Miracle-dz/UniFAR-FTUs huggingface dataset:
VC-PINN: Variable Coefficient Physical Information Neural Network For Forward And Inverse PDE Problems with Variable Coefficient

The paper proposes a deep learning method specifically dealing with the forward and inverse problem of variable coefficient partial differential equations -- Variable Coefficient Physical Information Neural Network (VC-PINN). The shortcut connections (ResNet structure) introduced into the network alleviates the"Vanishing gradient"and unifies the linear and nonlinear coefficients. The developed method was applied to four equations including the variable coefficient Sine-Gordon (vSG), the generalized variable coefficient Kadomtsev-Petviashvili equation (gvKP), the variable coefficient Korteweg-de Vries equation (vKdV), the variable coefficient Sawada-Kotera equation (vSK). Numerical results show that VC-PINN is successful in the case of high dimensionality, various variable coefficients (polynomials, trigonometric functions, fractions, oscillation attenuation coefficients), and the coexistence of multiple variable coefficients. We also conducted an in-depth analysis of VC-PINN in a combination of theory and numerical experiments, including four aspects, the necessity of ResNet, the relationship between the convexity of variable coefficients and learning, anti-noise analysis, the unity of forward and inverse problems/relationship with standard PINN.
The Progression of Disparities within the Criminal Justice System: Differential Enforcement and Risk Assessment Instruments

Algorithmic risk assessment instruments (RAIs) increasingly inform decision-making in criminal justice. RAIs largely rely on arrest records as a proxy for underlying crime. Problematically, the extent to which arrests reflect overall offending can vary with the person’s characteristics. We examine how the disconnect between crime and arrest rates impacts RAIs and their evaluation. Our main contribution is a method for quantifying this bias via estimation of the amount of unobserved offenses associated with particular demographics. These unobserved offenses are then used to augment real-world arrest records to create part real, part synthetic crime records. Using this data, we estimate that four currently deployed RAIs assign 0.5–2.8 percentage points higher risk scores to Black individuals than to White individuals with a similar arrest record, but the gap grows to 4.5–11.0 percentage points when we match on the semi-synthetic crime record. We conclude by discussing the potential risks around the use of RAIs, highlighting how they may exacerbate existing inequalities if the underlying disparities of the criminal justice system are not taken into account. In light of our findings, we provide recommendations to improve the development and evaluation of such tools.
Towards best practices in AGI safety and governance: A survey of expert opinion

A number of leading AI companies, including OpenAI, Google DeepMind, and Anthropic, have the stated goal of building artificial general intelligence (AGI) - AI systems that achieve or exceed human performance across a wide range of cognitive tasks. In pursuing this goal, they may develop and deploy AI systems that pose particularly significant risks. While they have already taken some measures to mitigate these risks, best practices have not yet emerged. To support the identification of best practices, we sent a survey to 92 leading experts from AGI labs, academia, and civil society and received 51 responses. Participants were asked how much they agreed with 50 statements about what AGI labs should do. Our main finding is that participants, on average, agreed with all of them. Many statements received extremely high levels of agreement. For example, 98% of respondents somewhat or strongly agreed that AGI labs should conduct pre-deployment risk assessments, dangerous capabilities evaluations, third-party model audits, safety restrictions on model usage, and red teaming. Ultimately, our list of statements may serve as a helpful foundation for efforts to develop best practices, standards, and regulations for AGI labs.
eXplainable Artificial Intelligence on Medical Images: A Survey

Over the last few years, the number of works about deep learning applied to the medical field has increased enormously. The necessity of a rigorous assessment of these models is required to explain these results to all people involved in medical exams. A recent field in the machine learning area is explainable artificial intelligence, also known as XAI, which targets to explain the results of such black box models to permit the desired assessment. This survey analyses several recent studies in the XAI field applied to medical diagnosis research, allowing some explainability of the machine learning results in several different diseases, such as cancers and COVID-19.
Expertise-based Weighting for Regression Models with Noisy Labels

Regression methods assume that accurate labels are available for training. However, in certain scenarios, obtaining accurate labels may not be feasible, and relying on multiple specialists with differing opinions becomes necessary. Existing approaches addressing noisy labels often impose restrictive assumptions on the regression function. In contrast, this paper presents a novel, more flexible approach. Our method consists of two steps: estimating each labeler's expertise and combining their opinions using learned weights. We then regress the weighted average against the input features to build the prediction model. The proposed method is formally justified and empirically demonstrated to outperform existing techniques on simulated and real data. Furthermore, its flexibility enables the utilization of any machine learning technique in both steps. In summary, this method offers a simple, fast, and effective solution for training regression models with noisy labels derived from diverse expert opinions.
The ConceptARC Benchmark: Evaluating Understanding and Generalization in the ARC Domain

