Multiobjective evolutionary algorithms (MOEAs) are major methods for solving multiobjective optimization problems (MOPs). Many MOEAs have been proposed in the past decades, of which the operators need carefully handcrafted design with domain knowledge. Recently, some attempts have been made to replace the manually designed operators in MOEAs with learning-based operators (e.g., neural network models). However, much effort is still required for designing and training such models, and the learned operators might not generalize well to solve new problems. To tackle the above challenges, this work investigates a novel approach that leverages the powerful large language model (LLM) to design MOEA operators. With proper prompt engineering, we successfully let a general LLM serve as a black-box search operator for decomposition-based MOEA (MOEA/D) in a zero-shot manner. In addition, by learning from the LLM behavior, we further design an explicit white-box operator with randomness and propose a new version of decomposition-based MOEA, termed MOEA/D-LO. Experimental studies on different test benchmarks show that our proposed method can achieve competitive performance with widely used MOEAs. It is also promising to see the operator only learned from a few instances can have robust generalization performance on unseen problems with quite different patterns and settings. The results reveal the potential benefits of using pre-trained LLMs in the design of MOEAs.
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Stochastic sampling algorithms such as Langevin Monte Carlo are inspired by physical systems in a heat bath. Their equilibrium distribution is the canonical ensemble given by a prescribed target distribution, so they must balance fluctuation and dissipation as dictated by the fluctuation-dissipation theorem. In contrast to the common belief, we show that the fluctuation-dissipation theorem is not required because only the configuration space distribution, and not the full phase space distribution, needs to be canonical. We propose a continuous-time Microcanonical Langevin Monte Carlo (MCLMC) as a dissipation-free system of stochastic differential equations (SDE). We derive the corresponding Fokker-Planck equation and show that the stationary distribution is the microcanonical ensemble with the desired canonical distribution on configuration space. We prove that MCLMC is ergodic for any nonzero amount of stochasticity, and for smooth, convex potentials, the expectation values converge exponentially fast. Furthermore, the deterministic drift and the stochastic diffusion separately preserve the stationary distribution. This uncommon property is attractive for practical implementations as it implies that the drift-diffusion discretization schemes are bias-free, so the only source of bias is the discretization of the deterministic dynamics. We applied MCLMC on a lattice $\phi^4$ model, where Hamiltonian Monte Carlo (HMC) is currently the state-of-the-art integrator. For the same accuracy, MCLMC converges 12 times faster than HMC on an $8\times8$ lattice. On a $64\times64$ lattice, it is already 32 times faster. The trend is expected to persist to larger lattices, which are of particular interest, for example, in lattice quantum chromodynamics.
We propose a novel machine learning algorithm for simulating radiative transfer. Our algorithm is based on physics informed neural networks (PINNs), which are trained by minimizing the residual of the underlying radiative tranfer equations. We present extensive experiments and theoretical error estimates to demonstrate that PINNs provide a very easy to implement, fast, robust and accurate method for simulating radiative transfer. We also present a PINN based algorithm for simulating inverse problems for radiative transfer efficiently.
We present FIMO, an innovative dataset comprising formal mathematical problem statements sourced from the International Mathematical Olympiad (IMO) Shortlisted Problems. Designed to facilitate advanced automated theorem proving at the IMO level, FIMO is currently tailored for the Lean formal language. It comprises 149 formal problem statements, accompanied by both informal problem descriptions and their corresponding LaTeX-based informal proofs. Through initial experiments involving GPT-4, our findings underscore the existing limitations in current methodologies, indicating a substantial journey ahead before achieving satisfactory IMO-level automated theorem proving outcomes.
Recently introduced cone distribution functions from statistics are turned into multi-criteria decision making (MCDM) tools. It is demonstrated that this procedure can be considered as an upgrade of the weighted sum scalarization insofar as it absorbs a whole collection of weighted sum scalarizations at once instead of fixing a particular one in advance. Moreover, situations are characterized in which different types of rank reversal occur, and it is explained why this might even be useful for analyzing the ranking procedure. A few examples will be discussed and a potential application in machine learning is outlined.
