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Augmenting Large Language Models (LLMs) with information retrieval capabilities (i.e., Retrieval-Augmented Generation (RAG)) has proven beneficial for knowledge-intensive tasks. However, understanding users' contextual search intent when generating responses is an understudied topic for conversational question answering (QA). This conversational extension leads to additional concerns when compared to single-turn QA as it is more challenging for systems to comprehend conversational context and manage retrieved passages over multiple turns. In this work, we propose a method for enabling LLMs to decide when to retrieve in RAG settings given a conversational context. When retrieval is deemed necessary, the LLM then rewrites the conversation for passage retrieval and judges the relevance of returned passages before response generation. Operationally, we build on the single-turn SELF-RAG framework (Asai et al., 2023) and propose SELF-multi-RAG for conversational settings. SELF-multi-RAG demonstrates improved capabilities over single-turn variants with respect to retrieving relevant passages (by using summarized conversational context) and assessing the quality of generated responses. Experiments on three conversational QA datasets validate the enhanced response generation capabilities of SELF-multi-RAG, with improvements of ~13% measured by human annotation., Comment: Accepted in EMNLP (findings) 2024

Current instruction-tuned language models are exclusively trained with textual preference data and thus are often not aligned with the unique requirements of other modalities, such as speech. To better align language models with the speech domain, we explore (i) prompting strategies grounded in radio-industry best practices and (ii) preference learning using a novel speech-based preference data of 20K samples, generated with a wide spectrum of prompts that induce varying dimensions of speech-suitability and labeled by annotators who listen to response pairs. Both human and automatic evaluation show that both prompting and preference learning increase the speech-suitability of popular instruction-tuned LLMs. Interestingly, we find that prompting and preference learning can be additive; combining them achieves the best win rates in head-to-head comparison, resulting in responses that are preferred or tied to the base model in 76.2% of comparisons on average. Lastly, we share lexical, syntactical, and qualitative analyses to showcase how each method contributes to improving the speech-suitability of generated responses., Comment: EMNLP2024

API call generation is the cornerstone of large language models' tool-using ability that provides access to the larger world. However, existing supervised and in-context learning approaches suffer from high training costs, poor data efficiency, and generated API calls that can be unfaithful to the API documentation and the user's request. To address these limitations, we propose an output-side optimization approach called FANTASE. Two of the unique contributions of FANTASE are its State-Tracked Constrained Decoding (SCD) and Reranking components. SCD dynamically incorporates appropriate API constraints in the form of Token Search Trie for efficient and guaranteed generation faithfulness with respect to the API documentation. The Reranking component efficiently brings in the supervised signal by leveraging a lightweight model as the discriminator to rerank the beam-searched candidate generations of the large language model. We demonstrate the superior performance of FANTASE in API call generation accuracy, inference efficiency, and context efficiency with DSTC8 and API Bank datasets.

Representation learning is a powerful tool that enables learning over large multitudes of agents or domains by enforcing that all agents operate on a shared set of learned features. However, many robotics or controls applications that would benefit from collaboration operate in settings with changing environments and goals, whereas most guarantees for representation learning are stated for static settings. Toward rigorously establishing the benefit of representation learning in dynamic settings, we analyze the regret of multi-task representation learning for linear-quadratic control. This setting introduces unique challenges. Firstly, we must account for and balance the $\textit{misspecification}$ introduced by an approximate representation. Secondly, we cannot rely on the parameter update schemes of single-task online LQR, for which least-squares often suffices, and must devise a novel scheme to ensure sufficient improvement. We demonstrate that for settings where exploration is "benign", the regret of any agent after $T$ timesteps scales as $\tilde O(\sqrt{T/H})$, where $H$ is the number of agents. In settings with "difficult" exploration, the regret scales as $\tilde O(\sqrt{d_u d_\theta} \sqrt{T} + T^{3/4}/H^{1/5})$, where $d_x$ is the state-space dimension, $d_u$ is the input dimension, and $d_\theta$ is the task-specific parameter count. In both cases, by comparing to the minimax single-task regret $O(\sqrt{d_x d_u^2}\sqrt{T})$, we see a benefit of a large number of agents. Notably, in the difficult exploration case, by sharing a representation across tasks, the effective task-specific parameter count can often be small $d_\theta < d_x d_u$. Lastly, we provide numerical validation of the trends we predict.

