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In the field of parameterized complexity theory, the study of graph width measures has been intimately connected with the development of width-based model checking algorithms for combinatorial properties on graphs. In this work, we introduce a general framework to convert a large class of width-based model-checking algorithms into algorithms that can be used to test the validity of graph-theoretic conjectures
on classes of graphs of bounded width. Our framework is modular and can be applied with respect to several well-studied width measures for graphs, including treewidth and cliquewidth. 

As a quantitative application of our framework, we prove analytically that for several long-standing graph-theoretic conjectures, there exists an algorithm that takes a number $k$ as input and correctly determines in time double-exponential in $k^O(1)$ whether the conjecture is valid on all graphs of treewidth at most $k$. These upper bounds, which may be regarded as upper-bounds on the size of proofs/disproofs for these conjectures on the class of graphs of treewidth at most $k$, improve significantly on theoretical upper bounds obtained using previously available techniques.

AAAI 2023

From Width-Based Model Checking to Width-Based Automated Theorem Proving

parameterized algorithms

width-based automated theorem proving

width-based model checking

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-23 is the Thirty-Seventh AAAI Conference on Artificial Intelligence. The theme of this conference is to create collaborative bridges within and beyond AI. Like previous AAAI conferences, AAAI-23 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and two new activities: a Bridge Program and a Lab Program. Many of these activities are tailored to the theme of bridges and all are selected according to the highest standards, with additional programs for students and young researchers. 
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The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines.

poster

We consider the problem of large-scale Fisher market equilibrium computation through scalable first-order optimization methods. It is well-known that market equilibria can be captured using structured convex programs such as the Eisenberg-Gale and Shmyrev convex programs. Highly performant deterministic full-gradient first-order methods have been developed for these programs. In this paper, we develop new block-coordinate first-order methods for computing Fisher market equilibria, and show that these methods have interpretations as tâtonnement-style or proportional response-style dynamics where either buyers or items show up one at a time. We reformulate these convex programs and solve them using proximal block coordinate descent methods, a class of methods that update only a small number of coordinates of the decision variable in each iteration. Leveraging recent advances in the convergence analysis of these methods and structures of the equilibrium-capturing convex programs, we establish fast convergence rates of these methods. 

Fast and Interpretable Dynamics for Fisher Markets via Block-Coordinate Updates

Persona-based dialogue systems aim to generate consistent responses based on historical context and predefined persona. Unlike conventional dialogue generation, the persona-based dialogue needs to consider both dialogue context and persona, posing a challenge for coherent training. Specifically, this requires a delicate weight balance between context and persona. To achieve that, in this paper, we propose an effective framework with Persona-Adaptive Attention (PAA), which adaptively integrates the weights from the persona and context information via our designed attention. In addition, a dynamic masking mechanism is applied to the PAA to not only drop redundant information in context and persona but also serve as a regularization mechanism to avoid overfitting. Experimental results demonstrate the superiority of the proposed PAA framework compared to the strong baselines in both automatic and human evaluation. Moreover, the proposed PAA approach can perform equivalently well in a low-resource regime compared to models trained in a full-data setting, which achieve a similar result with only 20% to 30% of data compared to the larger models trained in the full-data setting. To fully exploit the effectiveness of our design, we designed several variants for handling the weighted information in different ways, showing the necessity and sufficiency of our weighting and masking designs. 

Personalized Dialogue Generation with Persona-Adaptive Attention

We present a new paradigm for fine-tuning large-scale vision-language pre-trained models on downstream task, dubbed Prompt Regularization (ProReg). Different from traditional fine-tuning which easily overfits to the downstream task data, ProReg uses the prediction by prompting the pretrained model to regularize the fine-tuning. The motivation is: by prompting the large model “a photo of a [CLASS]”, the fill-in answer is only dependent on the pretraining encyclopedic knowledge while independent of the task data distribution, which is usually biased. Specifically, given a training sample prediction during fine-tuning, we first calculate its Kullback-Leibler loss of the prompt prediction and Cross-Entropy loss of the ground-truth label, and then combine them with a proposed sample-wise adaptive trade- off weight, which automatically adjusts the transfer between the pretrained and downstream domains. On various out-of-distribution benchmarks, we show the consistently strong performance of ProReg compared with conventional fine-tuning, zero-shot prompt, prompt tuning, and other state-of-the-art methods. 

