Enabling neural networks to learn complex logical constraints and fulfill symbolic reasoning is a critical challenge. Bridging this gap often requires guiding the neural network’s output distribution to move closer to the symbolic constraints. While diffusion models have shown remarkable generative capability across various domains, we employ the powerful architecture to perform neuro-symbolic learning and solve logical puzzles. Our diffusion-based pipeline adopts a two-stage training strategy: the first stage focuses on cultivating basic reasoning abilities, while the second emphasizes systematic learning of logical constraints. To impose hard constraints on neural outputs in the second stage, we formulate the diffusion reasoner as a Markov decision process and innovatively fine-tune it with an improved proximal policy optimization algorithm. We utilize a rule-based reward signal derived from the logical consistency of neural outputs and adopt a flexible strategy to optimize the diffusion reasoner's policy. We evaluate our methodology on some classical symbolic reasoning benchmarks, including Sudoku, Maze, pathfinding and preference learning. Experimental results demonstrate that our approach achieves outstanding accuracy and logical consistency among neural networks.

The reasoning capabilities of advanced large language models (LLMs) like o1 have revolutionized artificial intelligence applications. Nevertheless, evaluating and optimizing complex reasoning processes remain significant challenges due to diverse policy distributions and the inherent limitations of human effort and accuracy. In this paper, we present AURORA, a novel automated framework for training universal process reward models (PRMs) using ensemble prompting and reverse verification. The framework employs a two-phase approach: First, it uses diverse prompting strategies and ensemble methods to perform automated annotation and evaluation of processes, ensuring robust assessments for reward learning. Second, it leverages practical reference answers for reverse verification, enhancing the model's ability to validate outputs and improving training accuracy. To assess the framework's performance, we extend beyond the existing ProcessBench benchmark by introducing UniversalBench, which evaluates reward predictions across full trajectories under diverse policy distribtion with long Chain-of-Thought (CoT) outputs. Experimental results demonstrate that AURORA enhances process evaluation accuracy, improves PRMs' accuracy for diverse policy distributions and long-CoT responses.

Motor imagery (MI) is a widely used paradigm in brain-computer interfaces (BCIs). Despite recent advancements, MI classification still faces challenges such as limited data availability and poor performance for new users. In particular, feature alignment based on deep learning in zero-calibration cross-subject frameworks remains inadequately explored. To address these issues, we propose the Meta-MMD, a novel cross-subject MI classification method that integrates meta-learning and maximum mean discrepancy (MMD) strategies. Our method minimizes the discrepancy between support and query distributions within each learning task, enhancing robustness and generalization. Experimental evaluations on two public datasets, BCI Competition IV-2a and BCI Competition IV-2b, were conducted using two backbone networks, EEGNet and DeepConvNet.Based on EEGNet, the accuracies are 69.27% and 79.22%, respectively. Based on DeepConvNet, the accuracies are 67.36% and 78.17%, respectively. Our proposed method outperforms the current state-of-the-art methods. The effectiveness of our method was thus demonstrated.

Cognitive psychology investigates perception, attention, memory, language, problem-solving, decision-making, and reasoning. Kahneman’s dual-system theory elucidates the human decision-making process, distinguishing between the rapid, intuitive System 1 and the deliberative, rational System 2. Recent advancements have positioned large language Models (LLMs) as formidable tools nearing human-level proficiency in various cognitive tasks. Nonetheless, the presence of a dual-system framework analogous to human cognition in LLMs remains unexplored. This study introduces the CogniDual Framework for LLMs (CFLLMs), designed to assess whether LLMs can, through self-training, evolve from deliberate deduction to intuitive responses, thereby emulating the human process of acquiring and mastering new information. Our findings reveal the cognitive mechanisms behind LLMs’ response generation, enhancing our understanding of their capabilities in cognitive psychology. Practically, self-trained models can provide faster responses to certain queries, reducing computational demands during inference.

