Miracle-dz/UniFAR-FTUs huggingface dataset:
Thermalization of isolated quantum many-body system \`a la entanglement

Thermalization of an isolated quantum system has been a nontrivial problem since the early days of quantum mechanics. In generic isolated quantum systems, nonequilibrium dynamics is expected to result in thermalization, indicating the emergence of statistical mechanics from quantum dynamics. However, what feature of a many-body quantum system facilitates quantum thermalization is still not well understood. Recent experimental advancements have shown that entanglement may act as a thermalizing agent, not universally but particularly. Here, we theoretically show that the thermal averages of an observable in an isolated many-body quantum system with a large number of degrees of freedom emerge from the entangled energy eigenstates of the system. In particular, we show that the expectation values of an observable in entangled energy eigenstates and its marginals are equivalent to the microcanonical and canonical averages of the observable.
On the Performance of Empirical Risk Minimization with Smoothed Data

In order to circumvent statistical and computational hardness results in sequential decision-making, recent work has considered smoothed online learning, where the distribution of data at each time is assumed to have bounded likeliehood ratio with respect to a base measure when conditioned on the history. While previous works have demonstrated the benefits of smoothness, they have either assumed that the base measure is known to the learner or have presented computationally inefficient algorithms applying only in special cases. This work investigates the more general setting where the base measure is \emph{unknown} to the learner, focusing in particular on the performance of Empirical Risk Minimization (ERM) with square loss when the data are well-specified and smooth. We show that in this setting, ERM is able to achieve sublinear error whenever a class is learnable with iid data; in particular, ERM achieves error scaling as $\tilde O( \sqrt{\mathrm{comp}(\mathcal F)\cdot T} )$, where $\mathrm{comp}(\mathcal F)$ is the statistical complexity of learning $\mathcal F$ with iid data. In so doing, we prove a novel norm comparison bound for smoothed data that comprises the first sharp norm comparison for dependent data applying to arbitrary, nonlinear function classes. We complement these results with a lower bound indicating that our analysis of ERM is essentially tight, establishing a separation in the performance of ERM between smoothed and iid data.
Hierarchical Invariance for Robust and Interpretable Vision Tasks at Larger Scales

Developing robust and interpretable vision systems is a crucial step towards trustworthy artificial intelligence. In this regard, a promising paradigm considers embedding task-required invariant structures, e.g., geometric invariance, in the fundamental image representation. However, such invariant representations typically exhibit limited discriminability, limiting their applications in larger-scale trustworthy vision tasks. For this open problem, we conduct a systematic investigation of hierarchical invariance, exploring this topic from theoretical, practical, and application perspectives. At the theoretical level, we show how to construct over-complete invariants with a Convolutional Neural Networks (CNN)-like hierarchical architecture yet in a fully interpretable manner. The general blueprint, specific definitions, invariant properties, and numerical implementations are provided. At the practical level, we discuss how to customize this theoretical framework into a given task. With the over-completeness, discriminative features w.r. t. the task can be adaptively formed in a Neural Architecture Search (NAS)-like manner. We demonstrate the above arguments with accuracy, invariance, and efficiency results on texture, digit, and parasite classification experiments. Furthermore, at the application level, our representations are explored in real-world forensics tasks on adversarial perturbations and Artificial Intelligence Generated Content (AIGC). Such applications reveal that the proposed strategy not only realizes the theoretically promised invariance, but also exhibits competitive discriminability even in the era of deep learning. For robust and interpretable vision tasks at larger scales, hierarchical invariant representation can be considered as an effective alternative to traditional CNN and invariants.
Consistency-Guided Temperature Scaling Using Style and Content Information for Out-of-Domain Calibration

Research interests in the robustness of deep neural networks against domain shifts have been rapidly increasing in recent years. Most existing works, however, focus on improving the accuracy of the model, not the calibration performance which is another important requirement for trustworthy AI systems. Temperature scaling (TS), an accuracy-preserving post-hoc calibration method, has been proven to be effective in in-domain settings, but not in out-of-domain (OOD) due to the difficulty in obtaining a validation set for the unseen domain beforehand. In this paper, we propose consistency-guided temperature scaling (CTS), a new temperature scaling strategy that can significantly enhance the OOD calibration performance by providing mutual supervision among data samples in the source domains. Motivated by our observation that over-confidence stemming from inconsistent sample predictions is the main obstacle to OOD calibration, we propose to guide the scaling process by taking consistencies into account in terms of two different aspects - style and content - which are the key components that can well-represent data samples in multi-domain settings. Experimental results demonstrate that our proposed strategy outperforms existing works, achieving superior OOD calibration performance on various datasets. This can be accomplished by employing only the source domains without compromising accuracy, making our scheme directly applicable to various trustworthy AI systems.
Optimistic Information Directed Sampling