Debiased Fine-Tuning for Vision-language Models by Prompt Regularization

Knowledge graphs represent known facts using triplets. While existing knowledge graph embedding methods only consider the connections between entities, we propose considering the relationships between triplets. For example, let us consider two triplets T1 and T2 where T1 is (Academy_Awards, Nominates, Avatar) and T2 is (Avatar, Wins, Academy_Awards). Given these two base-level triplets, we see that T1 is a prerequisite for T2. In this paper, we define a higher-level triplet to represent a relationship between triplets, e.g., <T1, PrerequisiteFor, T2> where PrerequisiteFor is a higher-level relation. We define a bi-level knowledge graph that consists of the base-level and the higher-level triplets. We also propose a data augmentation strategy based on the random walks on the bi-level knowledge graph to augment plausible triplets. Our model called BiVE learns embeddings by taking into account the structures of the base-level and the higher-level triplets, with additional consideration of the augmented triplets. We propose two new tasks: triplet prediction and conditional link prediction. Given a triplet T1 and a higher-level relation, the triplet prediction predicts a triplet that is likely to be connected to T1 by the higher-level relation, e.g., <T1, PrerequisiteFor, ?>. The conditional link prediction predicts a missing entity in a triplet conditioned on another triplet, e.g., <T1, PrerequisiteFor, (Avatar, Wins, ?)>. Experimental results show that BiVE significantly outperforms all other methods in the two new tasks and the typical base-level link prediction in real-world bi-level knowledge graphs.

Learning Representations of Bi-Level Knowledge Graphs for Reasoning beyond Link Prediction

In contrast to the standard learning paradigm where all classes can be observed in training data, learning with augmented classes (LAC) tackles the problem where augmented classes unobserved in the training data may emerge in the test phase. Previous research showed that given unlabeled data, an unbiased risk estimator (URE) can be derived, which can be minimized for LAC with theoretical guarantees. However, this URE is only restricted to the specific type of one-versus-rest loss functions for multi-class classification, making it not flexible enough when the loss needs to be changed with the dataset in practice. In this paper, we propose a generalized URE that can be equipped with arbitrary loss functions while maintaining the theoretical guarantees, given unlabeled data for LAC. To alleviate the issue of negative empirical risk commonly encountered by previous studies, we further propose a novel risk-penalty regularization term. Experiments demonstrate the effectiveness of our proposed method.

A Generalized Unbiased Risk Estimator for Learning with Augmented Classes

We propose causal recurrent variational autoencoder (CR-VAE), a novel generative model that is able to learn a Granger causal graph from a multivariate time series x and incorporates the underlying causal mechanism into its data generation process. Distinct to the classical recurrent VAEs, our CR-VAE uses a multi-head decoder, in which the p-th head is responsible for generating the p-th dimension of x (i.e., x^p). By imposing a sparsity-inducing penalty on the weights (of the decoder) and encouraging specific sets of weights to be zero, our CR-VAE learns a sparse adjacency matrix that encodes causal relations between all pairs of variables. Thanks to this causal matrix, our decoder strictly obeys the underlying principles of Granger causality, thereby making the data generating process transparent. We develop a two-stage approach to train the overall objective. Empirically, we evaluate the behavior of our model in synthetic data and two real-world human brain datasets involving, respectively, the electroencephalography (EEG) signals and the functional magnetic resonance imaging (fMRI) data. Our model consistently outperforms state-of-the-art time series generative models both qualitatively and quantitatively. Moreover, it also discovers a faithful causal graph with similar or improved accuracy over existing Granger causality-based causal inference methods. 