Graph neural networks (GNNs) have shown considerable promise in computational chemistry. However, the limited availability of molecular data raises concerns regarding GNNs' ability to effectively capture the fundamental principles of physics and chemistry, which constrains their generalization capabilities. To address this challenge, we introduce a novel self-supervised approach termed Equivariant Masked Position Prediction (EMPP), grounded in intramolecular potential and force theory. Unlike conventional attribute masking techniques, EMPP formulates a nuanced position prediction task that is more well-defined and enhances the learning of quantum mechanical features. EMPP also bypasses the approximation of the Gaussian mixture distribution commonly used in denoising methods, allowing for more accurate acquisition of physical properties. Experimental results indicate that EMPP significantly enhances performance of advanced molecular architectures, surpassing state-of-the-art self-supervised approaches. Our code is released in https://github.com/ajy112/EMPP.

How to alleviate the hallucinations of Large Language Models (LLMs) has always been the fundamental goal pursued by the LLMs research community. Looking through numerous hallucination-related studies, a mainstream category of methods is to reduce hallucinations by optimizing the knowledge representation of LLMs to change their output. Considering that the core focus of these works is the knowledge acquired by models, and knowledge has long been a central theme in human societal progress, we believe that the process of models refining knowledge can greatly benefit from the way humans learn. In our work, by imitating the human learning process, we design an Adaptive Contrastive Learning strategy. Our method flexibly constructs different positive and negative samples for contrastive learning based on LLMs' actual mastery of knowledge. This strategy helps LLMs consolidate the correct knowledge they already possess, deepen their understanding of the correct knowledge they have encountered but not fully grasped, forget the incorrect knowledge they previously learned, and honestly acknowledge the knowledge they lack. Extensive experiments and detailed analyses on widely used datasets demonstrate the effectiveness and competitiveness of our method.

Leveraging mathematical Large Language Models (LLMs) for proof generation is a fundamental topic in LLMs research. We argue that the ability of current LLMs to prove statements largely depends on whether they have encountered the relevant proof process during training. This reliance limits their deeper understanding of mathematical theorems and related concepts. Inspired by the pedagogical method of "proof by counterexamples" commonly used in human mathematics education, our work aims to enhance LLMs’ ability to conduct mathematical reasoning and proof through counterexamples. Specifically, we manually create a high-quality, university-level mathematical benchmark, COUNTERMATH, which requires LLMs to prove mathematical statements by providing counterexamples, thereby assessing their grasp of mathematical concepts. Additionally, we develop a data engineering framework to automatically obtain training data for further model improvement. Extensive experiments and detailed analyses demonstrate that COUNTERMATH is challenging, indicating that LLMs, such as OpenAI o1, have insufficient counterexample-driven proof capabilities. Moreover, our exploration into model training reveals that strengthening LLMs’ counterexample-driven conceptual reasoning abilities is crucial for improving their overall mathematical capabilities. We believe that our work offers new perspectives on the community of mathematical LLMs.

Large Language Models (LLMs) have demonstrated outstanding performance in mathematical reasoning capabilities. However, we argue that current large-scale reasoning models primarily rely on scaling up training datasets with diverse mathematical problems and long thinking chains, which raises questions about whether LLMs genuinely acquire mathematical concepts and reasoning principles or merely remember the training data. In contrast, humans tend to break down complex problems into multiple fundamental atomic capabilities. Inspired by this, we propose a new paradigm for evaluating mathematical atomic capabilities. Our work categorizes atomic abilities into two dimensions: (1) field-specific abilities across four major mathematical fields, algebra, geometry, analysis, and topology, and (2) logical abilities at different levels, including conceptual understanding, forward multi-step reasoning with formal math language, and counterexample-driven backward reasoning. We propose corresponding training and evaluation datasets for each atomic capability unit, and conduct extensive experiments about how different atomic capabilities influence others, to explore the strategies to elicit the required specific atomic capability. Evaluation and experimental results on advanced models show many interesting discoveries and inspirations about the different performances of models on various atomic capabilities and the interactions between atomic capabilities. Our findings highlight the importance of decoupling mathematical intelligence into atomic components, providing new insights into model cognition and guiding the development of training strategies toward a more efficient, transferable, and cognitively grounded paradigm of "atomic thinking".