In this paper, we investigate which questions are challenging for retrieval-based Question Answering (QA). We (i) propose retrieval complexity (RC), a novel metric conditioned on the completeness of retrieved documents, which measures the difficulty of answering questions, and (ii) propose an unsupervised pipeline to measure RC given an arbitrary retrieval system. Our proposed pipeline measures RC more accurately than alternative estimators, including LLMs, on six challenging QA benchmarks. Further investigation reveals that RC scores strongly correlate with both QA performance and expert judgment across five of the six studied benchmarks, indicating that RC is an effective measure of question difficulty. Subsequent categorization of high-RC questions shows that they span a broad set of question shapes, including multi-hop, compositional, and temporal QA, indicating that RC scores can categorize a new subset of complex questions. Our system can also have a major impact on retrieval-based systems by helping to identify more challenging questions on existing datasets., Comment: Accepted to ACL 2024 (findings)

In arXiv:2404.19088, we initiated a program linking birational invariants with smooth ones and offering new interpretations of classical invariants, such as the Kervaire-Milnor invariants. Here, we rely on the profound geometric reasoning provided by Lupercio and Uribe in the early 00s to establish a connection between Chen-Ruan cohomology and several $G$-birational invariants introduced in the pioneering works Kontsevich, Kresch, Pestun, Tschinkel, along with presenting applications. Combined with the theory of atoms by Katzarkov, Kontsevich, Pantev, and Yu, the proposal in this paper program will lead to a theory of equivariant atoms., Comment: a) Clarified what kind of group actions we are considering. b) Recalled birationality for Deligne-Mumford (DM) stacks and explained how they still contain information on finite group actions. c) Explained the role of gerbes in twisting Chen-Ruan cohomology and presented details on how they can be useful in obstructing birational types of certain DM stacks. 32 pages. 1 Appendix

We address the problem of designing an LQR controller in a distributed setting, where M similar but not identical systems share their locally computed policy gradient (PG) estimates with a server that aggregates the estimates and computes a controller that, on average, performs well on all systems. Learning in a distributed setting has the potential to offer statistical benefits - multiple datasets can be leveraged simultaneously to produce more accurate policy gradient estimates. However, the interplay of heterogeneous trajectory data and varying levels of local computational power introduce bias to the aggregated PG descent direction, and prevents us from fully exploiting the parallelism in the distributed computation. The latter stems from synchronous aggregation, where straggler systems negatively impact the runtime. To address this, we propose an asynchronous policy gradient algorithm for LQR control design. By carefully controlling the "staleness" in the asynchronous aggregation, we show that the designed controller converges to each system's $\epsilon$-near optimal controller up to a heterogeneity bias. Furthermore, we prove that our asynchronous approach obtains exact local convergence at a sub-linear rate., Comment: Leonardo F. Toso and Han Wang contributed equally to this work

At the heart of the Pyramid evaluation method for text summarization lie human written summary content units (SCUs). These SCUs are concise sentences that decompose a summary into small facts. Such SCUs can be used to judge the quality of a candidate summary, possibly partially automated via natural language inference (NLI) systems. Interestingly, with the aim to fully automate the Pyramid evaluation, Zhang and Bansal (2021) show that SCUs can be approximated by automatically generated semantic role triplets (STUs). However, several questions currently lack answers, in particular: i) Are there other ways of approximating SCUs that can offer advantages? ii) Under which conditions are SCUs (or their approximations) offering the most value? In this work, we examine two novel strategies to approximate SCUs: generating SCU approximations from AMR meaning representations (SMUs) and from large language models (SGUs), respectively. We find that while STUs and SMUs are competitive, the best approximation quality is achieved by SGUs. We also show through a simple sentence-decomposition baseline (SSUs) that SCUs (and their approximations) offer the most value when ranking short summaries, but may not help as much when ranking systems or longer summaries., Comment: 10 Pages, 3 Figures, 3 Tables, camera ready version accepted at NAACL 2024

