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SGD learning on neural networks: leap complexity and saddle-to-saddle dynamics

arXiv.org Machine Learning

Deep learning has emerged as the standard approach to exploiting massive high-dimensional datasets. At the core of its success lies its capability to learn effective features with fairly blackbox architectures without suffering from the curse of dimensionality. To explain this success, two structural properties of data are commonly conjectured: (i) a low-dimensional structure that SGD-trained neural networks are able to adapt to; (ii) a hierarchical structure that neural networks can leverage with SGD training. In particular, From a statistical viewpoint: A line of work [Bac17, SH20, KK16, BK19] has investigated the sample complexity of learning with deep neural networks, decoupled from computational considerations. By directly considering global solutions of empirical risk minimization (ERM) problems over arbitrarily large neural networks and sparsity inducing norms, they showed that deep neural networks can overcome the curse of dimensionality on classes of functions with low-dimensional and hierarchical structures. However, this approach does not provide efficient algorithms: instead, a number of works have shown computational hardness of ERM problems [BR88, KS09, DLSS14] and it is unclear how much this line of work can inform practical neural networks, which are trained using SGD and variants.


Low-Rank Multitask Learning based on Tensorized SVMs and LSSVMs

arXiv.org Artificial Intelligence

Multitask learning (MTL) leverages task-relatedness to enhance performance. With the emergence of multimodal data, tasks can now be referenced by multiple indices. In this paper, we employ high-order tensors, with each mode corresponding to a task index, to naturally represent tasks referenced by multiple indices and preserve their structural relations. Based on this representation, we propose a general framework of low-rank MTL methods with tensorized support vector machines (SVMs) and least square support vector machines (LSSVMs), where the CP factorization is deployed over the coefficient tensor. Our approach allows to model the task relation through a linear combination of shared factors weighted by task-specific factors and is generalized to both classification and regression problems. Through the alternating optimization scheme and the Lagrangian function, each subproblem is transformed into a convex problem, formulated as a quadratic programming or linear system in the dual form. In contrast to previous MTL frameworks, our decision function in the dual induces a weighted kernel function with a task-coupling term characterized by the similarities of the task-specific factors, better revealing the explicit relations across tasks in MTL. Experimental results validate the effectiveness and superiority of our proposed methods compared to existing state-of-the-art approaches in MTL. The code of implementation will be available at https://github.com/liujiani0216/TSVM-MTL.


Improving Robustness and Accuracy of Ponzi Scheme Detection on Ethereum Using Time-Dependent Features

arXiv.org Artificial Intelligence

The rapid development of blockchain has led to more and more funding pouring into the cryptocurrency market, which also attracted cybercriminals' interest in recent years. The Ponzi scheme, an old-fashioned fraud, is now popular on the blockchain, causing considerable financial losses to many crypto-investors. A few Ponzi detection methods have been proposed in the literature, most of which detect a Ponzi scheme based on its smart contract source code or opcode. The contract-code-based approach, while achieving very high accuracy, is not robust: first, the source codes of a majority of contracts on Ethereum are not available, and second, a Ponzi developer can fool a contract-code-based detection model by obfuscating the opcode or inventing a new profit distribution logic that cannot be detected (since these models were trained on existing Ponzi logics only). A transaction-based approach could improve the robustness of detection because transactions, unlike smart contracts, are harder to be manipulated. However, the current transaction-based detection models achieve fairly low accuracy. We address this gap in the literature by developing new detection models that rely only on the transactions, hence guaranteeing the robustness, and moreover, achieve considerably higher Accuracy, Precision, Recall, and F1-score than existing transaction-based models. This is made possible thanks to the introduction of novel time-dependent features that capture Ponzi behaviours characteristics derived from our comprehensive data analyses on Ponzi and non-Ponzi data from the XBlock-ETH repository