Causal Recurrent Variational Autoencoder for Medical Time Series Generation

Efficient Transformers have been developed for long sequence modeling, due to their subquadratic memory and time complexity. Sparse Transformer is a popular approach to improving the efficiency of Transformers by restricting self-attention to locations specified by the predefined sparse patterns. However, leveraging sparsity may sacrifice expressiveness compared to full-attention, when important token correlations are multiple hops away. To combine advantages of both the efficiency of sparse transformer and the expressiveness of full-attention Transformer, we propose Diffuser, a new state-of-the-art efficient Transformer. Diffuser incorporates all token interactions within one attention layer while maintaining low computation and memory costs. The key idea is to expand the receptive field of sparse attention using Attention Diffusion, which computes multi-hop token correlations based on all paths between corresponding disconnected tokens, besides attention among neighboring tokens. Theoretically, we show the expressiveness of Diffuser as a universal sequence approximator for sequence-to-sequence modeling, and investigate its ability to approximate full-attention by analyzing the graph expander property from the spectral perspective. Experimentally, we investigate the effectiveness of Diffuser with extensive evaluations, including language modeling, image modeling, and Long Range Arena (LRA).  Evaluation results show that Diffuser achieves improvements by an average of 0.94% on text classification tasks and 2.30% on LRA, with 1.67x memory savings compared to state-of-the-art benchmarks, which demonstrates superior performance of Diffuser in both expressiveness and efficiency aspects.

Diffuser: Efficient Transformers with Multi-hop Attention Diffusion for Long Sequences

In many supervised learning scenarios, auxiliary losses are used in order to introduce additional information or constraints into the supervised learning objective. For instance, knowledge distillation aims to mimic outputs of a powerful teacher model; similarly, in rule-based approaches, weak labeling information is provided by labeling functions which may be noisy rule-based approximations to true labels. We tackle the problem of learning to combine these losses in a principled manner. Our proposal, AMAL, uses a bi-level optimization criterion on validation data to learn optimal mixing weights, at an instance-level, over the training data. We describe a meta-learning approach towards solving this bi-level objective, and show how it can be applied to different scenarios in supervised learning. Experiments in a number of knowledge distillation and rule denoising domains show that AMAL provides noticeable gains over competitive baselines in those domains. We empirically analyze our method and share insights into the mechanisms through which it provides performance gains.

Adaptive mixing of auxiliary losses in supervised learning

Multi-label text classification (MLTC) involves tagging a document with its most relevant subset of labels from a label set. In real applications, labels usually follow a long-tailed distribution, where most labels (called as tail-label) only contain a small number of documents and limit the performance of MLTC. To facilitate this low-resource problem, researchers introduced a simple but effective strategy, data augmentation (DA). However, most existing DA approaches struggle in multi-label settings. The main reason is that the augmented documents for one label may inevitably influence the other co-occurring labels and further exaggerate the long-tailed problem. To mitigate this issue, we propose a new pair-level augmentation framework for MLTC, called Label-Specific Feature Augmentation (LSFA), which merely augments positive feature-label pairs for the tail-labels. LSFA contains two main parts. The first is for label-specific document representation learning in the high-level latent space, the second is for augmenting tail-label features in latent space by transferring the documents second-order statistics (intra-class semantic variations) from head labels to tail labels. At last, we design a new loss function for adjusting classifiers based on augmented datasets. The whole learning procedure can be effectively trained. Comprehensive experiments on benchmark datasets have shown that the proposed LSFA outperforms the state-of-the-art counterparts.

Label-Specific Feature Augmentation for Long-Tailed Multi-Label Text Classification

Predict+Optimize is a recently proposed framework which combines machine learning and constrained optimization, tackling optimization problems that contain parameters that are unknown at solving time. The goal is to predict the unknown parameters and use the estimates to solve for an estimated optimal solution to the optimization problem. However, all prior works have focused on the case where unknown parameters appear only in the optimization objective and not the constraints, for the simple reason that if the constraints were not known exactly, the estimated optimal solution might not even be feasible under the true parameters. The contributions of this paper are two-fold. First, we propose a novel and practically relevant framework for the Predict+Optimize setting, but with unknown parameters in both the objective and the constraints. We introduce the notion of a correction function, and an additional penalty term in the loss function, modelling practical scenarios where an estimated optimal solution can be modified into a feasible solution after the true parameters are revealed, but at an additional cost. Second, we propose a corresponding algorithmic approach for our framework, which handles all packing and covering linear programs. Our approach is inspired by the prior work of Mandi and Guns, though with crucial modifications and re-derivations for our very different setting. Experimentation demonstrates the superior empirical performance of our method over classical approaches.

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Fast and Interpretable Dynamics for Fisher Markets via Block-Coordinate Updates

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