Since the advent of new pairwise non-diffeomorphic structures on smooth manifolds, it has been questioned whether two topologically identical manifolds could admit different geometries. Not surprisingly, physicists have wondered whether a smooth structure assumption different from some classical known models could produce different physical meanings. In this paper, we inaugurate a very computational manner to produce physical models on classical and exotic spheres that can be built equivariantly, such as the classical Gromoll--Meyer exotic spheres. As first applications, we produce Lorentzian metrics on homeomorphic but not diffeomorphic manifolds that enjoy the same physical properties, such as geodesic completeness, positive Ricci curvature, and compatible time orientation. These constructions can be pulled back to higher models, such as exotic ten spheres bounding spin manifolds, to be approached in forthcoming papers., Comment: Accepted paper. To appear in Differential Geometry and its Applications

The interplay between electronic and intramolecular high-frequency vibrational degrees of freedom is ubiquitous in natural light-harvesting systems. Recent studies have indicated that an intramolecular vibrational donor-acceptor frequency difference can enhance energy transport. Here, we analyze the extent to which different intramolecular donor-acceptor vibrational frequencies affect excitation energy transport in equilibrium (coherent light excitation) and the more natural nonequilibrium steady state (incoherent light excitation) configurations. It is found that if the Huang-Rhys factors remain constant, the acceptor population increases when the intramolecular vibrational frequency of the acceptor exceeds that of the donor. The increase in the acceptor population due to the vibrational frequency difference is higher for higher values of the Huang-Rhys factors or the vibronic coupling strengths. However, the nonequilibrium steady state results show that the vibrational donor-acceptor frequency difference does not significantly enhance energy transport in the natural scenario of incoherent light excitation and under biologically relevant parameters. Insight about a potential mechanism to optimize energy transfer in the NESS based on increasing the harvesting time at the reaction center is analyzed., Comment: 22 pages, 4 figures

This paper explores the existence and properties of \emph{basic} eigenvalues and eigenfunctions associated with the Riemannian Laplacian on closed, connected Riemannian manifolds featuring an effective isometric action by a compact Lie group. Our primary focus is on investigating the potential existence of homeomorphic yet not diffeomorphic smooth manifolds that can accommodate invariant metrics sharing common basic spectra. We establish the occurrence of such scenarios for specific homotopy spheres and connected sums. Moreover, the developed theory demonstrates that the ring of invariant admissible scalar curvature functions fails to recover the smooth structure in many examples. We show the existence of homotopy spheres with identical rings of invariant scalar curvature functions, irrespective of the underlying smooth structure., Comment: Accepted version. To appear in Advanced Nonlinear Studies

We investigate the problem of learning linear quadratic regulators (LQR) in a multi-task, heterogeneous, and model-free setting. We characterize the stability and personalization guarantees of a policy gradient-based (PG) model-agnostic meta-learning (MAML) (Finn et al., 2017) approach for the LQR problem under different task-heterogeneity settings. We show that our MAML-LQR algorithm produces a stabilizing controller close to each task-specific optimal controller up to a task-heterogeneity bias in both model-based and model-free learning scenarios. Moreover, in the model-based setting, we show that such a controller is achieved with a linear convergence rate, which improves upon sub-linear rates from existing work. Our theoretical guarantees demonstrate that the learned controller can efficiently adapt to unseen LQR tasks.

