representations for input, context encoder, and tag decoder. Next, we survey the most representative methods for recent applied techniques of deep learning in new NER problem settings and applications. Finally, we present readers with the challenges faced by NER systems and outline future directions in this area.