Traditional steganographic techniques have often relied on manually crafted attributes related to image residuals. These methods demand a significant level of expertise and face challenges in integrating diverse image residual characteristics. In this paper, we introduce an innovative deep learning-based methodology that seamlessly integrates image residuals, residual distances, and image local variance to autonomously learn embedding probabilities. Our framework includes an embedding probability generator and three pivotal guiding components: Residual guidance strives to facilitate embedding in complex-textured areas. Residual distance guidance aims to minimize the residual differences between cover and stego images. Local variance guidance effectively safeguards against modifications in regions characterized by uncomplicated or uniform textures. The three components collectively guide the learning process, enhancing the security performance. Comprehensive experimental findings underscore the superiority of our approach when compared to traditional steganographic methods and randomly initialized ReLOAD in the spatial domain.
Evolutionary algorithms face significant challenges when dealing with dynamic multi-objective optimization because Pareto optimal solutions and/or Pareto optimal fronts change. This paper proposes a unified paradigm, which combines the kernelized autoncoding evolutionary search and the centriod-based prediction (denoted by KAEP), for solving dynamic multi-objective optimization problems (DMOPs). Specifically, whenever a change is detected, KAEP reacts effectively to it by generating two subpopulations. The first subpoulation is generated by a simple centriod-based prediction strategy. For the second initial subpopulation, the kernel autoencoder is derived to predict the moving of the Pareto-optimal solutions based on the historical elite solutions. In this way, an initial population is predicted by the proposed combination strategies with good convergence and diversity, which can be effective for solving DMOPs. The performance of our proposed method is compared with five state-of-the-art algorithms on a number of complex benchmark problems. Empirical results fully demonstrate the superiority of our proposed method on most test instances.
We explore security aspects of a new computing paradigm that combines novel memristors and traditional Complimentary Metal Oxide Semiconductor (CMOS) to construct a highly efficient analog and/or digital fabric that is especially well-suited to Machine Learning (ML) inference processors for Radio Frequency (RF) signals. Memristors have different properties than traditional CMOS which can potentially be exploited by attackers. In addition, the mixed signal approximate computing model has different vulnerabilities than traditional digital implementations. However both the memristor and the ML computation can be leveraged to create security mechanisms and countermeasures ranging from lightweight cryptography, identifiers (e.g. Physically Unclonable Functions (PUFs), fingerprints, and watermarks), entropy sources, hardware obfuscation and leakage/attack detection methods. Three different threat models are proposed: 1) Supply Chain, 2) Physical Attacks, and 3) Remote Attacks. For each threat model, potential vulnerabilities and defenses are identified. This survey reviews a variety of recent work from the hardware and ML security literature and proposes open problems for both attack and defense. The survey emphasizes the growing area of RF signal analysis and identification in terms of the commercial space, as well as military applications and threat models. We differ from other other recent surveys that target ML in general, neglecting RF applications.
We introduce learning augmented algorithms to the online graph coloring problem. Although the simple greedy algorithm FirstFit is known to perform poorly in the worst case, we are able to establish a relationship between the structure of any input graph $G$ that is revealed online and the number of colors that FirstFit uses for $G$. Based on this relationship, we propose an online coloring algorithm FirstFitPredictions that extends FirstFit while making use of machine learned predictions. We show that FirstFitPredictions is both \emph{consistent} and \emph{smooth}. Moreover, we develop a novel framework for combining online algorithms at runtime specifically for the online graph coloring problem. Finally, we show how this framework can be used to robustify by combining it with any classical online coloring algorithm (that disregards the predictions).
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
Attention mechanism has been used as an ancillary means to help RNN or CNN. However, the Transformer (Vaswani et al., 2017) recently recorded the state-of-the-art performance in machine translation with a dramatic reduction in training time by solely using attention. Motivated by the Transformer, Directional Self Attention Network (Shen et al., 2017), a fully attention-based sentence encoder, was proposed. It showed good performance with various data by using forward and backward directional information in a sentence. But in their study, not considered at all was the distance between words, an important feature when learning the local dependency to help understand the context of input text. We propose Distance-based Self-Attention Network, which considers the word distance by using a simple distance mask in order to model the local dependency without losing the ability of modeling global dependency which attention has inherent. Our model shows good performance with NLI data, and it records the new state-of-the-art result with SNLI data. Additionally, we show that our model has a strength in long sentences or documents.
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