Manifold learning flows are a class of generative modelling techniques that assume a low-dimensional manifold description of the data. The embedding of such a manifold into the high-dimensional space of the data is achieved via learnable invertible transformations. Therefore, once the manifold is properly aligned via a reconstruction loss, the probability density is tractable on the manifold and maximum likelihood can be used to optimize the network parameters. Naturally, the lower-dimensional representation of the data requires an injective-mapping. Recent approaches were able to enforce that the density aligns with the modelled manifold, while efficiently calculating the density volume-change term when embedding to the higher-dimensional space. However, unless the injective-mapping is analytically predefined, the learned manifold is not necessarily an efficient representation of the data. Namely, the latent dimensions of such models frequently learn an entangled intrinsic basis, with degenerate information being stored in each dimension. Alternatively, if a locally orthogonal and/or sparse basis is to be learned, here coined canonical intrinsic basis, it can serve in learning a more compact latent space representation. Toward this end, we propose a canonical manifold learning flow method, where a novel optimization objective enforces the transformation matrix to have few prominent and non-degenerate basis functions. We demonstrate that by minimizing the off-diagonal manifold metric elements $\ell_1$-norm, we can achieve such a basis, which is simultaneously sparse and/or orthogonal. Canonical manifold flow yields a more efficient use of the latent space, automatically generating fewer prominent and distinct dimensions to represent data, and a better approximation of target distributions than other manifold flow methods in most experiments we conducted, resulting in lower FID scores.
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Deep learning methods have gained considerable interest in the numerical solution of various partial differential equations (PDEs). One particular focus is physics-informed neural networks (PINN), which integrate physical principles into neural networks. This transforms the process of solving PDEs into optimization problems for neural networks. To address a collection of advection-diffusion equations (ADE) in a range of difficult circumstances, this paper proposes a novel network structure. This architecture integrates the solver, a multi-scale deep neural networks (MscaleDNN) utilized in the PINN method, with a hard constraint technique known as HCPINN. This method introduces a revised formulation of the desired solution for ADE by utilizing a loss function that incorporates the residuals of the governing equation and penalizes any deviations from the specified boundary and initial constraints. By surpassing the boundary constraints automatically, this method improves the accuracy and efficiency of the PINN technique. To address the ``spectral bias'' phenomenon in neural networks, a subnetwork structure of MscaleDNN and a Fourier-induced activation function are incorporated into the HCPINN, resulting in a hybrid approach called SFHCPINN. The effectiveness of SFHCPINN is demonstrated through various numerical experiments involving ADE in different dimensions. The numerical results indicate that SFHCPINN outperforms both standard PINN and its subnetwork version with Fourier feature embedding. It achieves remarkable accuracy and efficiency while effectively handling complex boundary conditions and high-frequency scenarios in ADE.
Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to \textit{couple} the base and the target densities, whereby samples from the base are computed conditionally given samples from the target in a way that is different from (but does preclude) incorporating information about class labels or continuous embeddings. This enables us to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting.
To capture the extremal behaviour of complex environmental phenomena in practice, flexible techniques for modelling tail behaviour are required. In this paper, we introduce a variety of such methods, which were used by the Lancopula Utopiversity team to tackle the data challenge of the 2023 Extreme Value Analysis Conference. This data challenge was split into four sections, labelled C1-C4. Challenges C1 and C2 comprise univariate problems, where the goal is to estimate extreme quantiles for a non-stationary time series exhibiting several complex features. We propose a flexible modelling technique, based on generalised additive models, with diagnostics indicating generally good performance for the observed data. Challenges C3 and C4 concern multivariate problems where the focus is on estimating joint extremal probabilities. For challenge C3, we propose an extension of available models in the multivariate literature and use this framework to estimate extreme probabilities in the presence of non-stationary dependence. Finally, for challenge C4, which concerns a 50 dimensional random vector, we employ a clustering technique to achieve dimension reduction and use a conditional modelling approach to estimate extremal probabilities across independent groups of variables.
Age-Period-Cohort (APC) models are well used in the context of modelling health and demographic data to produce smooth estimates of each time trend. When smoothing in the context of APC models, there are two main schools, frequentist using penalised smoothing splines, and Bayesian using random processes with little crossover between them. In this article, we clearly lay out the theoretical link between the two schools, provide examples using simulated and real data to highlight similarities and difference, and help a general APC user understand potentially inaccessible theory from functional analysis. As intuition suggests, both approaches lead to comparable and almost identical in-sample predictions, but random processes within a Bayesian approach might be beneficial for out-of-sample prediction as the sources of uncertainty are captured in a more complete way.