Polaritonic chemistry has ushered in new avenues for controlling molecular dynamics. However, two key questions remain: (i) Can classical light sources elicit the same effects as certain quantum light sources on molecular systems? (ii) Can semiclassical treatments of light-matter interaction capture nontrivial quantum effects observed in molecular dynamics? This work presents a quantum-classical approach addressing issues of realizing cavity chemistry effects without actual cavities. It also highlights the limitations of the standard semiclassical light-matter interaction. It is demonstrated that classical light sources can mimic quantum effects up to the second order of light-matter interaction, provided that the mean-field contribution, symmetrized two-time correlation function, and the linear response function are the same in both situations. Numerical simulations show that the quantum-classical method aligns more closely with exact quantum molecular-only dynamics for quantum light states such as Fock states, superpositions of Fock states, and vacuum squeezed states than the conventional semiclassical approach., Comment: 31 pages, 4 figures

A singular foliation $\mathcal{F}$ on a complete Riemannian manifold $M$ is called Singular Riemannian foliation (SRF for short) if its leaves are locally equidistant, e.g., the partition of $M$ into orbits of an isometric action. In this paper, we investigate variational problems in compact Riemannian manifolds equipped with SRF with special properties, e.g. isoparametric foliations, SRF on fibers bundles with Sasaki metric, and orbit-like foliations. More precisely, we prove two results analogous to Palais' Principle of Symmetric Criticality, one is a general principle for $\mathcal{F}$ symmetric operators on the Hilbert space $W^{1,2}(M)$, the other one is for $\mathcal{F}$ symmetric integral operators on the Banach spaces $W^{1,p}(M)$. These results together with a $\mathcal{F}$ version of Rellich Kondrachov Hebey Vaugon Embedding Theorem allow us to circumvent difficulties with Sobolev's critical exponents when considering applications of Calculus of Variations to find solutions to PDEs. To exemplify this we prove the existence of weak solutions to a class of variational problems which includes $p$-Kirschoff problems., Comment: 54 pages

Readability refers to how easily a reader can understand a written text. Several factors affect the readability level, such as the complexity of the text, its subject matter, and the reader's background knowledge. Generating summaries based on different readability levels is critical for enabling knowledge consumption by diverse audiences. However, current text generation approaches lack refined control, resulting in texts that are not customized to readers' proficiency levels. In this work, we bridge this gap and study techniques to generate summaries at specified readability levels. Unlike previous methods that focus on a specific readability level (e.g., lay summarization), we generate summaries with fine-grained control over their readability. We develop three text generation techniques for controlling readability: (1) instruction-based readability control, (2) reinforcement learning to minimize the gap between requested and observed readability and (3) a decoding approach that uses lookahead to estimate the readability of upcoming decoding steps. We show that our generation methods significantly improve readability control on news summarization (CNN/DM dataset), as measured by various readability metrics and human judgement, establishing strong baselines for controllable readability in summarization., Comment: Accepted as an EMNLP 2023 main paper

We investigate the problem of learning an $\epsilon$-approximate solution for the discrete-time Linear Quadratic Regulator (LQR) problem via a Stochastic Variance-Reduced Policy Gradient (SVRPG) approach. Whilst policy gradient methods have proven to converge linearly to the optimal solution of the model-free LQR problem, the substantial requirement for two-point cost queries in gradient estimations may be intractable, particularly in applications where obtaining cost function evaluations at two distinct control input configurations is exceptionally costly. To this end, we propose an oracle-efficient approach. Our method combines both one-point and two-point estimations in a dual-loop variance-reduced algorithm. It achieves an approximate optimal solution with only $O\left(\log\left(1/\epsilon\right)^{\beta}\right)$ two-point cost information for $\beta \in (0,1)$.

We study a model-free federated linear quadratic regulator (LQR) problem where M agents with unknown, distinct yet similar dynamics collaboratively learn an optimal policy to minimize an average quadratic cost while keeping their data private. To exploit the similarity of the agents' dynamics, we propose to use federated learning (FL) to allow the agents to periodically communicate with a central server to train policies by leveraging a larger dataset from all the agents. With this setup, we seek to understand the following questions: (i) Is the learned common policy stabilizing for all agents? (ii) How close is the learned common policy to each agent's own optimal policy? (iii) Can each agent learn its own optimal policy faster by leveraging data from all agents? To answer these questions, we propose a federated and model-free algorithm named FedLQR. Our analysis overcomes numerous technical challenges, such as heterogeneity in the agents' dynamics, multiple local updates, and stability concerns. We show that FedLQR produces a common policy that, at each iteration, is stabilizing for all agents. We provide bounds on the distance between the common policy and each agent's local optimal policy. Furthermore, we prove that when learning each agent's optimal policy, FedLQR achieves a sample complexity reduction proportional to the number of agents M in a low-heterogeneity regime, compared to the single-agent setting.