Recently, slow-thinking systems like GPT-o1 and DeepSeek-R1 have demonstrated great potential in solving challenging problems through explicit reflection. They significantly outperform the best fast-thinking models, such as GPT-4o, on various math and science benchmarks. However, their multimodal reasoning capabilities remain on par with fast-thinking models. For instance, GPT-o1's performance on benchmarks like MathVista, MathVerse, and MathVision is similar to fast-thinking models. In this paper, we aim to enhance the slow-thinking capabilities of vision-language models using reinforcement learning (without relying on distillation) to advance the state of the art. First, we adapt the GRPO algorithm with a novel technique called Selective Sample Replay (SSR) to address the vanishing advantages problem. While this approach yields strong performance, the resulting RL-trained models exhibit limited self-reflection or self-verification. To further encourage slow-thinking, we introduce Forced Rethinking, which appends a rethinking trigger token to the end of rollouts in RL training, explicitly enforcing a self-reflection reasoning step. By combining these two techniques, our model, VL-Rethinker, advances state-of-the-art scores on MathVista, MathVerse to achieve 80.4%, 63.5% respectively. VL-Rethinker also achieves open-source SoTA on multi-disciplinary benchmarks such as MathVision, MMMU-Pro, EMMA, and MEGA-Bench, narrowing the gap with OpenAI-o1. We conduct comprehensive ablations and analysis to provide insights into the effectiveness of our approach.

Digital images captured by unstable imaging systems often simultaneously suffer from random noise and stripe noise. Due to the complex noise distribution, denoising and destriping methods based on simple handcrafted priors may leave residual noise. Although supervised methods have achieved some progress, they rely on large-scale noisy-clean image pairs, which are challenging to obtain in practice. To address these problems, we propose a self-supervised image denoising and destriping method based on blind-spot regularization, named Self-BSR. This method transforms the overall denoising and destriping problem into a modeling task for two spatially correlated signals: image and stripe. Specifically, blind-spot regularization leverages spatial continuity learned by the improved blind-spot network to separately constrain the reconstruction of image and stripe while suppressing pixel-wise independent noise. This regularization has two advantages: first, it is adaptively formulated based on implicit network priors, without any explicit parametric modeling of image and noise; second, it enables Self-BSR to learn denoising and destriping only from noisy images. In addition, we introduce the directional feature unshuffle in Self-BSR, which extracts multi-directional information to provide discriminative features for separating image from stripe. Furthermore, the feature-resampling refinement is proposed to improve the reconstruction ability of Self-BSR by resampling pixels with high spatial correlation in the receptive field. Extensive experiments on synthetic and real-world datasets demonstrate significant advantages of the proposed method over existing methods in denoising and destriping performance. The code will be publicly available at https://github.com/Jocobqc/Self-BSR.

The Execute-Order-Validate blockchain enhances performance by allowing parallel transaction execution, yet it also introduces transaction conflicts that can cause state inconsistencies in the ledger. Previous research has focused on resolving conflicts under the assumption of the “good” intent of the senders. In this paper, we explore an unstudied scenario where a malicious user can intentionally generate transaction collisions to disrupt the service request of a target user to the underlying decentralized application (DApp). We call it manipulated transaction collision (MTC) attack. We overcome the challenges of identifying the conditions and best strategies to launch this targeted attack under various network settings. Our experiment results show that the MTC attack can effectively cause the victim to be continuously rejected by the blockchain, i.e., over 90% success rate in all tested cases on the Hyperledger Fabric blockchain. To combat this new threat, we first propose a machine-learning-assisted detection method that helps identify the adversarial behavior within massive background traffic. To further enhance blockchain resilience, we propose a more precise transaction conflicts definition and present a novel mitigation method, which not only prevents the attack but also significantly reduces the probability of natural conflicts by up to 75% in the tested DApp compared to state-of-the-art optimization methods.

