We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of low-dimensional (generalized) eigenvalue decompositions, which facilitates high computational efficiency. Theoretically, we prove that this method achieves the minimax optimal rate of convergence under suitable assumptions. Furthermore, our algorithm involves a delicate reweighting scheme, which can significantly enhance the identifiability of the active set of covariates. Extensive numerical studies demonstrate high superiority of the proposed algorithm in comparison to competing methods.
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Semantic image editing requires inpainting pixels following a semantic map. It is a challenging task since this inpainting requires both harmony with the context and strict compliance with the semantic maps. The majority of the previous methods proposed for this task try to encode the whole information from erased images. However, when an object is added to a scene such as a car, its style cannot be encoded from the context alone. On the other hand, the models that can output diverse generations struggle to output images that have seamless boundaries between the generated and unerased parts. Additionally, previous methods do not have a mechanism to encode the styles of visible and partially visible objects differently for better performance. In this work, we propose a framework that can encode visible and partially visible objects with a novel mechanism to achieve consistency in the style encoding and final generations. We extensively compare with previous conditional image generation and semantic image editing algorithms. Our extensive experiments show that our method significantly improves over the state-of-the-art. Our method not only achieves better quantitative results but also provides diverse results. Please refer to the project web page for the released code and demo: //github.com/hakansivuk/DivSem.
The all pairs shortest path problem (APSP) is one of the foundational problems in computer science. For weighted dense graphs on $n$ vertices, no truly sub-cubic algorithms exist to compute APSP exactly even for undirected graphs. This is popularly known as the APSP conjecture and has played a prominent role in developing the field of fine-grained complexity. The seminal result of Seidel uses fast matrix multiplication (FMM) to compute APSP on unweighted undirected graphs exactly in $\tilde{O}(n^{\omega})$ time, where $\omega=2.372$. Even for unweighted undirected graphs, it is not possible to obtain a $(2-\epsilon)$-approximation of APSP in $o(n^\omega)$ time. In this paper, we provide a multitude of new results for multiplicative and additive approximations of APSP in undirected graphs for both unweighted and weighted cases. We provide new algorithms for multiplicative 2-approximation of unweighted graphs: a deterministic one that runs in $\tilde{O}(n^{2.072})$ time and a randomized one that runs in $\tilde{O}(n^{2.032})$ on expectation improving upon the best known bound of $\tilde{O}(n^{2.25})$ by Roditty (STOC, 2023). For $2$-approximating paths of length $\geq k$, $k \geq 4$, we provide the first improvement after Dor, Halperin, Zwick (2000) for dense graphs even just using combinatorial methods, and then improve it further using FMM. We next consider additive approximations, and provide improved bounds for all additive $\beta$-approximations, $\beta \geq 4$. For weighted graphs, we show that by allowing small additive errors along with an $(1+\epsilon)$-multiplicative approximation, it is possible to improve upon Zwick's $\tilde{O}(n^\omega)$ algorithm. Our results point out the crucial role that FMM can play even on approximating APSP on unweighted undirected graphs, and reveal new bottlenecks towards achieving a quadratic running time to approximate APSP.
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.