A powerful concept behind much of the recent progress in machine learning is the extraction of common features across data from heterogeneous sources or tasks. Intuitively, using all of one's data to learn a common representation function benefits both computational effort and statistical generalization by leaving a smaller number of parameters to fine-tune on a given task. Toward theoretically grounding these merits, we propose a general setting of recovering linear operators $M$ from noisy vector measurements $y = Mx + w$, where the covariates $x$ may be both non-i.i.d. and non-isotropic. We demonstrate that existing isotropy-agnostic representation learning approaches incur biases on the representation update, which causes the scaling of the noise terms to lose favorable dependence on the number of source tasks. This in turn can cause the sample complexity of representation learning to be bottlenecked by the single-task data size. We introduce an adaptation, $\texttt{De-bias & Feature-Whiten}$ ($\texttt{DFW}$), of the popular alternating minimization-descent scheme proposed independently in Collins et al., (2021) and Nayer and Vaswani (2022), and establish linear convergence to the optimal representation with noise level scaling down with the $\textit{total}$ source data size. This leads to generalization bounds on the same order as an oracle empirical risk minimizer. We verify the vital importance of $\texttt{DFW}$ on various numerical simulations. In particular, we show that vanilla alternating-minimization descent fails catastrophically even for iid, but mildly non-isotropic data. Our analysis unifies and generalizes prior work, and provides a flexible framework for a wider range of applications, such as in controls and dynamical systems., Comment: Appeared at ICLR 2024 (spotlight presentation)

The quasi-random discrete ordinates method (QRDOM) is here proposed for the approximation of transport problems. Its central idea is to explore a quasi Monte Carlo integration within the classical source iteration technique. It preserves the main characteristics of the discrete ordinates method, but it has the advantage of providing mitigated ray effect solutions. The QRDOM is discussed in details for applications to one-group transport problems with isotropic scattering in rectangular domains. The method is tested against benchmark problems for which DOM solutions are known to suffer from the ray effects. The numerical experiments indicate that the QRDOM provides accurate results and it demands less discrete ordinates per source iteration when compared against the classical DOM., Comment: 15 pages, 5 figures

The quasi-random discrete ordinates method (QRDOM) is here proposed for the approximation of transport problems. Its central idea is to explore a quasi Monte Carlo integration within the classical source iteration technique. It preserves the main characteristics of the discrete ordinates method, but it has the advantage of providing mitigated ray effect solutions. The QRDOM is discussed in details for applications to one-group transport problems with isotropic scattering in rectangular domains. The method is tested against benchmark problems for which DOM solutions are known to suffer from the ray effects. The numerical experiments indicate that the QRDOM provides accurate results and it demands less discrete ordinates per source iteration when compared against the classical DOM., Comment: 14 pages, 6 figures

The family of invariant Riemannian manifolds in the Wallach flag manifold $\mathrm{SU}(3)/\mathrm{T}^2$ is described by three parameters $(x,y,z)$ of positive real numbers. By restricting such a family of metrics in the \emph{tetrahedron} $\cal{T}:= x+y+z = 1$, in this paper, we describe all regions $\cal R \subset \cal T$ admitting metrics with curvature properties varying from positive sectional curvature to positive scalar curvature, including positive intermediate curvature notion's. We study the dynamics of such regions under the \emph{projected Ricci flow} in the plane $(x,y)$, concluding sign curvature maintenance and escaping. In addition, we obtain some results for positive intermediate Ricci curvature for a path of metrics on fiber bundles over $\mathrm{SU}(3)/\mathrm{T}^2$, further studying its evolution under the Ricci flow on the base., Comment: 15 pages, 12 figures. arXiv admin note: text overlap with arXiv:2305.06119