Equivariant message passing neural networks have emerged as the prevailing approach for predicting chemical properties of molecules due to their ability to leverage translation and rotation symmetries, resulting in a strong inductive bias. However, the equivariant operations in each layer can impose excessive constraints on the function form and network flexibility. To address these challenges, we introduce a novel network called the Hybrid Directional Graph Neural Network (HDGNN), which effectively combines strictly equivariant operations with learnable modules. We evaluate the performance of HDGNN on the QM9 dataset and the IS2RE dataset of OC20, demonstrating its state-of-the-art performance on several tasks and competitive performance on others. Our code is anonymously released on https://github.com/ajy112/HDGNN.

Integrating first-order logic constraints (FOLCs) with neural networks is a crucial but challenging problem since it involves modeling intricate correlations to satisfy the constraints. This paper proposes a novel neural layer, LogicMP, which performs mean-field variational inference over a Markov Logic Network (MLN). It can be plugged into any off-the-shelf neural network to encode FOLCs while retaining modularity and efficiency. By exploiting the structure and symmetries in MLNs, we theoretically demonstrate that our well-designed, efficient mean-field iterations greatly mitigate the difficulty of MLN inference, reducing the inference from sequential calculation to a series of parallel tensor operations. Empirical results in three kinds of tasks over images, graphs, and text show that LogicMP outperforms advanced competitors in both performance and efficiency.

Effective coordination is crucial for motion control with reinforcement learning, especially as the complexity of agents and their motions increases. However, many existing methods struggle to account for the intricate dependencies between joints. We introduce CoordiGraph, a novel architecture that leverages subequivariant principles from physics to enhance coordination of motion control with reinforcement learning. This method embeds the principles of equivariance as inherent patterns in the learning process under gravity influence, which aids in modeling the nuanced relationships between joints vital for motion control. Through extensive experimentation with sophisticated agents in diverse environments, we highlight the merits of our approach. Compared to current leading methods, CoordiGraph notably enhances generalization and sample efficiency.

We consider a sequential decision making problem where the agent faces the environment characterized by the stochastic discrete events and seeks an optimal intervention policy such that its long-term reward is maximized. This problem exists ubiquitously in social media, finance and health informatics but is rarely investigated by the conventional research in reinforcement learning. To this end, we present a novel framework of the model-based reinforcement learning where the agent's actions and observations are asynchronous stochastic discrete events occurring in continuous-time. We model the dynamics of the environment by Hawkes process with external intervention control term and develop an algorithm to embed such process in the Bellman equation which guides the direction of the value gradient. We demonstrate the superiority of our method in both synthetic simulator and real-data experiments.

Video nystagmography (VNG) is the diagnostic gold standard of benign paroxysmal positional vertigo (BPPV), which requires medical professionals to examine the direction, frequency, intensity, duration, and variation in the strength of nystagmus on a VNG video. This is a tedious process heavily influenced by the doctor’s experience, which is error-prone. Recent automatic VNG classification methods approach this problem from the perspective of video analysis without considering medical prior knowledge, resulting in unsatisfactory accuracy and limited diagnostic capability for nystagmographic types, thereby preventing their clinical application. In this paper, we propose an end-to-end data-driven novel BPPV diagnosis framework (TC-BPPV) by considering this problem as an eye trajectory classification problem due to the disease’s symptoms and experts’ prior knowledge. In this framework, we utilize an eye movement tracking system to capture the eye trajectory and propose the Gram-based attentive neural ordinary differential equations network (Gram-AODE) to perform classification. We validate our framework using the VNG dataset provided by the collaborative university hospital and achieve state-of-the-art performance. We also evaluate Gram-AODE on multiple open-source benchmarks to demonstrate its effectiveness in trajectory classification. Code is available at https://github.com/XiheQiu/Gram-AODE.

Typical machine learning applications always assume the data follows independent and identically distributed (IID) assumptions. In contrast, this assumption is frequently violated in real-world circumstances, leading to the Out-of-Distribution (OOD) generalization problem and a major drop in model robustness. To mitigate this issue, the invariant learning technique is leveraged to distinguish between spurious features and invariant features among all input features and to train the model purely on the basis of the invariant features. Numerous invariant learning strategies imply that the training data should contain domain information. Such information includes the environment index or auxiliary information acquired from prior knowledge. However, acquiring these information is typically impossible in practice. In this study, we present TIVA for environment-independent invariance learning, which requires no environment-specific information in training data. We discover and prove that, given certain mild data conditions, it is possible to train an environment partitioning policy based on attributes that are independent of the targets and then conduct invariant risk minimization. We examine our method in comparison to other baseline methods, which demonstrate superior performance and excellent robustness under OOD, using multiple benchmarks.

