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Memory-constrained algorithms for convex optimization 23

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Memory-constrained algorithms for convex optimization

Proceedings of the 37th International Conference on Neural Information Processing Systems

作者： Moïse Blanchard Junhui Zhang Patrick Jaillet Operations Research Center MIT Cambridge MA Department of Electrical Engineering and Computer Science MIT Cambridge MA

We propose a family of recursive cutting-plane algorithms to solve feasibility problems with constrained memory, which can also be used for first-order convex optimization. Precisely, in order to find a point within a ball of radius ε with a separation oracle in dimension d—or to minimize 1-Lipschitz convex functions to accuracy ε over the unit ball—our algorithms use O(d2/p ln 1/ε) bits of memory, and make O((C d/p ln 1/ε)p) oracle calls, for some universal constant C ≥ 1. The family is parametrized by p ∈ [d] and provides an oracle-complexity/memory trade-off in the sub-polynomial regime ln 1/ε ≫ ln d. While several works gave lower-bound trade-offs (impossibility results) [31, 5]—we explicit here their dependence with ln 1/ε, showing that these also hold in any sub-polynomial regime—to the best of our knowledge this is the first class of algorithms that provides a positive trade-off between gradient descent and cutting-plane methods in any regime with ε ≤ 1/√d. The algorithms divide the d variables into p blocks and optimize over blocks sequentially, with approximate separation vectors constructed using a variant of Vaidya's method. In the regime ε ≤ d-Ω(d), our algorithm with p = d achieves the information-theoretic optimal memory usage and improves the oracle-complexity of gradient descent.

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ITERATED ENTROPY DERIVATIVES AND BINARY ENTROPY INEQUALITIES

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arXiv 2023年

作者： Wakhare, Tanay Department of Electrical Engineering and Computer Science MIT CambridgeMA02139 United States

We embark on a systematic study of the (k + 1)-th derivative of xk−rH(xr), where H(x):= −x log x − (1 − x) log(1 − x) is the binary entropy and k ≥ r ≥ 1 are integers. Our motivation is the conjectural entropy inequality αkH(xk) ≥ xk−1H(x), where 0 k dxdkk+1+1 xk−rH(xr) as a rational function, an infinite series, and a sum over generalized Stirling numbers. This allows us to reduce the proof of the entropy inequality for real k to showing that an associated polynomial has only two real roots in the interval (0, 1), which also allows us to prove the inequality for fractional exponents such as k = 3/2. The proof suggests a new framework for proving tight inequalities for the sum of polynomials times the logarithms of polynomials, which converts the inequality into a statement about the real roots of a simpler associated *** Codes 94A17, 26C10, 11B65, 05A10 Copyright © 2023, The Authors. All rights reserved.

关键词： Rational functions

Employment Prediction System Based on Recommender System Using NLP, Content Filtering & Collaborative Filtering 10

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Employment Prediction System Based on Recommender System Usi...

10th International Conference on Smart Computing and Communication, ICSCC 2024

作者： Gupta, Sanjai Kakde, Vinodkumar Dharamshi, Ravindra R. Sakarkar, Gopal Abiyasa, Agus Putu University of Technology and Applied Sciences Nizwa Oman University of Nizwa Nizwa Oman Dr. Vishwanath Karad MIT World Peace University Department of Computer Science and Applications Pune India Universitas Pendidikan Nasional Department of Electrical Engineering Denpasar Indonesia

ISBN: (纸本)9798350363104

Employability is an important measure for Higher education Institutions/universities to measure success. Due to globalization, automation, and advances in Data analytics, the job market landscape is more dynamic than ever. All the stakeholders like employers, graduates, and Academic Institutions are extremely beneficial if they are aware of the factors affecting employability and skills requirements. For better career opportunities, students may need to know their strengths and weaknesses. Academic institutions, Universities, and others involved in designing curricula can develop more appropriate skill sets required for the job market. Recommender systems provide suggestions for items that a user may find useful. Using data obtained from job portals and social networking sites such as LinkedIn, in this research project we aim to develop a job recommendation system. Data collection and Analysis were done through web mining to acquire job portal data, social networking data for CVs/resumes, and curriculum data of various academic institutions in Oman. To extract meaningful information from this data, we use Natural Language Processing (NLP) techniques. To match job seekers with suitable job opportunities, our recommendation system utilizes cosine similarity based on content-based filtering. In this study, the effectiveness of the We also create a user-friendly interface that displays essential details such as skills needed, job roles, and company information based on the user's skills and resumes. The proposed model will be evaluated in terms of its ability to provide accurate recommendations. Users will benefit from an efficient and personalized job search process through this system. © 2024 IEEE.