The abilities to form and abstract concepts is key to human intelligence, but such abilities remain lacking in state-of-the-art AI systems. There has been substantial research on conceptual abstraction in AI, particularly using idealized domains such as Raven's Progressive Matrices and Bongard problems, but even when AI systems succeed on such problems, the systems are rarely evaluated in depth to see if they have actually grasped the concepts they are meant to capture. In this paper we describe an in-depth evaluation benchmark for the Abstraction and Reasoning Corpus (ARC), a collection of few-shot abstraction and analogy problems developed by Chollet [2019]. In particular, we describe ConceptARC, a new, publicly available benchmark in the ARC domain that systematically assesses abstraction and generalization abilities on a number of basic spatial and semantic concepts. ConceptARC differs from the original ARC dataset in that it is specifically organized around"concept groups"-- sets of problems that focus on specific concepts and that are vary in complexity and level of abstraction. We report results on testing humans on this benchmark as well as three machine solvers: the top two programs from a 2021 ARC competition and OpenAI's GPT-4. Our results show that humans substantially outperform the machine solvers on this benchmark, showing abilities to abstract and generalize concepts that are not yet captured by AI systems. We believe that this benchmark will spur improvements in the development of AI systems for conceptual abstraction and in the effective evaluation of such systems.
Are Machine Rationales (Not) Useful to Humans? Measuring and Improving Human Utility of Free-text Rationales

Among the remarkable emergent capabilities of large language models (LMs) is free-text rationalization; beyond certain scale, large LMs are capable of generating seemingly useful rationalizations, which in turn, can dramatically enhance their performances on leaderboards. This phenomenon raises a question: can machine generated rationales also be useful for humans, especially when lay humans try to answer questions based on those machine rationales? We observe that human utility of existing rationales is far from satisfactory and expensive to estimate with human studies. Existing metrics like task performance of the LM generating the rationales or similarity between generated and gold rationales are not good indicators of their human utility. While we observe that certain properties of rationales like conciseness and novelty are correlated with their human utility, estimating them without human involvement is challenging. We show that, by estimating a rationale’s helpfulness in answering similar unseen instances, we can measure its human utility to a better extent. We also translate this finding into an automated score, Gen-U, that we propose, which can help improve LMs’ ability to generate rationales with better human utility, while maintaining most of its task performance. Lastly, we release all code and collected data with this project.
Is ChatGPT a Good Causal Reasoner? A Comprehensive Evaluation

Causal reasoning ability is crucial for numerous NLP applications. Despite the impressive emerging ability of ChatGPT in various NLP tasks, it is unclear how well ChatGPT performs in causal reasoning. In this paper, we conduct the first comprehensive evaluation of the ChatGPT's causal reasoning capabilities. Experiments show that ChatGPT is not a good causal reasoner, but a good causal explainer. Besides, ChatGPT has a serious hallucination on causal reasoning, possibly due to the reporting biases between causal and non-causal relationships in natural language, as well as ChatGPT's upgrading processes, such as RLHF. The In-Context Learning (ICL) and Chain-of-Thought (CoT) techniques can further exacerbate such causal hallucination. Additionally, the causal reasoning ability of ChatGPT is sensitive to the words used to express the causal concept in prompts, and close-ended prompts perform better than open-ended prompts. For events in sentences, ChatGPT excels at capturing explicit causality rather than implicit causality, and performs better in sentences with lower event density and smaller lexical distance between events. The code is available on https://github.com/ArrogantL/ChatGPT4CausalReasoning .
Investigating the dynamics of a Bose Einstein condensate on an atom chip

In this thesis I discuss work that has been carried out on the dynamics of a Bose Einstein condensate of Rb 87 produced near an atom chip. A Bose Einstein Condensate (BEC) is a quantum state of matter where a single quantum state becomes occupied by a macroscopic number of identical Bosons. In our case this is achieved by cooling a system of trapped identical rubidium 87 atoms to its ground state. To reach temperatures of condensation we initially laser cool atoms from room temperature, before loading them into a magnetic trap. The magnetic trap is produced through a combination of uniform magnetic fields from coils outside our vacuum chamber and currents running through wires on an atom chip. The atom chip is a microfabricated device, produced by a coating a silicon chip with a thin layer of gold and etching wires into it. Together, these fields create a magnetic field minimum 120μm from the surface of the chip which can be used to confine low field seeking hyperfine states of the atom in an elongated harmonic trap. Once the atoms are confined in the magnetic trap we used force evaporative cooling out to reach the phase space densities required for Bose Einstein condensation. The BEC is used to investigate the relative dynamics between the fraction of the atoms in the condensate to those not in the condensate. Our atom chip provided a suitable environment to investigate this due to fragmentation of the magnetic potential close to the chip. Small imperfections in the wires on our atom chip mean that the trapping potential isn’t smooth. Small regions of higher trapping frequency or fragments are formed. Due to the small size of these fragments it is possible to find a position where a condensate can form in the fragment, and see a potential of high frequency, whereas a non-condensed atom will see a lower frequency potential. We exploit this to set the condensed fraction moving relative to the non condensed part and investigate the subsequent damping of their motion relative to each other.
Rate-Splitting Multiple Access: The First Prototype and Experimental Validation of its Superiority over SDMA and NOMA