Binary Code Similarity Detection (BCSD), which calculates the similarity between binary code snippets, plays a vital role in various security fields. Since binary functions have complete semantics, the main research objects in BCSD are binary functions. Current approaches face challenges in effectively capturing the semantic information of assembly instructions and the structural information of control flow graphs (CFG) in binary functions. This paper proposes a graph attention network (GAT) for BCSD, called BSGAT, to detect similarity between binary functions. Our contribution is twofold: first, we propose a strategy to generate rich representations of basic blocks in CFG; second, we introduce GAT, which assigns different weights to basic blocks in CFG, enabling the generation of more discriminative embeddings for target binary functions. We conduct experiments on a binary function similarity detection task and a real vulnerability detection task. The results show that our proposed model BSGAT outperforms existing models in both tasks. In the binary function similarity detection task, BSGAT achieved the highest average AUC value of 0.872. In the real vulnerability detection task, BSGAT achieves the highest average recall@10 0.378, surpassing the best-performing model Gemini (0.337) in the comparison models, with a significant improvement of 12.2%. Our code is available at https://github.com/quchao777/BSGAT.git.

In this paper, we present a low-latency odometry system designed for spinning lidars. Many existing lidar odometry methods wait for an entire sweep from the lidar before processing the data. This introduces a large delay between the first laser firing and its pose estimate. To reduce this latency, we treat the spinning lidar as a streaming sensor and process packets as they arrive. This effectively distributes expensive operations across time, resulting in a very fast and lightweight system with a much higher throughput and lower latency. Our open source implementation is available at https://github.com/versatran01/llol.

In this paper, we describe Direct Sparse Odometry Lite (DSOL), an improved version of Direct Sparse Odometry (DSO) [1]. We propose several algorithmic and implementation enhancements which speed up computation by a significant factor (on average 5x) even on resource-constrained platforms. The increase in speed allows us to process images at higher frame rates, which in turn provides better results on rapid motions. Our open-source implementation is available at https://github.com/versatran01/dso1.

Predictive autoscaling (autoscaling with workload forecasting) is an important mechanism that supports autonomous adjustment of computing resources in accordance with fluctuating workload demands in the Cloud. In recent works, Reinforcement Learning (RL) has been introduced as a promising approach to learn the resource management policies to guide the scaling actions under the dynamic and uncertain cloud environment. However, RL methods face the following challenges in steering predictive autoscaling, such as lack of accuracy in decision-making, inefficient sampling and significant variability in workload patterns that may cause policies to fail at test time. To this end, we propose an end-to-end predictive meta model-based RL algorithm, aiming to optimally allocate resource to maintain a stable CPU utilization level, which incorporates a specially-designed deep periodic workload prediction model as the input and embeds the Neural Process [11, 16] to guide the learning of the optimal scaling actions over numerous application services in the Cloud. Our algorithm not only ensures the predictability and accuracy of the scaling strategy, but also enables the scaling decisions to adapt to the changing workloads with high sample efficiency. Our method has achieved significant performance improvement compared to the existing algorithms and has been deployed online at Alipay, supporting the autoscaling of applications for the world-leading payment platform.

In this work we investigate the problem of uncertainty estimation for image-guided depth completion. We extend Deep Basis Fitting (DBF) [54] for depth completion within a Bayesian evidence framework to provide calibrated perpixel variance. The DBF approach frames the depth completion problem in terms of a network that produces a set of low-dimensional depth bases and a differentiable least squares fitting module that computes the basis weights using the sparse depths. By adopting a Bayesian treatment, our Bayesian Deep Basis Fitting (BDBF) approach is able to 1) predict high-quality uncertainty estimates and 2) enable depth completion with few or no sparse measurements. We conduct controlled experiments to compare BDBF against commonly used techniques for uncertainty estimation under various scenarios. Results show that our method produces better uncertainty estimates with accurate depth prediction.