关键词： Collaborative filtering

Locally Regularized Neural Differential Equations: Some Black Boxes Were Meant to Remain Closed!

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arXiv 2023年

作者： Pal, Avik Edelman, Alan Rackauckas, Christopher CSAIL MIT United States Department of Electrical Engineering and Computer Science MIT United States Department of Mathematics MIT United States

Implicit layer deep learning techniques, like Neural Differential Equations, have become an important modeling framework due to their ability to adapt to new problems automatically. Training a neural differential equation is effectively a search over a space of plausible dynamical systems. However, controlling the computational cost for these models is difficult since it relies on the number of steps the adaptive solver takes. Most prior works have used higher-order methods to reduce prediction timings while greatly increasing training time or reducing both training and prediction timings by relying on specific training algorithms, which are harder to use as a drop-in replacement due to strict requirements on automatic differentiation. In this manuscript, we use internal cost heuristics of adaptive differential equation solvers at stochastic time-points to guide the training towards learning a dynamical system that is easier to integrate. We "close the blackbox" and allow the use of our method with any adjoint technique for gradient calculations of the differential equation solution. We perform experimental studies to compare our method to global regularization to show that we attain similar performance numbers without compromising on the flexibility of implementation on ordinary differential equations (ODEs) and stochastic differential equations (SDEs). We develop two sampling strategies to trade-off between performance and training time. Our method reduces the number of function evaluations to 0.556 × −0.733× and accelerates predictions by 1.3 × −2×. © 2023, CC BY.

关键词： Forecasting

Resource Allocation and Energy Efficient Dynamic Particle Swarm Optimisation in Heterogeneous Wireless Communication Networks 4

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Resource Allocation and Energy Efficient Dynamic Particle Sw...

4th IEEE Asian Conference on Innovation in Technology, ASIANCON 2024

作者： Pawar, Anuradha Bhalerao Kannan, G. Anuradha, T. Vignesh, V. Kesavan, R. Jose Anand, A. Mit Academy of Engineering Department of Electronics Engineering Alandi Maharastra Pune412105 India Amrita College of Engineering and Technology Department of Electronics and Communication Engineering Tamil Nadu 629 901 India Kcg College of Technology Department of Electrical and Electronics Engineering Tamil Nadu 600097 India Karpagam College of Engineering Department of Computer Science and Engineering Tamil Nadu 641032 India Simts Institute of Computer Science and Engineering Saveetha School of Engineering Tamil Nadu 602105 India Kcg College of Technology Department of Electronics and Communication Engineering Tamil Nadu 600097 India

ISBN: (纸本)9798350354218

This paper investigates the difficult of beam policy in a multi-user peer-to-peer web linkage setting as part of our research. Using a network simulator, the dynamic particle swarm optimization is suggested for this. The challenge is to limit the maximum power consumption per relay, according to minimal Signal to Noise Ratio (SNR) guarantees, after a complete Channel State Information (CSI) is established. It has been established that the non-convex problem satisfies a potent duality. The twofold problem with the highest polynomial complexity was given as Semi Definite Programming (SDP). On the basis of the standards of the optimal dual variables, we looked at the best beam forming vectors for the initial problems in 3 different scenarios. This demonstrated whether the minimum Signal-to-Noise Ratio (SNR) prerequisite for each S-D pair has been met as well as whether a relay's electricity consumption varies among relays. © 2024 IEEE.

关键词： Particle swarm optimization (PSO)

Relaxed Equivariant Graph Neural Networks

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arXiv 2024年

作者： Hofgard, Elyssa Wang, Rui Walters, Robin Smidt, Tess Department of Electrical Engineering and Computer Science MIT United States College of Computing Sciences Northeastern University United States

3D Euclidean symmetry equivariant neural networks have demonstrated notable success in modeling complex physical systems. We introduce a framework for relaxed E(3) graph equivariant neural networks that can learn and represent symmetry breaking within continuous groups. Building on the existing e3nn framework, we propose the use of relaxed weights to allow for controlled symmetry breaking. We show empirically that these relaxed weights learn the correct amount of symmetry breaking. Copyright © 2024, The Authors. All rights reserved.

