arXiv subjects

Fan Chen

Publications and source records attributed to Fan Chen.

At least 91 records · Page 5Linked to original sources

arXiv2024

Emergence of multiphase condensates from a limited set of chemical building blocks

Biomolecules composed of a limited set of chemical building blocks can co-localize into distinct, spatially segregated compartments known as biomolecular condensates. While many condensates are known to form spontaneously via phase separation, it has been unclear how immiscible condensates with precisely controlled molecular compositions assemble from a small number of chemical building blocks. We address this question by establishing a connection between the specificity of biomolecular interactions and the thermodynamic stability of coexisting condensates. By computing the minimum interaction specificity required to assemble condensates with target molecular compositions, we show how to design heteropolymer mixtures that produce compositionally complex condensates using only a small number of monomer types. Our results provide insight into how compositional specificity arises in naturally occurring multicomponent condensates and demonstrate a rational algorithm for engineering complex artificial condensates from simple chemical building blocks.

cond-mat.soft↗

arXiv2024

Convergence Analysis of Stochastic Gradient Descent with MCMC Estimators

Understanding stochastic gradient descent (SGD) and its variants is essential for machine learning. However, most of the preceding analyses are conducted under amenable conditions such as unbiased gradient estimator and bounded objective functions, which does not encompass many sophisticated applications, such as variational Monte Carlo, entropy-regularized reinforcement learning and variational inference. In this paper, we consider the SGD algorithm that employ the Markov Chain Monte Carlo (MCMC) estimator to compute the gradient, called MCMC-SGD. Since MCMC reduces the sampling complexity significantly, it is an asymptotically convergent biased estimator in practice. Moreover, by incorporating a general class of unbounded functions, it is much more difficult to analyze the MCMC sampling error. Therefore, we assume that the function is sub-exponential and use the Bernstein inequality for non-stationary Markov chains to derive error bounds of the MCMC estimator. Consequently, MCMC-SGD is proven to have a first order convergence rate $O(\log K/\sqrt{n K})$ with $K$ iterations and a sample size $n$. It partially explains how MCMC influences the behavior of SGD. Furthermore, we verify the correlated negative curvature condition under reasonable assumptions. It is shown that MCMC-SGD escapes from saddle points and reaches $(ε,ε^{1/4})$ approximate second order stationary points or $ε^{1/2}$-variance points at least $O(ε^{-11/2}\log^{2}(1/ε) )$ steps with high probability. Our analysis unveils the convergence pattern of MCMC-SGD across a broad class of stochastic optimization problems, and interprets the convergence phenomena observed in practical applications.

stat.ML↗

arXiv2024

System Support for Environmentally Sustainable Computing in Data Centers

Modern data centers suffer from a growing carbon footprint due to insufficient support for environmental sustainability. While hardware accelerators and renewable energy have been utilized to enhance sustainability, addressing Quality of Service (QoS) degradation caused by renewable energy supply and hardware recycling remains challenging: (1) prior accelerators exhibit significant carbon footprints due to limited reconfigurability and inability to adapt to renewable energy fluctuations; (2) integrating recycled NAND flash chips in data centers poses challenges due to their short lifetime, increasing energy consumption; (3) the absence of a sustainability estimator impedes data centers and users in evaluating and improving their environmental impact. This study aims to improve system support for environmentally sustainable data centers by proposing a reconfigurable hardware accelerator for intensive computing primitives and developing a fractional NAND flash cell to extend the lifetime of recycled flash chips while supporting graceful capacity degradation. We also introduce a sustainability estimator to evaluate user task energy consumption and promote sustainable practices. We present our preliminary results and recognize this as an ongoing initiative with significant potential to advance environmentally sustainable computing in data centers and stimulate further exploration in this critical research domain.

