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Generative models aim to simulate realistic effects of various actions across different contexts, from text generation to visual effects. Despite efforts to build real-world simulators, leveraging generative models for virtual worlds, like financial markets, remains underexplored. In financial markets, generative models can simulate market effects of various behaviors, enabling interaction with market scenes and players, and training strategies without financial risk. This simulation relies on the finest structured data in financial market like orders thus building the finest realistic simulation. We propose Large Market Model (LMM), an order-level generative foundation model, for financial market simulation, akin to language modeling in the digital world. Our financial Market Simulation engine (MarS), powered by LMM, addresses the need for realistic, interactive and controllable order generation. Key objectives of this paper include evaluating LMM's scaling law in financial markets, assessing MarS's realism, balancing controlled generation with market impact, and demonstrating MarS's potential applications. We showcase MarS as a forecast tool, detection system, analysis platform, and agent training environment. Our contributions include pioneering a generative model for financial markets, designing MarS to meet domain-specific needs, and demonstrating MarS-based applications' industry potential., Comment: 19 pages, 12 figures

Order flow modeling stands as the most fundamental and essential financial task, as orders embody the minimal unit within a financial market. However, current approaches often result in unsatisfactory fidelity in generating order flow, and their generation lacks controllability, thereby limiting their application scenario. In this paper, we advocate incorporating controllability into the market generation process, and propose a Diffusion Guided meta Agent(DiGA) model to address the problem. Specifically, we utilize a diffusion model to capture dynamics of market state represented by time-evolving distribution parameters about mid-price return rate and order arrival rate, and define a meta agent with financial economic priors to generate orders from the corresponding distributions. Extensive experimental results demonstrate that our method exhibits outstanding controllability and fidelity in generation. Furthermore, we validate DiGA's effectiveness as generative environment for downstream financial applications.

Artificial Intelligence (AI) significantly influences many fields, largely thanks to the vast amounts of high-quality data for machine learning models. The emphasis is now on a data-centric AI strategy, prioritizing data development over model design progress. Automating this process is crucial. In this paper, we serve as the first work to introduce the automatic data-centric development (AD^2) task and outline its core challenges, which require domain-experts-like task scheduling and implementation capability, largely unexplored by previous work. By leveraging the strong complex problem-solving capabilities of large language models (LLMs), we propose an LLM-based autonomous agent, equipped with a strategy named Collaborative Knowledge-STudying-Enhanced Evolution by Retrieval (Co-STEER), to simultaneously address all the challenges. Specifically, our proposed Co-STEER agent enriches its domain knowledge through our proposed evolving strategy and develops both its scheduling and implementation skills by accumulating and retrieving domain-specific practical experience. With an improved schedule, the capability for implementation accelerates. Simultaneously, as implementation feedback becomes more thorough, the scheduling accuracy increases. These two capabilities evolve together through practical feedback, enabling a collaborative evolution process. Extensive experimental results demonstrate that our Co-STEER agent breaks new ground in AD^2 research, possesses strong evolvable schedule and implementation ability, and demonstrates the significant effectiveness of its components. Our Co-STEER paves the way for AD^2 advancements., Comment: 23 pages, 7 figures

The progress of humanity is driven by those successful discoveries accompanied by countless failed experiments. Researchers often seek the potential research directions by reading and then verifying them through experiments. The process imposes a significant burden on researchers. In the past decade, the data-driven black-box deep learning method has demonstrated its effectiveness in a wide range of real-world scenarios, which exacerbates the experimental burden of researchers and thus renders the potential successful discoveries veiled. Therefore, automating such a research and development (R&D) process is an urgent need. In this paper, we serve as the first effort to formalize the goal by proposing a Real-world Data-centric automatic R&D Benchmark, namely RD2Bench. RD2Bench benchmarks all the operations in data-centric automatic R&D (D-CARD) as a whole to navigate future work toward our goal directly. We focus on evaluating the interaction and synergistic effects of various model capabilities and aiding in selecting well-performing trustworthy models. Although RD2Bench is very challenging to the state-of-the-art (SOTA) large language model (LLM) named GPT-4, indicating ample research opportunities and more research efforts, LLMs possess promising potential to bring more significant development to D-CARD: They are able to implement some simple methods without adopting any additional techniques. We appeal to future work to take developing techniques for tackling automatic R&D into consideration, thus bringing the opportunities of the potential revolutionary upgrade to human productivity., Comment: 17 pages, 3 figures