In multi-user multi-antenna communications, it is well-known in theory that Rate-Splitting Multiple Access (RSMA) can achieve a higher spectral efficiency than both Space Division Multiple Access (SDMA) and Non-Orthogonal Multiple Access (NOMA). However, an experimental evaluation of RSMA's performance, relative to SDMA and NOMA, is missing in the literature, which is essential to address the ongoing debate between RSMA and NOMA over which is better suited to handle most efficiently the available resources and interference in 6G. In this paper, we address this critical knowledge gap by realizing the first-ever RSMA prototype using software-defined radios. Through measurements using our prototype, we empirically solve the modulation and coding scheme limited sum throughput maximization problem for RSMA, SDMA and NOMA for the two-user multiple-input single-output (MISO) scenario over (a) different pairs of line-of-sight channels that vary in terms of their relative pathloss and spatial correlation, and with (b) different channel state information quality. We observe that RSMA achieves the highest sum throughput across all these cases, whereas SDMA and NOMA are effective only in some cases. Furthermore, RSMA also achieves better fairness at a higher sum throughput than both SDMA and NOMA.
Online Learning Under A Separable Stochastic Approximation Framework

We propose an online learning algorithm for a class of machine learning models under a separable stochastic approximation framework. The essence of our idea lies in the observation that certain parameters in the models are easier to optimize than others. In this paper, we focus on models where some parameters have a linear nature, which is common in machine learning. In one routine of the proposed algorithm, the linear parameters are updated by the recursive least squares (RLS) algorithm, which is equivalent to a stochastic Newton method; then, based on the updated linear parameters, the nonlinear parameters are updated by the stochastic gradient method (SGD). The proposed algorithm can be understood as a stochastic approximation version of block coordinate gradient descent approach in which one part of the parameters is updated by a second-order SGD method while the other part is updated by a first-order SGD. Global convergence of the proposed online algorithm for non-convex cases is established in terms of the expected violation of a first-order optimality condition. Numerical experiments show that the proposed method accelerates convergence significantly and produces more robust training and test performance when compared to other popular learning algorithms. Moreover, our algorithm is less sensitive to the learning rate and outperforms the recently proposed slimTrain algorithm (Newman et al., 2022). The code has been uploaded to GitHub for validation.
Internal Wave Generation and Near-Resonant Interactions: Theory and Applications

Near-resonant triad interactions and wave generation theory are investigated for continuously stratified fluids. Interaction equations are derived for spatially-varying wave trains under the inviscid Boussinesq approximation. Rotational effects are included, and properties of the underlying eigenvalue problem are explored. To facilitate a numerical study of the near-resonant interactions, numerical methods are developed and an analysis of wave generation on a periodic domain is performed. Numerical experiments using laboratory and ocean-scale parameters are conducted, and the simulations confirm the validity of the wave forcing theory. Interaction experiments demonstrate a strong tendency for waves to exhibit nonlinear behaviour. While resonant interactions are observed in the laboratory scale simulations, nonlinear steepening effects and the formation of solitary-like waves dominate the ocean-scale experiments. The results suggest that the weakly-nonlinear interaction theory is only appropriate in a limited parameter regime. The problem of analyzing forced wave equations on an infinite domain is also considered. Motivated by the results obtained on a periodic domain, asymptotic analysis is applied to three important wave equations. The method of steepest descents is used to determine the large-time behaviour for the linearized Korteweg-de Vries, Benjamin-Bona-Mahony, and internal gravity wave equations. The asymptotic results are compared with numerical experiments and found to agree to high precision.
Family Floer SYZ singularities for the conifold transition

We show a mathematically precise version of the SYZ conjecture, proposed in the family Floer context, for the conifold with a conjectural mirror relation between smoothing and crepant resolution. The singular T-duality fibers are explicitly written and exactly correspond to the codimension-2 `missing points' in the mirror cluster variety, which confirms the speculation of Chan, Pomerleano, and Ueda but only in the non-archimedean setting. Concerning purely the area of Berkovich geometry and forgetting all the mirror symmetry background, our B-side analytic fibration is also a new explicit example of affinoid torus fibration with singular extension.
AGFormer: Efficient Graph Representation with Anchor-Graph Transformer

