An edit refers to a single insertion, deletion, or substitution. This paper aims to construct binary codes that can correct two edits. To do this, a necessary and sufficient condition for a code to be two-edit correctable is provided, showing that a code is a two-edit correcting code if and only if it can correct two deletions, up to two substitutions, and one deletion and up to one substitution, separately. This criterion allows for the construction of two-edit correcting codes leveraging these three types of error correcting codes. In the field of constructing codes for correcting two deletions, we modify the construction presented by Guruswami and H{\aa}stad and give an alternative proof. Moreover, our two-deletion correcting codes can also correct up to two substitutions after making a slight modification. In the field of constructing codes for correcting one deletion and up to one substitution, we present a construction with $(4+o(1)) \log n$ redundant bits, which outperforms the best previously known results $(6+o(1)) \log n$. Leveraging these codes, we obtain a construction of two-edit correcting codes with $(6+o(1)) \log n$ redundant bits, which outperforms the best previously known results $(8+o(1)) \log n$. Moreover, we also consider the list-decoding problem under the two-edit channel and construct a two-edit list-decodable code with a list size of two employing $(4+o(1)) \log n$ redundant bits.
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This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random variables. In quantum mechanics, a density matrix is the most general way to describe the state of a quantum system. This work extends the concept of density matrices by allowing them to be defined in a reproducing kernel Hilbert space. This abstraction allows the construction of differentiable models for density estimation, inference, and sampling, and enables their integration into end-to-end deep neural models. In doing so, we provide a versatile representation of marginal and joint probability distributions that allows us to develop a differentiable, compositional, and reversible inference procedure that covers a wide range of machine learning tasks, including density estimation, discriminative learning, and generative modeling. The broad applicability of the framework is illustrated by two examples: an image classification model that can be naturally transformed into a conditional generative model, and a model for learning with label proportions that demonstrates the framework's ability to deal with uncertainty in the training samples. The framework is implemented as a library and is available at: //github.com/fagonzalezo/kdm.
This paper first discusses the size and orientation of hat supertiles. Fibonacci and Lucas sequences, as well as a third integer sequence linearly related to the Lucas sequence are involved. The result is then generalized to any aperiodic tile in the hat family.
This paper discusses Life-Based Design (LBD) methodology within the context of designing technologies for reaching a state of solitude, the state where a person wishes to minimize her social contacts to get space or freedom.
This paper introduces a new class of explanation structures, called robust counterfactual witnesses (RCWs), to provide robust, both counterfactual and factual explanations for graph neural networks. Given a graph neural network M, a robust counterfactual witness refers to the fraction of a graph G that are counterfactual and factual explanation of the results of M over G, but also remains so for any "disturbed" G by flipping up to k of its node pairs. We establish the hardness results, from tractable results to co-NP-hardness, for verifying and generating robust counterfactual witnesses. We study such structures for GNN-based node classification, and present efficient algorithms to verify and generate RCWs. We also provide a parallel algorithm to verify and generate RCWs for large graphs with scalability guarantees. We experimentally verify our explanation generation process for benchmark datasets, and showcase their applications.
This paper explores the impact of incorporating sentiment, emotion, and domain-specific lexicons into a transformer-based model for depression symptom estimation. Lexicon information is added by marking the words in the input transcripts of patient-therapist conversations as well as in social media posts. Overall results show that the introduction of external knowledge within pre-trained language models can be beneficial for prediction performance, while different lexicons show distinct behaviours depending on the targeted task. Additionally, new state-of-the-art results are obtained for the estimation of depression level over patient-therapist interviews.
We propose a novel sensitivity analysis framework for linear estimators with identification failures that can be viewed as seeing the wrong outcome distribution. Our approach measures the degree of identification failure through the change in measure between the observed distribution and a hypothetical target distribution that would identify the causal parameter of interest. The framework yields a sensitivity analysis that generalizes existing bounds for Average Potential Outcome (APO), Regression Discontinuity (RD), and instrumental variables (IV) exclusion failure designs. Our partial identification results extend results from the APO context to allow even unbounded likelihood ratios. Our proposed sensitivity analysis consistently estimates sharp bounds under plausible conditions and estimates valid bounds under mild conditions. We find that our method performs well in simulations even when targeting a discontinuous and nearly infinite bound.
Counterfactual text generation aims to minimally change a text, such that it is classified differently. Judging advancements in method development for counterfactual text generation is hindered by a non-uniform usage of data sets and metrics in related work. We propose CEval, a benchmark for comparing counterfactual text generation methods. CEval unifies counterfactual and text quality metrics, includes common counterfactual datasets with human annotations, standard baselines (MICE, GDBA, CREST) and the open-source language model LLAMA-2. Our experiments found no perfect method for generating counterfactual text. Methods that excel at counterfactual metrics often produce lower-quality text while LLMs with simple prompts generate high-quality text but struggle with counterfactual criteria. By making CEval available as an open-source Python library, we encourage the community to contribute more methods and maintain consistent evaluation in future work.
Contextual embeddings, such as ELMo and BERT, move beyond global word representations like Word2Vec and achieve ground-breaking performance on a wide range of natural language processing tasks. Contextual embeddings assign each word a representation based on its context, thereby capturing uses of words across varied contexts and encoding knowledge that transfers across languages. In this survey, we review existing contextual embedding models, cross-lingual polyglot pre-training, the application of contextual embeddings in downstream tasks, model compression, and model analyses.
Benefit from the quick development of deep learning techniques, salient object detection has achieved remarkable progresses recently. However, there still exists following two major challenges that hinder its application in embedded devices, low resolution output and heavy model weight. To this end, this paper presents an accurate yet compact deep network for efficient salient object detection. More specifically, given a coarse saliency prediction in the deepest layer, we first employ residual learning to learn side-output residual features for saliency refinement, which can be achieved with very limited convolutional parameters while keep accuracy. Secondly, we further propose reverse attention to guide such side-output residual learning in a top-down manner. By erasing the current predicted salient regions from side-output features, the network can eventually explore the missing object parts and details which results in high resolution and accuracy. Experiments on six benchmark datasets demonstrate that the proposed approach compares favorably against state-of-the-art methods, and with advantages in terms of simplicity, efficiency (45 FPS) and model size (81 MB).
In this paper, we propose a conceptually simple and geometrically interpretable objective function, i.e. additive margin Softmax (AM-Softmax), for deep face verification. In general, the face verification task can be viewed as a metric learning problem, so learning large-margin face features whose intra-class variation is small and inter-class difference is large is of great importance in order to achieve good performance. Recently, Large-margin Softmax and Angular Softmax have been proposed to incorporate the angular margin in a multiplicative manner. In this work, we introduce a novel additive angular margin for the Softmax loss, which is intuitively appealing and more interpretable than the existing works. We also emphasize and discuss the importance of feature normalization in the paper. Most importantly, our experiments on LFW BLUFR and MegaFace show that our additive margin softmax loss consistently performs better than the current state-of-the-art methods using the same network architecture and training dataset. Our code has also been made available at //github.com/happynear/AMSoftmax
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