Recently, diffusion probabilistic models have attracted attention in generative time series forecasting due to their remarkable capacity to generate high-fidelity samples. However, the effective utilization of their strong modeling ability in the probabilistic time series forecasting task remains an open question, partially due to the challenge of instability arising from their stochastic nature. To address this challenge, we introduce a novel Multi-Granularity Time Series Diffusion (MG-TSD) model, which achieves state-of-the-art predictive performance by leveraging the inherent granularity levels within the data as given targets at intermediate diffusion steps to guide the learning process of diffusion models. The way to construct the targets is motivated by the observation that the forward process of the diffusion model, which sequentially corrupts the data distribution to a standard normal distribution, intuitively aligns with the process of smoothing fine-grained data into a coarse-grained representation, both of which result in a gradual loss of fine distribution features. In the study, we derive a novel multi-granularity guidance diffusion loss function and propose a concise implementation method to effectively utilize coarse-grained data across various granularity levels. More importantly, our approach does not rely on additional external data, making it versatile and applicable across various domains. Extensive experiments conducted on real-world datasets demonstrate that our MG-TSD model outperforms existing time series prediction methods., Comment: International Conference on Learning Representations (ICLR) 2024

In the wake of relentless digital transformation, data-driven solutions are emerging as powerful tools to address multifarious industrial tasks such as forecasting, anomaly detection, planning, and even complex decision-making. Although data-centric R&D has been pivotal in harnessing these solutions, it often comes with significant costs in terms of human, computational, and time resources. This paper delves into the potential of large language models (LLMs) to expedite the evolution cycle of data-centric R&D. Assessing the foundational elements of data-centric R&D, including heterogeneous task-related data, multi-facet domain knowledge, and diverse computing-functional tools, we explore how well LLMs can understand domain-specific requirements, generate professional ideas, utilize domain-specific tools to conduct experiments, interpret results, and incorporate knowledge from past endeavors to tackle new challenges. We take quantitative investment research as a typical example of industrial data-centric R&D scenario and verified our proposed framework upon our full-stack open-sourced quantitative research platform Qlib and obtained promising results which shed light on our vision of automatic evolving of industrial data-centric R&D cycle., Comment: 29 pages, 11 figures

High-frequency quantitative investment is a crucial aspect of stock investment. Notably, order flow data plays a critical role as it provides the most detailed level of information among high-frequency trading data, including comprehensive data from the order book and transaction records at the tick level. The order flow data is extremely valuable for market analysis as it equips traders with essential insights for making informed decisions. However, extracting and effectively utilizing order flow data present challenges due to the large volume of data involved and the limitations of traditional factor mining techniques, which are primarily designed for coarser-level stock data. To address these challenges, we propose a novel framework that aims to effectively extract essential factors from order flow data for diverse downstream tasks across different granularities and scenarios. Our method consists of a Context Encoder and an Factor Extractor. The Context Encoder learns an embedding for the current order flow data segment's context by considering both the expected and actual market state. In addition, the Factor Extractor uses unsupervised learning methods to select such important signals that are most distinct from the majority within the given context. The extracted factors are then utilized for downstream tasks. In empirical studies, our proposed framework efficiently handles an entire year of stock order flow data across diverse scenarios, offering a broader range of applications compared to existing tick-level approaches that are limited to only a few days of stock data. We demonstrate that our method extracts superior factors from order flow data, enabling significant improvement for stock trend prediction and order execution tasks at the second and minute level.