Interpretable AI tools are often motivated by the goal of understanding model behavior in out-of-distribution (OOD) contexts. Despite the attention this area of study receives, there are comparatively few cases where these tools have identified previously unknown bugs in models. We argue that this is due, in part, to a common feature of many interpretability methods: they analyze model behavior by using a particular dataset. This only allows for the study of the model in the context of features that the user can sample in advance. To address this, a growing body of research involves interpreting models using \emph{feature synthesis} methods that do not depend on a dataset. In this paper, we benchmark the usefulness of interpretability tools on debugging tasks. Our key insight is that we can implant human-interpretable trojans into models and then evaluate these tools based on whether they can help humans discover them. This is analogous to finding OOD bugs, except the ground truth is known, allowing us to know when an interpretation is correct. We make four contributions. (1) We propose trojan discovery as an evaluation task for interpretability tools and introduce a benchmark with 12 trojans of 3 different types. (2) We demonstrate the difficulty of this benchmark with a preliminary evaluation of 16 state-of-the-art feature attribution/saliency tools. Even under ideal conditions, given direct access to data with the trojan trigger, these methods still often fail to identify bugs. (3) We evaluate 7 feature-synthesis methods on our benchmark. (4) We introduce and evaluate 2 new variants of the best-performing method from the previous evaluation. A website for this paper and its code is at //benchmarking-interpretability.csail.mit.edu/
We introduce a new generalization of the $k$-core decomposition for temporal networks that respects temporal dynamics. In contrast to the standard definition and previous core-like decompositions for temporal graphs, our $(k,\Delta)$-core decomposition is an edge-based decomposition founded on the new notion of $\Delta$-degree. The $\Delta$-degree of an edge is defined as the minimum number of edges incident to one of its endpoints that have a temporal distance of at most~$\Delta$. Moreover, we define a new notion of temporal connectedness leading to an efficiently computable equivalence relation between so-called $\Delta$-connected components of the temporal network. We provide efficient algorithms for the $(k,\Delta)$-core decomposition and $\Delta$-connectedness, and apply them to solve community search problems, where we are given a query node and want to find a densely connected community containing the query node. Such a community is an edge-induced temporal subgraph representing densely connected groups of nodes with frequent interactions, which also captures changes over time. We provide an efficient algorithm for community search for the case without restricting the number of nodes. If the number of nodes is restricted, we show that the decision version is NP-complete. In our evaluation, we show how in a real-world social network, the inner $(k,\Delta)$-cores contain only the spreading of misinformation and that the $\Delta$-connected components of the cores are highly edge-homophilic, i.e., the majorities of the edges in the $\Delta$-connected components represent either misinformation or fact-checking. Moreover, we demonstrate how our algorithms for $\Delta$-community search successfully and efficiently identify informative structures in collaboration networks.
A hypothesis class admits a sample compression scheme, if for every sample labeled by a hypothesis from the class, it is possible to retain only a small subsample, using which the labels on the entire sample can be inferred. The size of the compression scheme is an upper bound on the size of the subsample produced. Every learnable binary hypothesis class (which must necessarily have finite VC dimension) admits a sample compression scheme of size only a finite function of its VC dimension, independent of the sample size. For multiclass hypothesis classes, the analog of VC dimension is the DS dimension. We show that the analogous statement pertaining to sample compression is not true for multiclass hypothesis classes: every learnable multiclass hypothesis class, which must necessarily have finite DS dimension, does not admit a sample compression scheme of size only a finite function of its DS dimension.
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.
2D-based Industrial Anomaly Detection has been widely discussed, however, multimodal industrial anomaly detection based on 3D point clouds and RGB images still has many untouched fields. Existing multimodal industrial anomaly detection methods directly concatenate the multimodal features, which leads to a strong disturbance between features and harms the detection performance. In this paper, we propose Multi-3D-Memory (M3DM), a novel multimodal anomaly detection method with hybrid fusion scheme: firstly, we design an unsupervised feature fusion with patch-wise contrastive learning to encourage the interaction of different modal features; secondly, we use a decision layer fusion with multiple memory banks to avoid loss of information and additional novelty classifiers to make the final decision. We further propose a point feature alignment operation to better align the point cloud and RGB features. Extensive experiments show that our multimodal industrial anomaly detection model outperforms the state-of-the-art (SOTA) methods on both detection and segmentation precision on MVTec-3D AD dataset. Code is available at //github.com/nomewang/M3DM.
Graph Neural Networks (GNN) is an emerging field for learning on non-Euclidean data. Recently, there has been increased interest in designing GNN that scales to large graphs. Most existing methods use "graph sampling" or "layer-wise sampling" techniques to reduce training time. However, these methods still suffer from degrading performance and scalability problems when applying to graphs with billions of edges. This paper presents GBP, a scalable GNN that utilizes a localized bidirectional propagation process from both the feature vectors and the training/testing nodes. Theoretical analysis shows that GBP is the first method that achieves sub-linear time complexity for both the precomputation and the training phases. An extensive empirical study demonstrates that GBP achieves state-of-the-art performance with significantly less training/testing time. Most notably, GBP can deliver superior performance on a graph with over 60 million nodes and 1.8 billion edges in less than half an hour on a single machine.
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.
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