Multi-Objective Decision Transformers for Offline Reinforcement Learning

arXiv.org Artificial Intelligence

Offline Reinforcement Learning (RL) is structured to derive policies from static trajectory data without requiring real-time environment interactions. Recent studies have shown the feasibility of framing offline RL as a sequence modeling task, where the sole aim is to predict actions based on prior context using the transformer architecture. However, the limitation of this single task learning approach is its potential to undermine the transformer model's attention mechanism, which should ideally allocate varying attention weights across different tokens in the input context for optimal prediction. To address this, we reformulate offline RL as a multi-objective optimization problem, where the prediction is extended to states and returns. We also highlight a potential flaw in the trajectory representation used for sequence modeling, which could generate inaccuracies when modeling the state and return distributions. This is due to the non-smoothness of the action distribution within the trajectory dictated by the behavioral policy. To mitigate this issue, we introduce action space regions to the trajectory representation. Our experiments on D4RL benchmark locomotion tasks reveal that our propositions allow for more effective utilization of the attention mechanism in the transformer model, resulting in performance that either matches or outperforms current state-of-the art methods.


Symmetry Preservation in Hamiltonian Systems: Simulation and Learning

arXiv.org Artificial Intelligence

This work presents a general geometric framework for simulating and learning the dynamics of Hamiltonian systems that are invariant under a Lie group of transformations. This means that a group of symmetries is known to act on the system respecting its dynamics and, as a consequence, Noether's Theorem, conserved quantities are observed. We propose to simulate and learn the mappings of interest through the construction of $G$-invariant Lagrangian submanifolds, which are pivotal objects in symplectic geometry. A notable property of our constructions is that the simulated/learned dynamics also preserves the same conserved quantities as the original system, resulting in a more faithful surrogate of the original dynamics than non-symmetry aware methods, and in a more accurate predictor of non-observed trajectories. Furthermore, our setting is able to simulate/learn not only Hamiltonian flows, but any Lie group-equivariant symplectic transformation. Our designs leverage pivotal techniques and concepts in symplectic geometry and geometric mechanics: reduction theory, Noether's Theorem, Lagrangian submanifolds, momentum mappings, and coisotropic reduction among others. We also present methods to learn Poisson transformations while preserving the underlying geometry and how to endow non-geometric integrators with geometric properties. Thus, this work presents a novel attempt to harness the power of symplectic and Poisson geometry towards simulating and learning problems.


Impact of Visual Context on Noisy Multimodal NMT: An Empirical Study for English to Indian Languages

arXiv.org Artificial Intelligence

The study investigates the effectiveness of utilizing multimodal information in Neural Machine Translation (NMT). While prior research focused on using multimodal data in low-resource scenarios, this study examines how image features impact translation when added to a large-scale, pre-trained unimodal NMT system. Surprisingly, the study finds that images might be redundant in this context. Additionally, the research introduces synthetic noise to assess whether images help the model deal with textual noise. Multimodal models slightly outperform text-only models in noisy settings, even with random images. The study's experiments translate from English to Hindi, Bengali, and Malayalam, outperforming state-of-the-art benchmarks significantly. Interestingly, the effect of visual context varies with source text noise: no visual context works best for non-noisy translations, cropped image features are optimal for low noise, and full image features work better in high-noise scenarios. This sheds light on the role of visual context, especially in noisy settings, opening up a new research direction for Noisy Neural Machine Translation in multimodal setups. The research emphasizes the importance of combining visual and textual information for improved translation in various environments.


EnsembleFollower: A Hybrid Car-Following Framework Based On Reinforcement Learning and Hierarchical Planning

arXiv.org Artificial Intelligence

Car-following models have made significant contributions to our understanding of longitudinal driving behavior. However, they often exhibit limited accuracy and flexibility, as they cannot fully capture the complexity inherent in car-following processes, or may falter in unseen scenarios due to their reliance on confined driving skills present in training data. It is worth noting that each car-following model possesses its own strengths and weaknesses depending on specific driving scenarios. Therefore, we propose EnsembleFollower, a hierarchical planning framework for achieving advanced human-like car-following. The EnsembleFollower framework involves a high-level Reinforcement Learning-based agent responsible for judiciously managing multiple low-level car-following models according to the current state, either by selecting an appropriate low-level model to perform an action or by allocating different weights across all low-level components. Moreover, we propose a jerk-constrained kinematic model for more convincing car-following simulations. We evaluate the proposed method based on real-world driving data from the HighD dataset. The experimental results illustrate that EnsembleFollower yields improved accuracy of human-like behavior and achieves effectiveness in combining hybrid models, demonstrating that our proposed framework can handle diverse car-following conditions by leveraging the strengths of various low-level models.