Order execution is a fundamental task in quantitative finance, aiming at finishing acquisition or liquidation for a number of trading orders of the specific assets. Recent advance in model-free reinforcement learning (RL) provides a data-driven solution to the order execution problem. However, the existing works always optimize execution for an individual order, overlooking the practice that multiple orders are specified to execute simultaneously, resulting in suboptimality and bias. In this paper, we first present a multi-agent RL (MARL) method for multi-order execution considering practical constraints. Specifically, we treat every agent as an individual operator to trade one specific order, while keeping communicating with each other and collaborating for maximizing the overall profits. Nevertheless, the existing MARL algorithms often incorporate communication among agents by exchanging only the information of their partial observations, which is inefficient in complicated financial market. To improve collaboration, we then propose a learnable multi-round communication protocol, for the agents communicating the intended actions with each other and refining accordingly. It is optimized through a novel action value attribution method which is provably consistent with the original learning objective yet more efficient. The experiments on the data from two real-world markets have illustrated superior performance with significantly better collaboration effectiveness achieved by our method., Comment: Accepted in KDD 2023; The website is at https://seqml.github.io/marl4fin

Multi-agent market model is a stock trading simulation system, which generates order flow given the agent variable of the model. We study calibrating the agent variable to simulate the order flow of any given historical trading day. In contrast to the traditional calibration that relies on the inefficient iterative search, we propose DeepCal, the first search-free approach that uses deep learning to calibrate multi-agent market model. DeepCal learns from a novel surrogate-trading loss function to address the non-differentiable issue induced by the multi-agent model and introduces a condition-aware variable estimator, adapting the trading simulation to different market conditions to enhance explainability. Through extensive experiments on real order-book data over a whole year, DeepCal has demonstrated comparable simulation accuracy (<0.36 in Kolmogorov-Smirnov statistic) to traditional search-based approaches without the need for variable search, and can effectively capture the correlation between agent variable and multiple market-condition indexes~(PPI, PMI, CPI, market trend and market noise).

Off-Policy reinforcement learning has been a driving force for the state-of-the-art conversational AIs leading to more natural humanagent interactions and improving the user satisfaction for goal-oriented agents. However, in large-scale commercial settings, it is often challenging to balance between policy improvements and experience continuity on the broad spectrum of applications handled by such system. In the literature, off-policy evaluation and guard-railing on aggregate statistics has been commonly used to address this problem. In this paper, we propose a method for curating and leveraging high-precision samples sourced from historical regression incident reports to validate, safe-guard, and improve policies prior to the online deployment. We conducted extensive experiments using data from a real-world conversational system and actual regression incidents. The proposed method is currently deployed in our production system to protect customers against broken experiences and enable long-term policy improvements., Comment: Accepted at ACL 2023 Industry Track

Modeling sequential patterns from data is at the core of various time series forecasting tasks. Deep learning models have greatly outperformed many traditional models, but these black-box models generally lack explainability in prediction and decision making. To reveal the underlying trend with understandable mathematical expressions, scientists and economists tend to use partial differential equations (PDEs) to explain the highly nonlinear dynamics of sequential patterns. However, it usually requires domain expert knowledge and a series of simplified assumptions, which is not always practical and can deviate from the ever-changing world. Is it possible to learn the differential relations from data dynamically to explain the time-evolving dynamics? In this work, we propose an learning framework that can automatically obtain interpretable PDE models from sequential data. Particularly, this framework is comprised of learnable differential blocks, named $P$-blocks, which is proved to be able to approximate any time-evolving complex continuous functions in theory. Moreover, to capture the dynamics shift, this framework introduces a meta-learning controller to dynamically optimize the hyper-parameters of a hybrid PDE model. Extensive experiments on times series forecasting of financial, engineering, and health data show that our model can provide valuable interpretability and achieve comparable performance to state-of-the-art models. From empirical studies, we find that learning a few differential operators may capture the major trend of sequential dynamics without massive computational complexity., Comment: Published in ACM SIGKDD 2022

