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Satisfaction of the strict saddle property has become a standard assumption in non-convex optimization, and it ensures that many first-order optimization
algorithms will almost always escape saddle points. However, functions exist in machine learning that do not satisfy this property, such as the loss function of a neural network with at least two hidden layers. First-order methods such as gradient descent may converge to non-strict saddle points of such functions, and there do not currently exist any first-order methods that reliably escape non-strict saddle points. To address this need, we demonstrate that regularizing a function with a linear term enforces the strict saddle property, and we provide justification for only regularizing locally, i.e., when the norm of the gradient falls below a certain threshold. We analyze bifurcations that may result from this form of regularization, and then we provide a selection rule for regularizers that depends only on the gradient of an objective function. This rule is shown to guarantee that gradient descent will escape the neighborhoods around a broad class of non-strict saddle points, and this behavior is demonstrated on numerical examples of non-strict saddle points common in the optimization literature.

AAAI 2023

Linear Regularizers Enforce the Strict Saddle Property

optimization

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

Generative Adversarial Networks (GANs) have shown compelling results in various tasks and applications in recent years. However, mode collapse remains a critical problem in GANs. In this paper, we propose a novel training pipeline to address the mode collapse issue of GANs. Different from existing methods, we propose to generalize the discriminator as feature embedding and maximize the entropy of distributions in the embedding space learned by the discriminator. Specifically, two regularization terms, i.e., Deep Local Linear Embedding (DLLE) and Deep Isometric feature Mapping (DIsoMap), are designed to encourage the discriminator to learn the structural information embedded in the data, such
that the embedding space learned by the discriminator can be well-formed. Based on the well-learned embedding space supported by the discriminator, a non-parametric entropy estimator is designed to efficiently maximize the entropy of embedding vectors, playing as an approximation of maximizing the entropy of the generated distribution. By improving the discriminator and maximizing the distance of the most similar samples in the embedding space, our pipeline effectively reduces the mode collapse without sacrificing the quality of generated samples. Extensive experimental results show the effectiveness of our method which outperforms the GAN baseline, MaF-GAN on CelebA (9.13 vs. 12.43 in FID) and surpasses the recent state-of-the-art energy-based model on the ANIMEFACE dataset (2.80 vs. 2.26 in Inception score).

Combating Mode Collapse via Offline Manifold Entropy Estimation

Understanding the informative structures of scenes is essential for low-level vision tasks. Unfortunately, it is difficult to obtain a concrete visual definition of the informative structures because influences of visual features are task-specific.
In this paper, we propose a single general neural network architecture for extracting task-specific structure guidance for scenes. To do this, we first analyze traditional spectral clustering methods, which computes a set of eigenvectors to model a segmented graph forming small compact structures on image domains. We then unfold the traditional graph-partitioning problem into a learnable network, named Scene Structure Guidance Network (SSGNet), to represent the task-specific informative structures.  The SSGNet yields a set of coefficients of eigenvectors that produces explicit feature representations of image structures. In addition, our SSGNet is light-weight ($\sim$ 55K parameters), and can be used as a plug-and-play module for off-the-shelf architectures. We optimize the SSGNet without any supervision by proposing two novel training losses that enforce task-specific scene structure generation during training. Our main contribution is to show that such a simple network can achieve state-of-the art results for several low-level vision applications including joint upsampling and image denoising. Our submitted source codes also demonstrate that our SSGNet generalizes well on unseen datasets, compared to existing methods which use structural embedding frameworks.

Task-specific Scene Structure Representations

Spatial-temporal (ST) graph modeling, such as traffic speed forecasting and taxi demand prediction, is an important task in deep learning area.
However, for the nodes in the graph, their ST patterns can vary greatly in difficulties for modeling, owning to the heterogeneous nature of ST data. We argue that unveiling the nodes to the model in a meaningful order, from easy to complex, can provide performance improvements over traditional training procedure. The idea has its root in Curriculum Learning, which suggests in the early stage of training models can be sensitive to noise and difficult samples. In this paper, we propose ST-Curriculum Dropout, a novel and easy-to-implement strategy for spatial-temporal graph modeling. Specifically, we evaluate the learning difficulty of each node in high-level feature space and drop those difficult ones out to ensure the model only needs to handle fundamental ST relations at the beginning, before gradually moving to hard ones. Our strategy can be applied to any canonical deep learning architecture without extra trainable parameters, and extensive experiments on a wide range of datasets are conducted to illustrate that, by controlling the difficulty level of ST relations as the training progresses, the model is able to capture better representation of the data and thus yields better generalization. 

Easy Begun is Half Done: Spatial-Temporal Graph Modeling with ST-Curriculum Dropout

Recently, the joint learning framework (JOINT) integrates matching based transductive reasoning and online inductive learning to achieve accurate and robust semi-supervised video object segmentation (SVOS). However, using the mask embedding as the label to guide the generation of target features in the two branches may result in inadequate target representation and degrade the performance. Besides, how to reasonably fuse the target features in the two different branches rather than simply adding them together to avoid the adverse effect of one dominant branch has not been investigated. In this paper, we propose a novel framework that emphasizes Learning to Learn Better (LLB) target features for SVOS, termed LLB, where we design the discriminative label generation module (DLGM) and the adaptive fusion module to address these issues. Technically, the DLGM takes the background-filtered frame instead of the target mask as input and adopts a lightweight encoder to generate the target features, which serves as the label of the online few-shot learner and the value of the decoder in the transformer to guide the two branches to learn more discriminative target representation. The adaptive fusion module maintains a learnable gate for each branch, which reweighs the element-wise feature representation and allows an adaptive amount of target information in each branch flowing to the fused target feature, thus preventing one branch from being dominant and making the target feature more robust to distractor. Extensive experiments on public benchmarks show that our proposed LLB method achieves state-of-the-art performance.