cs.AR↗

arXiv2024

JustQ: Automated Deployment of Fair and Accurate Quantum Neural Networks

Despite the success of Quantum Neural Networks (QNNs) in decision-making systems, their fairness remains unexplored, as the focus primarily lies on accuracy. This work conducts a design space exploration, unveiling QNN unfairness, and highlighting the significant influence of QNN deployment and quantum noise on accuracy and fairness. To effectively navigate the vast QNN deployment design space, we propose JustQ, a framework for deploying fair and accurate QNNs on NISQ computers. It includes a complete NISQ error model, reinforcement learning-based deployment, and a flexible optimization objective incorporating both fairness and accuracy. Experimental results show JustQ outperforms previous methods, achieving superior accuracy and fairness. This work pioneers fair QNN design on NISQ computers, paving the way for future investigations.

quant-ph↗

arXiv2024

QuantumLeak: Stealing Quantum Neural Networks from Cloud-based NISQ Machines

Variational quantum circuits (VQCs) have become a powerful tool for implementing Quantum Neural Networks (QNNs), addressing a wide range of complex problems. Well-trained VQCs serve as valuable intellectual assets hosted on cloud-based Noisy Intermediate Scale Quantum (NISQ) computers, making them susceptible to malicious VQC stealing attacks. However, traditional model extraction techniques designed for classical machine learning models encounter challenges when applied to NISQ computers due to significant noise in current devices. In this paper, we introduce QuantumLeak, an effective and accurate QNN model extraction technique from cloud-based NISQ machines. Compared to existing classical model stealing techniques, QuantumLeak improves local VQC accuracy by 4.99\%$\sim$7.35\% across diverse datasets and VQC architectures.

quant-ph↗

arXiv2024

TITAN: A Distributed Large-Scale Trapped-Ion NISQ Computer

Trapped-Ion (TI) technology offers potential breakthroughs for Noisy Intermediate Scale Quantum (NISQ) computing. TI qubits offer extended coherence times and high gate fidelity, making them appealing for large-scale NISQ computers. Constructing such computers demands a distributed architecture connecting Quantum Charge Coupled Devices (QCCDs) via quantum matter-links and photonic switches. However, current distributed TI NISQ computers face hardware and system challenges. Entangling qubits across a photonic switch introduces significant latency, while existing compilers generate suboptimal mappings due to their unawareness of the interconnection topology. In this paper, we introduce TITAN, a large-scale distributed TI NISQ computer, which employs an innovative photonic interconnection design to reduce entanglement latency and an advanced partitioning and mapping algorithm to optimize matter-link communications. Our evaluations show that TITAN greatly enhances quantum application performance by 56.6% and fidelity by 19.7% compared to existing systems.

quant-ph↗

arXiv2024

QDoor: Exploiting Approximate Synthesis for Backdoor Attacks in Quantum Neural Networks

Quantum neural networks (QNNs) succeed in object recognition, natural language processing, and financial analysis. To maximize the accuracy of a QNN on a Noisy Intermediate Scale Quantum (NISQ) computer, approximate synthesis modifies the QNN circuit by reducing error-prone 2-qubit quantum gates. The success of QNNs motivates adversaries to attack QNNs via backdoors. However, naïvely transplanting backdoors designed for classical neural networks to QNNs yields only low attack success rate, due to the noises and approximate synthesis on NISQ computers. Prior quantum circuit-based backdoors cannot selectively attack some inputs or work with all types of encoding layers of a QNN circuit. Moreover, it is easy to detect both transplanted and circuit-based backdoors in a QNN. In this paper, we propose a novel and stealthy backdoor attack, QDoor, to achieve high attack success rate in approximately-synthesized QNN circuits by weaponizing unitary differences between uncompiled QNNs and their synthesized counterparts. QDoor trains a QNN behaving normally for all inputs with and without a trigger. However, after approximate synthesis, the QNN circuit always predicts any inputs with a trigger to a predefined class while still acts normally for benign inputs. Compared to prior backdoor attacks, QDoor improves the attack success rate by $13\times$ and the clean data accuracy by $65\%$ on average. Furthermore, prior backdoor detection techniques cannot find QDoor attacks in uncompiled QNN circuits.