关键词： Graph neural networks

Regression coefficient estimation from remote sensing maps

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arXiv 2024年

作者： Lu, Kerri Kluger, Dan M. Bates, Stephen Wang, Sherrie Laboratory for Information and Decision Systems MIT United States Department of Electrical Engineering and Computer Science MIT United States Department of Mechanical Engineering MIT United States Institute for Data Systems and Society MIT United States

Remote sensing map products are used to estimate regression coefficients relating environmental variables, such as the effect of conservation zones on deforestation. However, the quality of map products varies, and — because maps are outputs of complex machine learning algorithms that take in a variety of remotely sensed variables as inputs — errors are difficult to characterize. Thus, population-level estimates from such maps may be biased. In this paper, we apply prediction-powered inference (PPI) to regression coefficient estimation. PPI generates unbiased estimates by using a small amount of randomly sampled ground truth data to correct for bias in large-scale remote sensing map products. Applying PPI across multiple remote sensing use cases in regression coefficient estimation, we find that it results in estimates that are (1) more reliable than using the map product as if it were 100% accurate and (2) have lower uncertainty than using only the ground truth and ignoring the map product. Empirically, we observe effective sample size increases of up to 17-fold using PPI compared to only using ground truth data. This is the first work to estimate remote sensing regression coefficients without assumptions on the structure of map product errors. Data and code are available at https://***/Earth-Intelligence-Lab/ uncertainty-quantification. © 2024, CC BY.

关键词： Regression analysis

Analysis of a Toothed Consequent-Pole Flux Reversal Motor with Assisting Permanent Magnets

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Analysis of a Toothed Consequent-Pole Flux Reversal Motor wi...

electrical Machines and Drives (ICEMD), International Conference on

作者： Mohammad Reza Sarshar Jamshid Kavianpour Mohammad Amin Jalali Kondelaji Mojtaba Mirsalim Amir Khorsandi Department of Electrical Engineering Amirkabir University of Technology (Tehran Polytechnic) Tehran Iran Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology (MIT) Cambridge USA

ISBN: (数字)9798331507510

ISBN: (纸本)9798331507527

This article studies three new toothed consequent-pole flux-reversal permanent magnet (FRPM) motors, each with specific combined PM arrays. The PM arrays comprise the biased-flux (BF) and flux-reversal (FR) effects. The FR effect is added mainly to boost the output torque production, and applying a magnetic-equivalent circuit (MEC) shows that the BF effect lowers the saturation risk in the stator core. Also, using finite element analysis (FEA), the main proposed motor generates the sinusoidal back-EMF waveform with an RMS value of 11.3V. Additionally, the full-load results show that the proposed motor produces 1.76N.m torque with 3.5% ripple. Furthermore, the flux density distribution of motors shows the importance of the BF effect in overload performances and verifies the analytical MEC results.

关键词： Stator cores Torque Windings Production Motors Permanent magnets Finite element analysis Torque measurement Optimization Saturation magnetization

Study of a Modular Consequent-Pole Flux Reversal Motor with the Synergy of Biased-Flux Effect

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Study of a Modular Consequent-Pole Flux Reversal Motor with ...

electrical Machines and Drives (ICEMD), International Conference on

作者： Mohammad Reza Sarshar Mohammad Afrank Mohammad Amin Jalali Kondelaji Mojtaba Mirsalim Javad Shokrollahi Moghani Department of Electrical Engineering Amirkabir University of Technology (Tehran Polytechnic) Tehran Iran Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology (MIT) Cambridge USA

ISBN: (数字)9798331507510

ISBN: (纸本)9798331507527

This paper studies a novel flux reversal permanent magnet (FRPM) motor in which PMs are positioned in consequent-pole and intermodular pattern. The proposed structure applies the synergies of flux reversal and biased flux effects to improve the torque density. The motor is optimized with multi-objective genetic algorithm (GA) to achieve a high torque with low torque ripple. Also, the FRPM is compared with the conventional intermodular PM motor (IMPM) to outline its superiorities. By means of finite element analysis (FEA), the motors are compared under the no-load and full-load conditions, and the results in terms of back-EMF and its harmonic distribution, air-gap flux density distributions, and full-load torque and ripple are analyzed. The FEA results shows that the proposed structure enhances the output torque by 40% compared to the IMPM while reducing the PM volume.

关键词： Torque Motors Harmonic analysis Permanent magnets Topology Finite element analysis Scattering parameters Torque measurement Optimization Genetic algorithms