In this paper we consider the task of image-guided depth completion where our system must infer the depth at every pixel of an input image based on the image content and a sparse set of depth measurements. We propose a novel approach that builds upon the strengths of modern deep learning techniques and classical optimization algorithms and significantly improves performance. The proposed method replaces the final 1 × 1 convolutional layer employed in most depth completion networks with a least squares fitting module which computes weights by fitting the implicit depth bases to the given sparse depth measurements. In addition, we show how our proposed method can be naturally extended to a multi-scale formulation for improved self-supervised training. We demonstrate through extensive experiments on various datasets that our approach achieves consistent improvements over state-of-the-art baseline methods with small computational overhead.

We devise a distributional variant of gradient temporal-difference (TD) learning. Distributional reinforcement learning has been demonstrated to outperform the regular one in the recent study \citep{bellemare2017distributional}. In the policy evaluation setting, we design two new algorithms called distributional GTD2 and distributional TDC using the Cram{é}r distance on the distributional version of the Bellman error objective function, which inherits advantages of both the nonlinear gradient TD algorithms and the distributional RL approach. In the control setting, we propose the distributional Greedy-GQ using similar derivation. We prove the asymptotic almost-sure convergence of distributional GTD2 and TDC to a local optimal solution for general smooth function approximators, which includes neural networks that have been widely used in recent study to solve the real-life RL problems. In each step, the computational complexity of above three algorithms is linear w.r.t. the number of the parameters of the function approximator, thus can be implemented efficiently for neural networks.

We consider the networked multi-agent reinforcement learning (MARL) problem in a fully decentralized setting, where agents learn to coordinate to achieve joint success. This problem is widely encountered in many areas including traffic control, distributed control, and smart grids. We assume each agent is located at a node of a communication network and can exchange information only with its neighbors. Using softmax temporal consistency, we derive a primal-dual decentralized optimization method and obtain a principled and data-efficient iterative algorithm named {\em value propagation}. We prove a non-asymptotic convergence rate of $\mathcal{O}(1/T)$ with nonlinear function approximation. To the best of our knowledge, it is the first MARL algorithm with a convergence guarantee in the control, off-policy, non-linear function approximation, fully decentralized setting.

We investigate a projection free optimization method, namely non-convex conditional gradient sliding (NCGS) for non-convex optimization problems on the batch, stochastic and finite-sum settings. Conditional gradient sliding (CGS) method, by integrating Nesterov’s accelerated gradient method with Frank-Wolfe (FW) method in a smart way, outperforms FW for convex optimization, by reducing the amount of gradient computations. However, the study of CGS in the non-convex setting is limited. In this paper, we propose the non-convex conditional gradient sliding (NCGS) methods and analyze their convergence properties. We also leverage the idea of variance reduction from the recent progress in convex optimization to obtain a new algorithm termed variance reduced NCGS (NCGS-VR), and obtain faster convergence rate than the batch NCGS in the finite-sum setting. We show that NCGS algorithms outperform their Frank-Wolfe counterparts both in theory and in practice, for all three settings, namely the batch, stochastic and finite-sum setting. This significantly improves our understanding of optimizing non-convex functions with complicated feasible sets (where projection is prohibitively expensive).

We present a novel fruit counting pipeline that combines deep segmentation, frame to frame tracking, and 3D localization to accurately count visible fruits across a sequence of images. Our pipeline works on image streams from a monocular camera, both in natural light, as well as with controlled illumination at night. We first train a Fully Convolutional Network (FCN) and segment video frame images into fruit and non-fruit pixels. We then track fruits across frames using the Hungarian Algorithm where the objective cost is determined from a Kalman Filter corrected Kanade-Lucas-Tomasi (KLT) Tracker. In order to correct the estimated count from tracking process, we combine tracking results with a Structure from Motion (SfM) algorithm to calculate relative 3D locations and size estimates to reject outliers and double counted fruit tracks. We evaluate our algorithm by comparing with ground-truth human-annotated visual counts. Our results demonstrate that our pipeline is able to accurately and reliably count fruits across image sequences, and the correction step can significantly improve the counting accuracy and robustness. Although discussed in the context of fruit counting, our work can extend to detection, tracking, and counting of a variety of other stationary features of interest such as leaf-spots, wilt, and blossom.