CLSE: Corpus of Linguistically Significant Entities

arXiv.org Artificial Intelligence

One of the biggest challenges of natural language generation (NLG) is the proper handling of named entities. Named entities are a common source of grammar mistakes such as wrong prepositions, wrong article handling, or incorrect entity inflection. Without factoring linguistic representation, such errors are often underrepresented when evaluating on a small set of arbitrarily picked argument values, or when translating a dataset from a linguistically simpler language, like English, to a linguistically complex language, like Russian. However, for some applications, broadly precise grammatical correctness is critical -- native speakers may find entity-related grammar errors silly, jarring, or even offensive. To enable the creation of more linguistically diverse NLG datasets, we release a Corpus of Linguistically Significant Entities (CLSE) annotated by linguist experts. The corpus includes 34 languages and covers 74 different semantic types to support various applications from airline ticketing to video games. To demonstrate one possible use of CLSE, we produce an augmented version of the Schema-Guided Dialog Dataset, SGD-CLSE. Using the CLSE's entities and a small number of human translations, we create a linguistically representative NLG evaluation benchmark in three languages: French (high-resource), Marathi (low-resource), and Russian (highly inflected language). We establish quality baselines for neural, template-based, and hybrid NLG systems and discuss the strengths and weaknesses of each approach.


MGNN: Graph Neural Networks Inspired by Distance Geometry Problem

arXiv.org Artificial Intelligence

Graph Neural Networks (GNNs) have emerged as a prominent research topic in the field of machine learning. Existing GNN models are commonly categorized into two types: spectral GNNs, which are designed based on polynomial graph filters, and spatial GNNs, which utilize a message-passing scheme as the foundation of the model. For the expressive power and universality of spectral GNNs, a natural approach is to improve the design of basis functions for better approximation ability. As for spatial GNNs, models like Graph Isomorphism Networks (GIN) analyze their expressive power based on Graph Isomorphism Tests. Recently, there have been attempts to establish connections between spatial GNNs and geometric concepts like curvature and cellular sheaves, as well as physical phenomena like oscillators. However, despite the recent progress, there is still a lack of comprehensive analysis regarding the universality of spatial GNNs from the perspectives of geometry and physics. In this paper, we propose MetricGNN (MGNN), a spatial GNN model inspired by the congruent-insensitivity property of classifiers in the classification phase of GNNs. We demonstrate that a GNN model is universal in the spatial domain if it can generate embedding matrices that are congruent to any given embedding matrix. This property is closely related to the Distance Geometry Problem (DGP). Since DGP is an NP-Hard combinatorial optimization problem, we propose optimizing an energy function derived from spring networks and the Multi-Dimensional Scaling (MDS) problem. This approach also allows our model to handle both homophilic and heterophilic graphs. Finally, we propose employing the iteration method to optimize our energy function. We extensively evaluate the effectiveness of our model through experiments conducted on both synthetic and real-world datasets. Our code is available at: https://github.com/GuanyuCui/MGNN.


On-Demand Communication for Asynchronous Multi-Agent Bandits

arXiv.org Machine Learning

This paper studies a cooperative multi-agent multi-armed stochastic bandit problem where agents operate asynchronously -- agent pull times and rates are unknown, irregular, and heterogeneous -- and face the same instance of a K-armed bandit problem. Agents can share reward information to speed up the learning process at additional communication costs. We propose ODC, an on-demand communication protocol that tailors the communication of each pair of agents based on their empirical pull times. ODC is efficient when the pull times of agents are highly heterogeneous, and its communication complexity depends on the empirical pull times of agents. ODC is a generic protocol that can be integrated into most cooperative bandit algorithms without degrading their performance. We then incorporate ODC into the natural extensions of UCB and AAE algorithms and propose two communication-efficient cooperative algorithms. Our analysis shows that both algorithms are near-optimal in regret.