It is challenging for reinforcement learning (RL) algorithms to succeed in real-world applications like financial trading and logistic system due to the noisy observation and environment shifting between training and evaluation. Thus, it requires both high sample efficiency and generalization for resolving real-world tasks. However, directly applying typical RL algorithms can lead to poor performance in such scenarios. Considering the great performance of ensemble methods on both accuracy and generalization in supervised learning (SL), we design a robust and applicable method named Ensemble Proximal Policy Optimization (EPPO), which learns ensemble policies in an end-to-end manner. Notably, EPPO combines each policy and the policy ensemble organically and optimizes both simultaneously. In addition, EPPO adopts a diversity enhancement regularization over the policy space which helps to generalize to unseen states and promotes exploration. We theoretically prove EPPO increases exploration efficacy, and through comprehensive experimental evaluations on various tasks, we demonstrate that EPPO achieves higher efficiency and is robust for real-world applications compared with vanilla policy optimization algorithms and other ensemble methods. Code and supplemental materials are available at https://seqml.github.io/eppo., Comment: Accepted in IJCAI 2022. The codes are available at https://seqml.github.io/eppo

In many real-world scenarios, we often deal with streaming data that is sequentially collected over time. Due to the non-stationary nature of the environment, the streaming data distribution may change in unpredictable ways, which is known as concept drift. To handle concept drift, previous methods first detect when/where the concept drift happens and then adapt models to fit the distribution of the latest data. However, there are still many cases that some underlying factors of environment evolution are predictable, making it possible to model the future concept drift trend of the streaming data, while such cases are not fully explored in previous work. In this paper, we propose a novel method DDG-DA, that can effectively forecast the evolution of data distribution and improve the performance of models. Specifically, we first train a predictor to estimate the future data distribution, then leverage it to generate training samples, and finally train models on the generated data. We conduct experiments on three real-world tasks (forecasting on stock price trend, electricity load and solar irradiance) and obtain significant improvement on multiple widely-used models., Comment: Accepted by AAAI'22

Many real-world graphs (networks) are heterogeneous with different types of nodes and edges. Heterogeneous graph embedding, aiming at learning the low-dimensional node representations of a heterogeneous graph, is vital for various downstream applications. Many meta-path based embedding methods have been proposed to learn the semantic information of heterogeneous graphs in recent years. However, most of the existing techniques overlook the graph structure information when learning the heterogeneous graph embeddings. This paper proposes a novel Structure-Aware Heterogeneous Graph Neural Network (SHGNN) to address the above limitations. In detail, we first utilize a feature propagation module to capture the local structure information of intermediate nodes in the meta-path. Next, we use a tree-attention aggregator to incorporate the graph structure information into the aggregation module on the meta-path. Finally, we leverage a meta-path aggregator to fuse the information aggregated from different meta-paths. We conducted experiments on node classification and clustering tasks and achieved state-of-the-art results on the benchmark datasets, which shows the effectiveness of our proposed method.

Learning the embeddings of knowledge graphs (KG) is vital in artificial intelligence, and can benefit various downstream applications, such as recommendation and question answering. In recent years, many research efforts have been proposed for knowledge graph embedding (KGE). However, most previous KGE methods ignore the semantic similarity between the related entities and entity-relation couples in different triples since they separately optimize each triple with the scoring function. To address this problem, we propose a simple yet efficient contrastive learning framework for tensor decomposition based (TDB) KGE, which can shorten the semantic distance of the related entities and entity-relation couples in different triples and thus improve the performance of KGE. We evaluate our proposed method on three standard KGE datasets: WN18RR, FB15k-237 and YAGO3-10. Our method can yield some new state-of-the-art results, achieving 51.2% MRR, 46.8% Hits@1 on the WN18RR dataset, 37.8% MRR, 28.6% Hits@1 on FB15k-237 dataset, and 59.1% MRR, 51.8% Hits@1 on the YAGO3-10 dataset.