quant-ph↗

arXiv2024

Uniform-in-time propagation of chaos for kinetic mean field Langevin dynamics

We study the kinetic mean field Langevin dynamics under the functional convexity assumption of the mean field energy functional. Using hypocoercivity, we first establish the exponential convergence of the mean field dynamics and then show the corresponding $N$-particle system converges exponentially in a rate uniform in $N$ modulo a small error. Finally we study the short-time regularization effects of the dynamics and prove its uniform-in-time propagation of chaos property in both the Wasserstein and entropic sense. Our results can be applied to the training of two-layer neural networks with momentum and we include the numerical experiments.

math.PR↗

arXiv2024

LLMCarbon: Modeling the end-to-end Carbon Footprint of Large Language Models

The carbon footprint associated with large language models (LLMs) is a significant concern, encompassing emissions from their training, inference, experimentation, and storage processes, including operational and embodied carbon emissions. An essential aspect is accurately estimating the carbon impact of emerging LLMs even before their training, which heavily relies on GPU usage. Existing studies have reported the carbon footprint of LLM training, but only one tool, mlco2, can predict the carbon footprint of new neural networks prior to physical training. However, mlco2 has several serious limitations. It cannot extend its estimation to dense or mixture-of-experts (MoE) LLMs, disregards critical architectural parameters, focuses solely on GPUs, and cannot model embodied carbon footprints. Addressing these gaps, we introduce \textit{\carb}, an end-to-end carbon footprint projection model designed for both dense and MoE LLMs. Compared to mlco2, \carb~significantly enhances the accuracy of carbon footprint estimations for various LLMs. The source code is released at \url{https://github.com/SotaroKaneda/MLCarbon}.

cs.CL↗

arXiv2023

DISTWAR: Fast Differentiable Rendering on Raster-based Rendering Pipelines

Differentiable rendering is a technique used in an important emerging class of visual computing applications that involves representing a 3D scene as a model that is trained from 2D images using gradient descent. Recent works (e.g. 3D Gaussian Splatting) use a rasterization pipeline to enable rendering high quality photo-realistic imagery at high speeds from these learned 3D models. These methods have been demonstrated to be very promising, providing state-of-art quality for many important tasks. However, training a model to represent a scene is still a time-consuming task even when using powerful GPUs. In this work, we observe that the gradient computation phase during training is a significant bottleneck on GPUs due to the large number of atomic operations that need to be processed. These atomic operations overwhelm atomic units in the L2 partitions causing stalls. To address this challenge, we leverage the observations that during the gradient computation: (1) for most warps, all threads atomically update the same memory locations; and (2) warps generate varying amounts of atomic traffic (since some threads may be inactive). We propose DISTWAR, a software-approach to accelerate atomic operations based on two key ideas: First, we enable warp-level reduction of threads at the SM sub-cores using registers to leverage the locality in intra-warp atomic updates. Second, we distribute the atomic computation between the warp-level reduction at the SM and the L2 atomic units to increase the throughput of atomic computation. Warps with many threads performing atomic updates to the same memory locations are scheduled at the SM, and the rest using L2 atomic units. We implement DISTWAR using existing warp-level primitives. We evaluate DISTWAR on widely used raster-based differentiable rendering workloads. We demonstrate significant speedups of 2.44x on average (up to 5.7x).

cs.CV↗

arXiv2023

ReFloat: Low-Cost Floating-Point Processing in ReRAM for Accelerating Iterative Linear Solvers