We study the problem of online learning in contextual bandit problems where the loss function is assumed to belong to a known parametric function class. We propose a new analytic framework for this setting that bridges the Bayesian theory of information-directed sampling due to Russo and Van Roy (2018) and the worst-case theory of Foster, Kakade, Qian, and Rakhlin (2021) based on the decision-estimation coefficient. Drawing from both lines of work, we propose a algorithmic template called Optimistic Information-Directed Sampling and show that it can achieve instance-dependent regret guarantees similar to the ones achievable by the classic Bayesian IDS method, but with the major advantage of not requiring any Bayesian assumptions. The key technical innovation of our analysis is introducing an optimistic surrogate model for the regret and using it to define a frequentist version of the Information Ratio of Russo and Van Roy (2018), and a less conservative version of the Decision Estimation Coefficient of Foster et al. (2021). Keywords: Contextual bandits, information-directed sampling, decision estimation coefficient, first-order regret bounds.
The Behavioural House Indicator: A faster and real time small-area indicative deprivation measure for England

Researchers have been long preoccupied with the measuring and monitoring of economic and social deprivation at small scales, neighbourhood, level in order to provide official government agencies and policy makers with more precise data insights. Whist valuable methodologies have been developed, the exercise of data collection associated with these methods tend to be expensive, time consuming, published infrequently with significant time delays, and subject to recurring changes to methodology. Here, we propose a novel method based on a straightforward methodology and data sources to generate a faster and real time indicator for deprivation at different scaling, small to larger areas. The results of our work show that our method provides a consistent view of deprivation across the regions of England and Wales, which are inline with the other indexes, but also highlight specific flash points of deep rural and highly dense urban deprivation areas that are not well captured by existing indexes. Our method is intended to aid researchers and policy makers by complementing existing but infrequent indexes.
Two new species of the echinoid genus Monostychia from the Miocene of Victoria and a redescription of M. etheridgei Tenison-Woods, 1877

Sadler, T. , Holmes, F.C. , & Gallagher, S.J., 8 January 2019. Two new species of the echinoid genus Monostychia from the Miocene of Victoria and a redescription of M. etheridgei Tenison-Woods, 1877. Alcheringa 43, 279–290. ISSN 0311-5518. Two new species of the clypeasteroid Monostychia Laube, 1869, are described; M. merrimanensis sp. nov. from the East Gippsland region of Victoria and M. glenelgensis sp. nov. from the Gambier Embayment of southwestern Victoria. M. etheridgei Tenison-Woods, 1877, from northern Tasmania, which closely resembles M. merrimanensis sp. nov., is redescribed. A comparison is also made between M. elongata Duncan, 1877, and M. glenelgensis, as both are present in the same strata. The new taxa differ from previously described Monostychia species in size and shape and in the number of post-basicoronal plates on the oral surface. It is concluded that the use of oral plate counts and their variation across a population may be diagnostically useful at species level, particularly those of the paired interambulacra and the unpaired ambulacrum III. Tony Sadler* [t.sadler@student.unimelb.edu.au] Earth Sciences, The University of Melbourne, Melbourne, 2010 Australia; Francis C. Holmes [fholmes@bigpond.net. au] Invertebrate Palaeontology, Museum Victoria, Melbourne, Victoria, 3001 Australia; Stephen J. Gallagher [sjgall@unimelb.edu.au] School of Earth Sciences, The University of Melbourne, Melbourne, 3010 Australia.
Distributionally Robust Off-Dynamics Reinforcement Learning: Provable Efficiency with Linear Function Approximation

We study off-dynamics Reinforcement Learning (RL), where the policy is trained on a source domain and deployed to a distinct target domain. We aim to solve this problem via online distributionally robust Markov decision processes (DRMDPs), where the learning algorithm actively interacts with the source domain while seeking the optimal performance under the worst possible dynamics that is within an uncertainty set of the source domain's transition kernel. We provide the first study on online DRMDPs with function approximation for off-dynamics RL. We find that DRMDPs' dual formulation can induce nonlinearity, even when the nominal transition kernel is linear, leading to error propagation. By designing a $d$-rectangular uncertainty set using the total variation distance, we remove this additional nonlinearity and bypass the error propagation. We then introduce DR-LSVI-UCB, the first provably efficient online DRMDP algorithm for off-dynamics RL with function approximation, and establish a polynomial suboptimality bound that is independent of the state and action space sizes. Our work makes the first step towards a deeper understanding of the provable efficiency of online DRMDPs with linear function approximation. Finally, we substantiate the performance and robustness of DR-LSVI-UCB through different numerical experiments.
Farm-based anaerobic digesters as an energy and odor control technology: Background and policy issues