To alleviate the local receptive issue of GCN, Transformers have been exploited to capture the long range dependences of nodes for graph data representation and learning. However, existing graph Transformers generally employ regular self-attention module for all node-to-node message passing which needs to learn the affinities/relationships between all node's pairs, leading to high computational cost issue. Also, they are usually sensitive to graph noises. To overcome this issue, we propose a novel graph Transformer architecture, termed Anchor Graph Transformer (AGFormer), by leveraging an anchor graph model. To be specific, AGFormer first obtains some representative anchors and then converts node-to-node message passing into anchor-to-anchor and anchor-to-node message passing process. Thus, AGFormer performs much more efficiently and also robustly than regular node-to-node Transformers. Extensive experiments on several benchmark datasets demonstrate the effectiveness and benefits of proposed AGFormer.
Improving Zero-shot Multilingual Neural Machine Translation by Leveraging Cross-lingual Consistency Regularization

The multilingual neural machine translation (NMT) model has a promising capability of zero-shot translation, where it could directly translate between language pairs unseen during training. For good transfer performance from supervised directions to zero-shot directions, the multilingual NMT model is expected to learn universal representations across different languages. This paper introduces a cross-lingual consistency regularization, CrossConST, to bridge the representation gap among different languages and boost zero-shot translation performance. The theoretical analysis shows that CrossConST implicitly maximizes the probability distribution for zero-shot translation, and the experimental results on both low-resource and high-resource benchmarks show that CrossConST consistently improves the translation performance. The experimental analysis also proves that CrossConST could close the sentence representation gap and better align the representation space. Given the universality and simplicity of CrossConST, we believe it can serve as a strong baseline for future multilingual NMT research.
First-order phase transitions in Yang-Mills theories and the density of state method

When studied at finite temperature, Yang-Mills theories in $3+1$ dimensions display the presence of confinement/deconfinement phase transitions, which are known to be of first order -- the $SU(2)$ gauge theory being the exception. Theoretical as well as phenomenological considerations indicate that it is essential to establish a precise characterisation of these physical systems in proximity of such phase transitions. We present and test a new method to study the critical region of parameter space in non-Abelian quantum field theories on the lattice, based upon the Logarithmic Linear Relaxation (LLR) algorithm. We apply this method to the $SU(3)$ Yang Mills lattice gauge theory, and perform extensive calculations with one fixed choice of lattice size. We identify the critical temperature, and measure interesting physical quantities near the transition. Among them, we determine the free energy of the model in the critical region, exposing for the first time its multi-valued nature with a numerical calculation from first principles, providing this novel evidence in support of a first order phase transition. This study sets the stage for future high precision measurements, by demonstrating the potential of the method.
ActUp: Analyzing and Consolidating tSNE and UMAP

TSNE and UMAP are popular dimensionality reduction algorithms due to their speed and interpretable low-dimensional embeddings. Despite their popularity, however, little work has been done to study their full span of differences. We theoretically and experimentally evaluate the space of parameters in the TSNE and UMAP algorithms and observe that a single one -- the normalization -- is responsible for switching between them. This, in turn, implies that a majority of the algorithmic differences can be toggled without affecting the embeddings. We discuss the implications this has on several theoretic claims behind UMAP, as well as how to reconcile them with existing TSNE interpretations. Based on our analysis, we provide a method (GDR) that combines previously incompatible techniques from TSNE and UMAP and can replicate the results of either algorithm. This allows our method to incorporate further improvements, such as an acceleration that obtains either method's outputs faster than UMAP. We release improved versions of TSNE, UMAP, and GDR that are fully plug-and-play with the traditional libraries.
3D modeling of positive streamers in air with inhomogeneous density

We study the effect of an inhomogeneous gas density on positive streamer discharges in air using a 3D fluid model with stochastic photoionization, generalizing earlier work with a 2D axisymmetric model by Starikovskiy and Aleksandrov (2019 Plasma Sources Sci. Technol. 28 095022). We consider various types of planar and (hemi)spherical gas density gradients. Streamers propagate from a region of density n0 towards a region of higher or lower gas density n1 , where n0 corresponds to 300K and 1bar . We observe that streamers can always propagate into a region with a lower gas density. When streamers enter a region with a higher gas density, branching can occur at the density gradient, with branches growing in a flower-like pattern over the gradient surface. Depending on the gas density ratio, the gradient width and other factors, narrow branches are able to propagate into the higher-density gas. In a planar geometry, we find that such propagation is possible up to a gas density slope of 3.5n0/mm , although this value depends on a number of conditions, such as the gradient angle. Surprisingly, a higher applied voltage makes it more difficult for streamers to penetrate into the high-density region, due to an increase of the primary streamer’s radius.