Stock trend forecasting, which forecasts stock prices' future trends, plays an essential role in investment. The stocks in a market can share information so that their stock prices are highly correlated. Several methods were recently proposed to mine the shared information through stock concepts (e.g., technology, Internet Retail) extracted from the Web to improve the forecasting results. However, previous work assumes the connections between stocks and concepts are stationary, and neglects the dynamic relevance between stocks and concepts, limiting the forecasting results. Moreover, existing methods overlook the invaluable shared information carried by hidden concepts, which measure stocks' commonness beyond the manually defined stock concepts. To overcome the shortcomings of previous work, we proposed a novel stock trend forecasting framework that can adequately mine the concept-oriented shared information from predefined concepts and hidden concepts. The proposed framework simultaneously utilize the stock's shared information and individual information to improve the stock trend forecasting performance. Experimental results on the real-world tasks demonstrate the efficiency of our framework on stock trend forecasting. The investment simulation shows that our framework can achieve a higher investment return than the baselines.

The multivariate time series forecasting has attracted more and more attention because of its vital role in different fields in the real world, such as finance, traffic, and weather. In recent years, many research efforts have been proposed for forecasting multivariate time series. Although some previous work considers the interdependencies among different variables in the same timestamp, existing work overlooks the inter-connections between different variables at different time stamps. In this paper, we propose a simple yet efficient instance-wise graph-based framework to utilize the inter-dependencies of different variables at different time stamps for multivariate time series forecasting. The key idea of our framework is aggregating information from the historical time series of different variables to the current time series that we need to forecast. We conduct experiments on the Traffic, Electricity, and Exchange-Rate multivariate time series datasets. The results show that our proposed model outperforms the state-of-the-art baseline methods.

Modeling and managing portfolio risk is perhaps the most important step to achieve growing and preserving investment performance. Within the modern portfolio construction framework that built on Markowitz's theory, the covariance matrix of stock returns is a required input to calculate portfolio risk. Traditional approaches to estimate the covariance matrix are based on human-designed risk factors, which often require tremendous time and effort to design better risk factors to improve the covariance estimation. In this work, we formulate the quest of mining risk factors as a learning problem and propose a deep learning solution to effectively ``design'' risk factors with neural networks. The learning objective is also carefully set to ensure the learned risk factors are effective in explaining the variance of stock returns as well as having desired orthogonality and stability. Our experiments on the stock market data demonstrate the effectiveness of the proposed solution: our method can obtain $1.9\%$ higher explained variance measured by $R^2$ and also reduce the risk of a global minimum variance portfolio. The incremental analysis further supports our design of both the architecture and the learning objective., Comment: Published at ICAIF'21: ACM International Conference on AI in Finance

Successful quantitative investment usually relies on precise predictions of the future movement of the stock price. Recently, machine learning based solutions have shown their capacity to give more accurate stock prediction and become indispensable components in modern quantitative investment systems. However, the i.i.d. assumption behind existing methods is inconsistent with the existence of diverse trading patterns in the stock market, which inevitably limits their ability to achieve better stock prediction performance. In this paper, we propose a novel architecture, Temporal Routing Adaptor (TRA), to empower existing stock prediction models with the ability to model multiple stock trading patterns. Essentially, TRA is a lightweight module that consists of a set of independent predictors for learning multiple patterns as well as a router to dispatch samples to different predictors. Nevertheless, the lack of explicit pattern identifiers makes it quite challenging to train an effective TRA-based model. To tackle this challenge, we further design a learning algorithm based on Optimal Transport (OT) to obtain the optimal sample to predictor assignment and effectively optimize the router with such assignment through an auxiliary loss term. Experiments on the real-world stock ranking task show that compared to the state-of-the-art baselines, e.g., Attention LSTM and Transformer, the proposed method can improve information coefficient (IC) from 0.053 to 0.059 and 0.051 to 0.056 respectively. Our dataset and code used in this work are publicly available: https://github.com/microsoft/qlib/tree/main/examples/benchmarks/TRA., Comment: Accepted by KDD 2021 (research track)

Model complexity is a fundamental problem in deep learning. In this paper we conduct a systematic overview of the latest studies on model complexity in deep learning. Model complexity of deep learning can be categorized into expressive capacity and effective model complexity. We review the existing studies on those two categories along four important factors, including model framework, model size, optimization process and data complexity. We also discuss the applications of deep learning model complexity including understanding model generalization, model optimization, and model selection and design. We conclude by proposing several interesting future directions.

