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Qiao-Chu He

Publications and source records attributed to Qiao-Chu He.

5 recordsLinked to original sources

LeetDecoding: A PyTorch Library for Exponentially Decaying Causal Linear Attention with CUDA Implementations

The machine learning and data science community has made significant while dispersive progress in accelerating transformer-based large language models (LLMs), and one promising approach is to replace the original causal attention in a generative pre-trained transformer (GPT) with \emph{exponentially decaying causal linear attention}. In this paper, we present LeetDecoding, which is the first Python package that provides a large set of computation routines for this fundamental operator. The launch of LeetDecoding was motivated by the current lack of (1) clear understanding of the complexity regarding this operator, (2) a comprehensive collection of existing computation methods (usually spread in seemingly unrelated fields), and (3) CUDA implementations for fast inference on GPU. LeetDecoding's design is easy to integrate with existing linear-attention LLMs, and allows for researchers to benchmark and evaluate new computation methods for exponentially decaying causal linear attention. The usage of LeetDecoding does not require any knowledge of GPU programming and the underlying complexity analysis, intentionally making LeetDecoding accessible to LLM practitioners. The source code of LeetDecoding is provided at \href{https://github.com/Computational-Machine-Intelligence/LeetDecoding}{this GitHub repository}, and users can simply install LeetDecoding by the command \texttt{pip install leet-decoding}.

cs.LG

High-Dimensional Linear Regression via Implicit Regularization

Many statistical estimators for high-dimensional linear regression are M-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined through a discretized gradient dynamic system under overparameterization. We show that under suitable restricted isometry conditions, overparameterization leads to implicit regularization: if we directly apply gradient descent to the residual sum of squares with sufficiently small initial values, then under some proper early stopping rule, the iterates converge to a nearly sparse rate-optimal solution that improves over explicitly regularized approaches. In particular, the resulting estimator does not suffer from extra bias due to explicit penalties, and can achieve the parametric root-n rate when the signal-to-noise ratio is sufficiently high. We also perform simulations to compare our methods with high dimensional linear regression with explicit regularization. Our results illustrate the advantages of using implicit regularization via gradient descent after overparameterization in sparse vector estimation.

math.ST

Integrated Design of Unmanned Aerial Mobility Network: A Data-Driven Risk-Averse Approach

The real challenge in drone-logistics is to develop an economically-feasible Unmanned Aerial Mobility Network (UAMN). In this paper, we propose an integrated airport location (strategic decision) and routes planning (operational decision) optimization framework to minimize the total cost of the network, while guaranteeing flow constraints, capacity constraints, and electricity constraints. To facility expensive long-term infrastructure planning facing demand uncertainty, we develop a data-driven risk-averse two-stage stochastic optimization model based on the Wasserstein distance. We develop a reformulation technique which simplifies the worst-case expectation term in the original model, and obtain a fractable Min-Max solution procedure correspondingly. Using Lagrange multipliers, we successfully decompose decision variables and reduce the complexity of computation. To provide managerial insights, we design specific numerical examples. For example, we find that the optimal network configuration is affected by the "pooling effects" in channel capacities. A nice feature of our DRO framework is that the optimal network design is relatively robust under demand uncertainty. Interestingly, a candidate node without historical demand records can be chosen to locate an airport. We demonstrate the application of our model for a real medical resources transportation problem with our industry partner, collecting donated blood to a blood bank in Hangzhou, China.

math.OC

Integrated Facility Location and Production Scheduling in Multi-Generation Energy Systems

In this paper, we investigate the energy system design problems with the multi-generation technologies, i.e., simultaneous generation of multiple types of energy. We propose a long-term planning model which integrates macro-level strategic decisions such as facility location and multi-generation technology investment, and micro-level operational decisions such as production planning and energy transportation. Our results illustrate the economic value of multi-generation technologies in lieu of the spatio-temporal demand uncertainty for energy. In particular, we show that the multi-generation technologies can reduce demand uncertainty by risk pooling both within and across different facilities.

math.OC

Information Management for Decentralized Energy Storages under Market Uncertainties

In this paper, we propose a model of decentralized energy storages, who serve as instruments to shift energy supply intertemporally. From storages' perspective, we investigate their optimal buying or selling decisions under market uncertainty. The goal of this paper is to understand the economic value of future market information, as energy storages mitigate market uncertainty by forward-looking strategies. At a system level, we evaluate different information management policies to coordinate storages' actions and improve their aggregate profitability: (1) providing a publicly available market forecasting channel; (2) encouraging decentralized storages to share their private forecasts with each other; (3) releasing additional market information to a targeted subset of storages exclusively. We highlight the perils of too much market information provision and advice on exclusiveness of market forecast channel.

math.OC