This report summarizes the existing literature and analytical perspectives on farm-based digesters, highlights major efforts in the United States and Europe to expand digester usage, and discusses key policy issues affecting digester economics. The study was largely a review of the “gray literature” on digesters, and it serves as a snapshot overview of the industry. Digesters are fairly capital-intensive when viewed primarily as an energy source. On a strictly market basis, current U.S. average electricity prices do not appear to provide suffi cient economic justifi cation for digesters to move beyond a fairly limited niche. Digesters make the most sense today where the odor and nutrient management benefi ts are important, or where the electricity or heat has a higher-than-average value. Digester biogas is mainly methane, which is destroyed when fl ared or used for electricity. This methane destruction is benefi cial in terms of climate change. The associated carbon credits may become a more signifi cant farm revenue source in the future.
Causal Graph Discovery with Retrieval-Augmented Generation based Large Language Models

Causal graph recovery is essential in the field of causal inference. Traditional methods are typically knowledge-based or statistical estimation-based, which are limited by data collection biases and individuals' knowledge about factors affecting the relations between variables of interests. The advance of large language models (LLMs) provides opportunities to address these problems. We propose a novel method that utilizes the extensive knowledge contained within a large corpus of scientific literature to deduce causal relationships in general causal graph recovery tasks. This method leverages Retrieval Augmented-Generation (RAG) based LLMs to systematically analyze and extract pertinent information from a comprehensive collection of research papers. Our method first retrieves relevant text chunks from the aggregated literature. Then, the LLM is tasked with identifying and labelling potential associations between factors. Finally, we give a method to aggregate the associational relationships to build a causal graph. We demonstrate our method is able to construct high quality causal graphs on the well-known SACHS dataset solely from literature.
Turbulent flows over porous and rough substrates

Turbulent flows over porous substrates are studied via a systematic exploration of the dependence of the flow properties on the substrate parameters, including permeability $K$, grain size $L$, and depth $h$. The study uses direct numerical simulations for staggered-cube substrates with $L^+\approx10$ - $50$, $\sqrt{K}/L\approx0.01$ - $0.25$, and depths from $h=O(L)$ to $h\gg L$, ranging from typical impermeable rough surfaces to deep porous substrates. The results indicate that the permeability has significantly greater relevance than the grain size for the properties of the overlying flow, including the mean-flow slip and the shear across the interface, the drag increase relative to smooth-wall flow, and the statistics and spectra of the overlying turbulence, whereas the direct effect of grain size is only noticeable near the interface as grain-coherent flow fluctuations. The substrate depth also has a significant effect, with shallower substrates suppressing the effective transpiration at the interface excited by pressure fluctuations. We propose an empirical `equivalent permeability' $K_{eq}^t$, that incorporates this effect and scales well the overlying turbulence for substrates with different depths. Based on this, we propose a conceptual $h^+$-$\sqrt{K^+}$ regime diagram where turbulence transitions smoothly from that over impermeable rough surfaces with $h=O(L)$ to that over deep porous substrates with $h^+\gtrsim50$, with the latter limit determined by the typical lengthscale of the overlying pressure fluctuations.
A Fast Direct Solver for Elliptic PDEs on a Hierarchy of Adaptively Refined Quadtrees

We describe a fast, direct solver for elliptic partial differential equations on a two-dimensional hierarchy of adaptively refined, Cartesian meshes. Our solver, inspired by the Hierarchical Poincar\'e-Steklov (HPS) method introduced by Gillman and Martinsson (SIAM J. Sci. Comput., 2014) uses fast solvers on locally uniform Cartesian patches stored in the leaves of a quadtree and is the first such solver that works directly with the adaptive quadtree mesh managed using the grid management library \pforest (C. Burstedde, L. Wilcox, O. Ghattas, SIAM J. Sci. Comput. 2011). Within each Cartesian patch, stored in leaves of the quadtree, we use a second order finite volume discretization on cell-centered meshes. Key contributions of our algorithm include 4-to-1 merge and split implementations for the HPS build stage and solve stage, respectively. We demonstrate our solver on Poisson and Helmholtz problems with a mesh adapted to the high local curvature of the right-hand side.
Ill-posedness and global solution for the $b$-equation

In this paper, we consider the Cauchy problem for the $b$-equation. Firstly, for $s>\frac32,$ if $u_{0}(x)\in H^{s}(\mathbb{R})$ and $m_{0}(x)=u_{0}(x)-u_{0xx}(x)\in L^{1}(\mathbb{R}),$ the global solutions of the $b$-equation is established when $b\geq1$ or $b\leq1. $ It's worth noting that our global result is a new result which doesn't need the condition that $m_{0}(x)$ keeps its sign. For $s<\frac32,$ it is shown (see [13]) that the Cauchy problem of the $b$-equation is ill-posed in Sobolev space $H^{s}(\mathbb{R})$ when $b>1$ or $b<1. $ In the present paper, for $s=\frac32,$ we prove that the Cauchy problem of the $b$-equation is also ill-posed in $H^{\frac32}(\mathbb{R})$ in the sense of norm inflation by constructing a class of special initial data when $b\neq1. $
Non-Invertible Duality Interfaces in Field Theories with Exotic Symmetries