Stock trend forecasting, aiming at predicting the stock future trends, is crucial for investors to seek maximized profits from the stock market. Many event-driven methods utilized the events extracted from news, social media, and discussion board to forecast the stock trend in recent years. However, existing event-driven methods have two main shortcomings: 1) overlooking the influence of event information differentiated by the stock-dependent properties; 2) neglecting the effect of event information from other related stocks. In this paper, we propose a relational event-driven stock trend forecasting (REST) framework, which can address the shortcoming of existing methods. To remedy the first shortcoming, we propose to model the stock context and learn the effect of event information on the stocks under different contexts. To address the second shortcoming, we construct a stock graph and design a new propagation layer to propagate the effect of event information from related stocks. The experimental studies on the real-world data demonstrate the efficiency of our REST framework. The results of investment simulation show that our framework can achieve a higher return of investment than baselines.

As a fundamental problem in algorithmic trading, order execution aims at fulfilling a specific trading order, either liquidation or acquirement, for a given instrument. Towards effective execution strategy, recent years have witnessed the shift from the analytical view with model-based market assumptions to model-free perspective, i.e., reinforcement learning, due to its nature of sequential decision optimization. However, the noisy and yet imperfect market information that can be leveraged by the policy has made it quite challenging to build up sample efficient reinforcement learning methods to achieve effective order execution. In this paper, we propose a novel universal trading policy optimization framework to bridge the gap between the noisy yet imperfect market states and the optimal action sequences for order execution. Particularly, this framework leverages a policy distillation method that can better guide the learning of the common policy towards practically optimal execution by an oracle teacher with perfect information to approximate the optimal trading strategy. The extensive experiments have shown significant improvements of our method over various strong baselines, with reasonable trading actions., Comment: Accepted in AAAI 2021, the code and the supplementary materials are in https://seqml.github.io/opd/

Stock trend forecasting has become a popular research direction that attracts widespread attention in the financial field. Though deep learning methods have achieved promising results, there are still many limitations, for example, how to extract clean features from the raw stock data. In this paper, we introduce an \emph{Augmented Disentanglement Distillation (ADD)} approach to remove interferential features from the noised raw data. Specifically, we present 1) a disentanglement structure to separate excess and market information from the stock data to avoid the two factors disturbing each other's own prediction. Besides, by applying 2) a dynamic self-distillation method over the disentanglement framework, other implicit interference factors can also be removed. Further, thanks to the decoder module in our framework, 3) a novel strategy is proposed to augment the training samples based on the different excess and market features to improve performance. We conduct experiments on the Chinese stock market data. Results show that our method significantly improves the stock trend forecasting performances, as well as the actual investment income through backtesting, which strongly demonstrates the effectiveness of our approach.

Quantitative investment aims to maximize the return and minimize the risk in a sequential trading period over a set of financial instruments. Recently, inspired by rapid development and great potential of AI technologies in generating remarkable innovation in quantitative investment, there has been increasing adoption of AI-driven workflow for quantitative research and practical investment. In the meantime of enriching the quantitative investment methodology, AI technologies have raised new challenges to the quantitative investment system. Particularly, the new learning paradigms for quantitative investment call for an infrastructure upgrade to accommodate the renovated workflow; moreover, the data-driven nature of AI technologies indeed indicates a requirement of the infrastructure with more powerful performance; additionally, there exist some unique challenges for applying AI technologies to solve different tasks in the financial scenarios. To address these challenges and bridge the gap between AI technologies and quantitative investment, we design and develop Qlib that aims to realize the potential, empower the research, and create the value of AI technologies in quantitative investment.