Learning to Learn Better for Video Object Segmentation

Goal Recognition is the task of discerning the intended goal of an agent given a sequence of observations, whereas Plan Recognition consists of identifying the plan to achieve such intended goal. Regardless of the underlying techniques, most recognition approaches are directly affected by the quality of the available observations. In this paper, we develop neuro-symbolic recognition approaches that can combine learning and planning techniques, compensating for noise and missing observations using prior data. We evaluate our approaches in standard human-designed planning domains as well as domain models automatically learned from real-world data. Empirical experimentation shows that our approaches reliably infer goals and compute correct plans in the experimental datasets. An ablation study shows that outperform approaches that rely exclusively on the domain model, or exclusively on machine learning in problems with both noisy observations and low observability.

Robust Neuro-Symbolic Goal and Plan Recognition

Unsupervised text-graph alignment (UTGA) is a fundamental task that bidirectionally generates texts and graphs without parallel data. Most available models of UTGA suffer from information asymmetry, a common phenomenon that texts and graphs include additional information invisible to each other. On the one hand, these models fail to supplement asymmetric information effectively due to the lack of ground truths. On the other hand, it is challenging to indicate asymmetric information with explicit indicators because it cannot be decoupled from the data directly. To address the challenge posed by information asymmetry, we propose the assumption that asymmetric information is encoded in unobservable latent variables and only affects the one-way generation processes. These latent variables corresponding to asymmetric information should obey prior distributions recovered approximately from original data. Therefore, we first propose a taxonomy of the latent variable that classifies the latent variable into transferrable (TV) and non-transferable (NTV) variables and further distinguish NTV as the dependent variable (DV) and the independent variable (IV). Next, we propose three latent VAE-based regularizations on TV, DV, and IV to constrain their distributions to well-designed prior distributions to introduce asymmetric information into models and enhance the preservation of shared contents. Finally, we impose the three proposed constraints on a cycle-consistent learning framework, back-translation (BT), named ConstrainedBT. Experimental results on three UTGA tasks demonstrate the effectiveness of ConstrainedBT on the information-asymmetric challenge.

Latent Constraints on Unsupervised Text-Graph Alignment with Information Asymmetry

Multimodal named entity recognition (MNER) is a critical step in information extraction, which aims to detect entity spans and classify them to corresponding entity types given a sentence-image pair. Existing methods either (1) obtain named entities with coarse-grained visual clues from attention mechanisms, or (2) first detect fine-grained visual regions with toolkits and then recognize named entities. However, they suffer from improper alignment between entity types and visual regions or error propagation in the two-stage manner, which finally imports irrelevant visual information into texts. In this paper, we propose a novel end-to-end framework named MNER-QG that can simultaneously perform MRC-based multimodal named entity recognition and query grounding. Specifically, with the assistance of queries, MNER-QG can provide prior knowledge of entity types and visual regions, and further enhance representations of both text and image. To conduct the query grounding task, we provide manual annotations and weak supervisions that are obtained via training a highly flexible visual grounding model with transfer learning. We conduct extensive experiments on two public MNER datasets, Twitter2015 and Twitter2017. Experimental results show that MNER-QG outperforms the current state-of-the-art models on the MNER task, and also improves the query grounding performance.

MNER-QG: An End-to-End MRC Framework for Multimodal Named Entity Recognition with Query Grounding

To estimate item frequencies of data streams with limited space, sketches are widely used in real applications, including real-time web analytics, network monitoring, and self-driving. Sketches can be viewed as a model which maps the identifier of a stream item to the corresponding frequency domain. Starting from the premise, we envision a neural data structure, which we term the meta-sketch, to go beyond the basic structure of conventional sketches. The meta-sketch learns basic sketching abilities from meta-tasks constituted with synthetic datasets following Zipf distributions in the pre-training phase, and can be fast adapted to real (skewed) distributions in the adaption phase. Extensive experiments demonstrate the performance gains of the meta-sketch and offer insights into our proposals.

Meta-sketch: A Neural Data Structure for Estimating Item Frequencies of Data Streams

The opioid overdose epidemic represents a serious public health crisis, with fatality rates rising considerably over the past several years. To help address the abuse of prescription opioids, state governments collect data on dispensed prescriptions, yet the use of these data is typically limited to manual searches. In this paper, we propose a novel graph-based framework for detecting anomalous opioid prescribing patterns in state Prescription Drug Monitoring Program (PDMP) data, which could aid governments in deterring opioid diversion and abuse. Specifically, we seek to identify connected networks of opioid prescribers and dispensers who engage in high-risk and possibly illicit activity. We develop and apply a novel extension of the Non-Parametric Heterogeneous Graph Scan (NPHGS) to two years of de-identified PDMP data from the state of Kansas, and find that NPHGS identifies subgraphs that are significantly more anomalous than those detected by other graph-based methods. NPHGS also reveals clusters of potentially illicit activity, which may strengthen state law enforcement and regulatory capabilities. Our paper is the first to demonstrate how prescription data can systematically identify anomalous opioid prescribers and dispensers, as well as illustrating the efficacy of a network-based approach. Additionally, our technical extensions to NPHGS offer both improved flexibility and graph density reduction, enabling the framework to be replicated across jurisdictions and extended to other problem domains.

Linear Regularizers Enforce the Strict Saddle Property

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