In recent years, the concept of global symmetry has generalized considerably. Two dramatic examples of this generalization are the exotic symmetries that govern theories with fractons and non-invertible symmetries, which do not fuse according to a group law. Only recently has the interplay between these two been examined. In this paper, we provide further examples of the interplay in the XY plaquette model, XY cube model, 1+1 d theory with global dipole symmetry, and the 2+1 d Lifshitz theory. They are analogs of the duality symmetries in 2d CTFs and are constructed by first gauging a finite subgroup of the momentum symmetry on half of spacetime and then performing a duality transformation. We analyze the fusion rules of the symmetries and find that they are condensation defects from an analog of higher gauging exotic symmetries. We also address their dependence on the UV cutoff when relevant.
Fine-tuning Large Language Models for Domain-specific Machine Translation

Large language models (LLMs) have made significant progress in machine translation (MT). However, their potential in domain-specific MT remains under-explored. Current LLM-based MT systems still face several challenges. First, for LLMs with in-context learning, their effectiveness is highly sensitive to input translation examples, and processing them can increase inference costs. They often require extra post-processing due to over-generation. Second, LLMs with fine-tuning on domain-specific data often require high training costs for domain adaptation, and may weaken the zero-shot MT capabilities of LLMs due to over-specialization. The aforementioned methods can struggle to translate rare words in domain transfer scenarios. To address these challenges, this paper proposes a prompt-oriented fine-tuning method, denoted as LlamaIT, to effectively and efficiently fine-tune a general-purpose LLM for domain-specific MT tasks. First, we construct a task-specific mix-domain dataset, which is then used to fine-tune the LLM with LoRA. This can eliminate the need for input translation examples, post-processing, or over-specialization. By zero-shot prompting with instructions, we adapt the MT tasks to the target domain at inference time. To further elicit the MT capability for rare words, we construct new prompts by incorporating domain-specific bilingual vocabulary. We also conduct extensive experiments on both publicly available and self-constructed datasets. The results show that our LlamaIT can significantly enhance the domain-specific MT capabilities of the LLM, meanwhile preserving its zero-shot MT capabilities.
Investigation of Travel Behaviour of Visitors to Scotland

Tourism in Scotland is both an important and extensive land use and a major contributor to Gross Domestic Product. In 2005, it is estimated that Scotland received around 10.5 million visitors from outside Scotland. Just over 76% of the visits originated in the rest of the United Kingdom, with the remainder having an international origin. Tourism relies heavily on passenger transport both to access the destination, but also to travel around within it. However, there has been a lack of attention to the internal accessibility of Scotland from the visitor perspective. Whilst some attempts have been suggested and prioritised for facilitating tourists' travel around Scotland, such efforts are mainly undertaken by tourism organisations throughout Scotland, whose ultimate power to enable changes to transport systems is largely limited to lobbying. Moreover, without a clear picture of how accessible Scotland is internally as a destination, or of the transport demands of visitors in terms of internal accessibility, any measures taken to enhance visitor transportation remain largely uninformed. How tourists travel around Scotland, the extent to which they are reliant on public transport and the importance of existing transport provision in their travel behaviour and experience of the destination, including the areas they ultimately visit, merits further clarification. To this end, this study was commissioned by the Transport Department of The Scottish Executive to provide an overview of existing research into the travel behaviour of visitors to Scotland. The principal aim of the study was to review and collate existing sources of information on the use of transport by those visiting Scotland for leisure, recreation and business purposes. In conjunction with the objectives of the Scottish Executive, a thorough review of the literature and secondary data sources pertaining to the use of transport by visitors to Scotland for leisure, tourism and business purposes was conducted.
Iteration and Stochastic First-order Oracle Complexities of Stochastic Gradient Descent using Constant and Decaying Learning Rates

The performance of stochastic gradient descent (SGD), which is the simplest first-order optimizer for training deep neural networks, depends on not only the learning rate but also the batch size. They both affect the number of iterations and the stochastic first-order oracle (SFO) complexity needed for training. In particular, the previous numerical results indicated that, for SGD using a constant learning rate, the number of iterations needed for training decreases when the batch size increases, and the SFO complexity needed for training is minimized at a critical batch size and that it increases once the batch size exceeds that size. Here, we study the relationship between batch size and the iteration and SFO complexities needed for nonconvex optimization in deep learning with SGD using constant or decaying learning rates and show that SGD using the critical batch size minimizes the SFO complexity. We also provide numerical comparisons of SGD with the existing first-order optimizers and show the usefulness of SGD using a critical batch size. Moreover, we show that measured critical batch sizes are close to the sizes estimated from our theoretical results.