Sequence learning has attracted much research attention from the machine learning community in recent years. In many applications, a sequence learning task is usually associated with multiple temporally correlated auxiliary tasks, which are different in terms of how much input information to use or which future step to predict. For example, (i) in simultaneous machine translation, one can conduct translation under different latency (i.e., how many input words to read/wait before translation); (ii) in stock trend forecasting, one can predict the price of a stock in different future days (e.g., tomorrow, the day after tomorrow). While it is clear that those temporally correlated tasks can help each other, there is a very limited exploration on how to better leverage multiple auxiliary tasks to boost the performance of the main task. In this work, we introduce a learnable scheduler to sequence learning, which can adaptively select auxiliary tasks for training depending on the model status and the current training data. The scheduler and the model for the main task are jointly trained through bi-level optimization. Experiments show that our method significantly improves the performance of simultaneous machine translation and stock trend forecasting., Comment: Accepted to ICML 2021

Recently, the concept of teaching has been introduced into machine learning, in which a teacher model is used to guide the training of a student model (which will be used in real tasks) through data selection, loss function design, etc. Learning to reweight, which is a specific kind of teaching that reweights training data using a teacher model, receives much attention due to its simplicity and effectiveness. In existing learning to reweight works, the teacher model only utilizes shallow/surface information such as training iteration number and loss/accuracy of the student model from training/validation sets, but ignores the internal states of the student model, which limits the potential of learning to reweight. In this work, we propose an improved data reweighting algorithm, in which the student model provides its internal states to the teacher model, and the teacher model returns adaptive weights of training samples to enhance the training of the student model. The teacher model is jointly trained with the student model using meta gradients propagated from a validation set. Experiments on image classification with clean/noisy labels and neural machine translation empirically demonstrate that our algorithm makes significant improvement over previous methods., Comment: Accepted to AAAI-2021

It is fundamental to measure model complexity of deep neural networks. The existing literature on model complexity mainly focuses on neural networks with piecewise linear activation functions. Model complexity of neural networks with general curve activation functions remains an open problem. To tackle the challenge, in this paper, we first propose the linear approximation neural network (LANN for short), a piecewise linear framework to approximate a given deep model with curve activation function. LANN constructs individual piecewise linear approximation for the activation function of each neuron, and minimizes the number of linear regions to satisfy a required approximation degree. Then, we analyze the upper bound of the number of linear regions formed by LANNs, and derive the complexity measure based on the upper bound. To examine the usefulness of the complexity measure, we experimentally explore the training process of neural networks and detect overfitting. Our results demonstrate that the occurrence of overfitting is positively correlated with the increase of model complexity during training. We find that the $L^1$ and $L^2$ regularizations suppress the increase of model complexity. Finally, we propose two approaches to prevent overfitting by directly constraining model complexity, namely neuron pruning and customized $L^1$ regularization., Comment: KDD 2020

The effects of periodically modulated coupling on amplitude death in two coupled nonidentical oscillators are explored. The AD domain could be significantly influenced by tuning the modulation amplitude and the modulation frequency of the modulated coupling strength. There is an optimal value of modulation amplitude for the modulated coupling with which the largest AD domain is observed in the parameter space. The AD domain is enlarged with the decrease of the modulation frequency for a given small modulation amplitude, while is shrunk with decrease of the modulation frequency for a given large modulation amplitude. The mechanism of AD in the presence of periodic modulation in the coupling is investigated via the local condition Lyapunov exponent of the coupled system. The stability of AD state can be well characterized by conditional Lyapunov exponent. The coupled system experiencing from the oscillatory state to AD is clearly indicated by the observation that the conditional Lyapunov exponent transits from positive to negative. Our results are helpful to many potential applications for the research of neuroscience and dynamical control in engineering., Comment: 11 figures, 8 pages