With the fast development of mobile Internet, Internet of Things (IoT) has been found in many important applications recently. However, it still faces many challenges in security and privacy. Blockchain (BC) technology, which underpins the cryptocurrency Bitcoin, has played an important role in the development of decentralized and data intensive applications running on millions of devices. In this paper, to establish the relationship between IoT and BC for device credibility verification, we propose a framework with layers, intersect, and self-organization Blockchain Structures (BCS). In this new framework, each BCS is organized by Blockchain technology. We describe the credibility verification method and show how it provide the verification. The efficiency and security analysis are also given in this paper, including its response time, storage efficiency, and verification. The conducted experiments have been shown to demonstrate the validity of the proposed method in satisfying the credible requirement achieved by Blockchain technology and certain advantages in storage space and response time.

In this paper, we revisit three fundamental and popular stochastic optimization algorithms (namely, Online Proximal Gradient, Regularized Dual Averaging method and ADMM with online proximal gradient) and analyze their convergence speed under conditions weaker than those in literature. In particular, previous works showed that these algorithms converge at a rate of O (\ln T/T) when the loss function is strongly convex, and O (1 /\sqrtT) in the weakly convex case. In contrast, we relax the strong convexity assumption of the loss function, and show that the algorithms converge at a rate O (\ln T/T) if the \em expectation of the loss function is \em locally strongly convex. This is a much weaker assumption and is satisfied by many practical formulations including Lasso and Logistic Regression. Our analysis thus extends the applicability of these three methods, as well as provides a general recipe for improving analysis of convergence rate for stochastic and online optimization algorithms.

This paper considers the subspace clustering problem where the data contains irrelevant or corrupted features. We propose a method termed ``robust Dantzig selector'' which can successfully identify the clustering structure even with the presence of irrelevant features. The idea is simple yet powerful: we replace the inner product by its robust counterpart, which is insensitive to the irrelevant features given an upper bound of the number of irrelevant features. We establish theoretical guarantees for the algorithm to identify the correct subspace, and demonstrate the effectiveness of the algorithm via numerical simulations. To the best of our knowledge, this is the first method developed to tackle subspace clustering with irrelevant features.

Neurons tuned to binocular disparity in area V1 are hypothesized to be responsible for short latency binocular vergence movements, which align the two eyes on the same object as it moves in depth. Disparity selective neurons in V1 are not only selective to disparity, but also to other visual stimulus dimensions, in particular orientation. In this work, we explore the role of neurons tuned to different orientations in binocular vergence control. We trained an artificial binocular vision system to execute corrective vergence movements based on the outputs of disparity selective neurons tuned to different orientations and scales. As might be expected, we find that neurons tuned to vertical orientations have the strongest effect on the vergence eye movements. The effect of neurons tuned to other orientations decreases as the tuned orientation approaches horizontal. Although adding neurons tuned to non-vertical orientations does not appear to improve vergence tracking accuracy, we find that neurons tuned to non-vertical orientations still play critical roles in binocular vergence control. First, they decrease the time required to learn the vergence control strategy. Second, they also increase the effective range of vergence control.

This paper describes a new bipartite formulation for word-document co-clustering such that hyperclique patterns, strongly affiliated documents in this case, are guaranteed not to be split into different clusters. Our approach for pattern preserving clustering consists of three steps: mine maximal hyperclique patterns, form the bipartite, and partition it. With hyperclique patterns of documents preserved, the topic of each cluster can be represented by both the top words from that cluster and the documents in the patterns, which are expected to be more compact and representative than those in the standard bipartite formulation. Experiments with real-world datasets show that, with hyperclique patterns as starting points, we can improve the clustering results in terms of various external clustering criteria. Also, the partitioned bipartite with preserved topical sets of documents naturally lends itself to different functions in search engines