The field of adversarial textual attack has significantly grown over the last few years, where the commonly considered objective is to craft adversarial examples (AEs) that can successfully fool the target model. However, the imperceptibility of attacks, which is also essential for practical attackers, is often left out by previous studies. In consequence, the crafted AEs tend to have obvious structural and semantic differences from the original human-written text, making them easily perceptible. In this work, we advocate leveraging multi-objectivization to address such issue. Specifically, we reformulate the problem of crafting AEs as a multi-objective optimization problem, where the attack imperceptibility is considered as an auxiliary objective. Then, we propose a simple yet effective evolutionary algorithm, dubbed HydraText, to solve this problem. To the best of our knowledge, HydraText is currently the only approach that can be effectively applied to both score-based and decision-based attack settings. Exhaustive experiments involving 44237 instances demonstrate that HydraText consistently achieves competitive attack success rates and better attack imperceptibility than the recently proposed attack approaches. A human evaluation study also shows that the AEs crafted by HydraText are more indistinguishable from human-written text. Finally, these AEs exhibit good transferability and can bring notable robustness improvement to the target model by adversarial training.
We use Stein characterisations to derive new moment-type estimators for the parameters of several multivariate distributions in the i.i.d. case; we also derive the asymptotic properties of these estimators. Our examples include the multivariate truncated normal distribution and several spherical distributions. The estimators are explicit and therefore provide an interesting alternative to the maximum-likelihood estimator. The quality of these estimators is assessed through competitive simulation studies in which we compare their behaviour to the performance of other estimators available in the literature.
Parameter sharing, as an important technique in multi-agent systems, can effectively solve the scalability issue in large-scale agent problems. However, the effectiveness of parameter sharing largely depends on the environment setting. When agents have different identities or tasks, naive parameter sharing makes it difficult to generate sufficiently differentiated strategies for agents. Inspired by research pertaining to the brain in biology, we propose a novel parameter sharing method. It maps each type of agent to different regions within a shared network based on their identity, resulting in distinct subnetworks. Therefore, our method can increase the diversity of strategies among different agents without introducing additional training parameters. Through experiments conducted in multiple environments, our method has shown better performance than other parameter sharing methods.
We propose reinforcement learning to control the dynamical self-assembly of the dodecagonal quasicrystal (DDQC) from patchy particles. The patchy particles have anisotropic interactions with other particles and form DDQC. However, their structures at steady states are significantly influenced by the kinetic pathways of their structural formation. We estimate the best policy of temperature control trained by the Q-learning method and demonstrate that we can generate DDQC with few defects using the estimated policy. The temperature schedule obtained by reinforcement learning can reproduce the desired structure more efficiently than the conventional pre-fixed temperature schedule, such as annealing. To clarify the success of the learning, we also analyse a simple model describing the kinetics of structural changes through the motion in a triple-well potential. We have found that reinforcement learning autonomously discovers the critical temperature at which structural fluctuations enhance the chance of forming a globally stable state. The estimated policy guides the system toward the critical temperature to assist the formation of DDQC.
The generalized additive Runge-Kutta (GARK) framework provides a powerful approach for solving additively partitioned ordinary differential equations. This work combines the ideas of symplectic GARK schemes and multirate GARK schemes to efficiently solve additively partitioned Hamiltonian systems with multiple time scales. Order conditions, as well as conditions for symplecticity and time-reversibility, are derived in the general setting of non-separable Hamiltonian systems. Investigations of the special case of separable Hamiltonian systems are also carried out. We show that particular partitions may introduce stability issues, and discuss partitions that enable an implicit-explicit integration leading to improved stability properties. Higher-order symplectic multirate GARK schemes based on advanced composition techniques are discussed. The performance of the schemes is demonstrated by means of the Fermi-Pasta-Ulam problem.
Graph-centric artificial intelligence (graph AI) has achieved remarkable success in modeling interacting systems prevalent in nature, from dynamical systems in biology to particle physics. The increasing heterogeneity of data calls for graph neural architectures that can combine multiple inductive biases. However, combining data from various sources is challenging because appropriate inductive bias may vary by data modality. Multimodal learning methods fuse multiple data modalities while leveraging cross-modal dependencies to address this challenge. Here, we survey 140 studies in graph-centric AI and realize that diverse data types are increasingly brought together using graphs and fed into sophisticated multimodal models. These models stratify into image-, language-, and knowledge-grounded multimodal learning. We put forward an algorithmic blueprint for multimodal graph learning based on this categorization. The blueprint serves as a way to group state-of-the-art architectures that treat multimodal data by choosing appropriately four different components. This effort can pave the way for standardizing the design of sophisticated multimodal architectures for highly complex real-world problems.
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