Resistive random access memory (ReRAM) is a promising technology that can perform low-cost and in-situ matrix-vector multiplication (MVM) in analog domain. Scientific computing requires high-precision floating-point (FP) processing. However, performing floating-point computation in ReRAM is challenging because of high hardware cost and execution time due to the large FP value range. In this work we present ReFloat, a data format and an accelerator architecture, for low-cost and high-performance floating-point processing in ReRAM for iterative linear solvers. ReFloat matches the ReRAM crossbar hardware and represents a block of FP values with reduced bits and an optimized exponent base for a high range of dynamic representation. Thus, ReFloat achieves less ReRAM crossbar consumption and fewer processing cycles and overcomes the noncovergence issue in a prior work. The evaluation on the SuiteSparse matrices shows ReFloat achieves 5.02x to 84.28x improvement in terms of solver time compared to a state-of-the-art ReRAM based accelerator.

cs.AR↗

arXiv2023

Some results on the saturation number for unions of cliques

Graph $G$ is $H$-saturated if $H$ is not a subgraph of $G$ and $H$ is a subgraph of $G+e$ for any edge $e$ not in $G$. The saturation number for a graph $H$ is the minimal number of edges in any $H$-saturated graph of order $n$. In this paper, the saturation number for $K_p\cup (t-1)K_q$ ($t\geqslant 3$ and $2\leqslant p<q$) is determined, and the extremal graph for $K_p\cup 2K_q$ is determined. Moreover, the saturation number and the extremal graph for $K_p\cup K_q\cup K_r$ ($ r\geqslant p+q$) are completely determined.

math.CO↗

arXiv2023

On the Optimal Lower and Upper Complexity Bounds for a Class of Composite Optimization Problems

We study the optimal lower and upper complexity bounds for finding approximate solutions to the composite problem $\min_x\ f(x)+h(Ax-b)$, where $f$ is smooth and $h$ is convex. Given access to the proximal operator of $h$, for strongly convex, convex, and nonconvex $f$, we design efficient first order algorithms with complexities $\tilde{O}\left(κ_A\sqrt{κ_f}\log\left(1/ε\right)\right)$, $\tilde{O}\left(κ_A\sqrt{L_f}D/\sqrtε\right)$, and $\tilde{O}\left(κ_A L_fΔ/ε^2\right)$, respectively. Here, $κ_A$ is the condition number of the matrix $A$ in the composition, $L_f$ is the smoothness constant of $f$, and $κ_f$ is the condition number of $f$ in the strongly convex case. $D$ is the initial point distance and $Δ$ is the initial function value gap. Tight lower complexity bounds for the three cases are also derived and they match the upper bounds up to logarithmic factors, thereby demonstrating the optimality of both the upper and lower bounds proposed in this paper.

math.OC↗

arXiv2023

A New Basis for Sparse Principal Component Analysis

Previous versions of sparse principal component analysis (PCA) have presumed that the eigen-basis (a $p \times k$ matrix) is approximately sparse. We propose a method that presumes the $p \times k$ matrix becomes approximately sparse after a $k \times k$ rotation. The simplest version of the algorithm initializes with the leading $k$ principal components. Then, the principal components are rotated with an $k \times k$ orthogonal rotation to make them approximately sparse. Finally, soft-thresholding is applied to the rotated principal components. This approach differs from prior approaches because it uses an orthogonal rotation to approximate a sparse basis. One consequence is that a sparse component need not to be a leading eigenvector, but rather a mixture of them. In this way, we propose a new (rotated) basis for sparse PCA. In addition, our approach avoids "deflation" and multiple tuning parameters required for that. Our sparse PCA framework is versatile; for example, it extends naturally to a two-way analysis of a data matrix for simultaneous dimensionality reduction of rows and columns. We provide evidence showing that for the same level of sparsity, the proposed sparse PCA method is more stable and can explain more variance compared to alternative methods. Through three applications -- sparse coding of images, analysis of transcriptome sequencing data, and large-scale clustering of social networks, we demonstrate the modern usefulness of sparse PCA in exploring multivariate data.

stat.ML↗

arXiv2023

Entropic Fictitious Play for Mean Field Optimization Problem

We study two-layer neural networks in the mean field limit, where the number of neurons tends to infinity. In this regime, the optimization over the neuron parameters becomes the optimization over the probability measures, and by adding an entropic regularizer, the minimizer of the problem is identified as a fixed point. We propose a novel training algorithm named entropic fictitious play, inspired by the classical fictitious play in game theory for learning Nash equilibriums, to recover this fixed point, and the algorithm exhibits a two-loop iteration structure. Exponential convergence is proved in this paper and we also verify our theoretical results by simple numerical examples.

math.OC↗

arXiv2023

CryptoQFL: Quantum Federated Learning on Encrypted Data

Recent advancements in Quantum Neural Networks (QNNs) have demonstrated theoretical and experimental performance superior to their classical counterparts in a wide range of applications. However, existing centralized QNNs cannot solve many real-world problems because collecting large amounts of training data to a common public site is time-consuming and, more importantly, violates data privacy. Federated Learning (FL) is an emerging distributed machine learning framework that allows collaborative model training on decentralized data residing on multiple devices without breaching data privacy. Some initial attempts at Quantum Federated Learning (QFL) either only focus on improving the QFL performance or rely on a trusted quantum server that fails to preserve data privacy. In this work, we propose CryptoQFL, a QFL framework that allows distributed QNN training on encrypted data. CryptoQFL is (1) secure, because it allows each edge to train a QNN with local private data, and encrypt its updates using quantum \homo~encryption before sending them to the central quantum server; (2) communication-efficient, as CryptoQFL quantize local gradient updates to ternary values, and only communicate non-zero values to the server for aggregation; and (3) computation-efficient, as CryptoQFL presents an efficient quantum aggregation circuit with significantly reduced latency compared to state-of-the-art approaches.

quant-ph↗

arXiv2023

Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection

Neural sequence models based on the transformer architecture have demonstrated remarkable \emph{in-context learning} (ICL) abilities, where they can perform new tasks when prompted with training and test examples, without any parameter update to the model. This work first provides a comprehensive statistical theory for transformers to perform ICL. Concretely, we show that transformers can implement a broad class of standard machine learning algorithms in context, such as least squares, ridge regression, Lasso, learning generalized linear models, and gradient descent on two-layer neural networks, with near-optimal predictive power on various in-context data distributions. Using an efficient implementation of in-context gradient descent as the underlying mechanism, our transformer constructions admit mild size bounds, and can be learned with polynomially many pretraining sequences. Building on these ``base'' ICL algorithms, intriguingly, we show that transformers can implement more complex ICL procedures involving \emph{in-context algorithm selection}, akin to what a statistician can do in real life -- A \emph{single} transformer can adaptively select different base ICL algorithms -- or even perform qualitatively different tasks -- on different input sequences, without any explicit prompting of the right algorithm or task. We both establish this in theory by explicit constructions, and also observe this phenomenon experimentally. In theory, we construct two general mechanisms for algorithm selection with concrete examples: pre-ICL testing, and post-ICL validation. As an example, we use the post-ICL validation mechanism to construct a transformer that can perform nearly Bayes-optimal ICL on a challenging task -- noisy linear models with mixed noise levels. Experimentally, we demonstrate the strong in-context algorithm selection capabilities of standard transformer architectures.

cs.LG↗

arXiv2023

Turán problem for $\mathcal{K}_4^-$-free signed graphs

Suppose that $\dot{G}$ is an unbalanced signed graph of order $n$ with $e(\dot{G})$ edges. Let $ρ(\dot{G})$ be the spectral radius of $\dot{G}$, and $\mathcal{K}_4^-$ be the set of the unbalanced $K_4$. In this paper, we prove that if $\dot{G}$ is a $\mathcal{K}_4^-$-free unbalanced signed graph of order $n$, then $e(\dot{G})\leqslant \frac{n(n-1)}{2}-(n-3)$ and $ρ(\dot{G})\leqslant n-2$. Moreover, the extremal graphs are completely characterized.

math.CO↗