Long-horizon task planning is essential for the development of intelligent assistive and service robots. In this work, we investigate the applicability of a smaller class of large language models (LLMs), specifically GPT-2, in robotic task planning by learning to decompose tasks into subgoal specifications for a planner to execute sequentially. Our method grounds the input of the LLM on the domain that is represented as a scene graph, enabling it to translate human requests into executable robot plans, thereby learning to reason over long-horizon tasks, as encountered in the ALFRED benchmark. We compare our approach with classical planning and baseline methods to examine the applicability and generalizability of LLM-based planners. Our findings suggest that the knowledge stored in an LLM can be effectively grounded to perform long-horizon task planning, demonstrating the promising potential for the future application of neuro-symbolic planning methods in robotics., Comment: 21 pages, 6 figures

In this note, we show that the classical Wallach manifold $\mathrm{SU}(3)/\mathrm{T}^2$-admits metrics of positive intermediate Ricci curvature $(\mathrm{Ric}_d >0)$ for $d = 1, 2, 3, 4, 5$ that lose these properties under the homogeneous Ricci flow for $d=1, 2, 3, 5$. We make the same analyses to the family of Riemannian flag manifolds $\mathrm{SU}(m+2p)/\mathrm{S}(\mathrm{U}(m)\times\mathrm{U}(p)\times \mathrm{U}(p))$, concluding similar results. These explicitly verify some claims expected to be true among experts (see \cite{BW}) for positive Ricci curvature and intermediate positive Ricci curvature. Our technique is only possible due to the global behavior understanding of the homogeneous Ricci flow for invariant metrics on these manifolds., Comment: Accepted version. To appear in the Special Issue of the Workshop on Geometric Structures and Moduli Spaces (WGSMS). Revista Matem\'atica Contempor\^anea

We address the problem of learning linear system models from observing multiple trajectories from different system dynamics. This framework encompasses a collaborative scenario where several systems seeking to estimate their dynamics are partitioned into clusters according to their system similarity. Thus, the systems within the same cluster can benefit from the observations made by the others. Considering this framework, we present an algorithm where each system alternately estimates its cluster identity and performs an estimation of its dynamics. This is then aggregated to update the model of each cluster. We show that under mild assumptions, our algorithm correctly estimates the cluster identities and achieves an approximate sample complexity that scales inversely with the number of systems in the cluster, thus facilitating a more efficient and personalized system identification process.

This paper is concerned with the study of the fractional finite sums theory. We present the classes of functions for which it is possible to characterize the constant related to the derivative of fractional sums (denominated by essence of a function). Examples of the essences of functions are presented, including the Bernoulli numbers, which are obtained as essences of the functions $f(x)=x^a$, $a \in \mathbb{N}^*$. Based on the new results, we can expand the comprehension of the Euler-Maclaurin summation formula for a real number instead of only considering natural numbers. Moreover, we utilize the concept of the essence of a function to propose a new regularization method for divergent series., Comment: 26 pages, 1 figure

We realize specific classical symmetric spaces, like the semi-K\"ahler symmetric spaces discovered by Berger, as cotangent bundles of symmetric flag manifolds. These realizations enable us to describe these cotangent bundles' geodesics and Lagrangian submanifolds. As a final application, we present the first examples of vector bundles over simply connected manifolds with nonnegative curvature that cannot accommodate metrics with nonnegative sectional curvature, even though their associated unit sphere bundles can indeed accommodate such metrics. Our examples are derived from explicit bundle constructions over symmetric flag spaces., Comment: accepted version. To appear in Revista Matem\'atica Complutense

In this work, a multifractal framework is proposed to investigate the effects of current sheets in solar wind turbulence. By using multifractal detrended fluctuation analysis coupled with surrogate methods and volatility, two solar wind magnetic field time series are investigated, one with current sheets and one without current sheets. Despite the lack of extreme-events intermittent bursts in the current sheet-free series, both series are shown to be strongly multifractal, although the current sheet-free series displays an almost linear behavior for the scaling exponent of structure functions. Long-range correlations are shown to be the main source of multifractality for the series without current sheets, while a combination of heavy-tail distribution and nonlinear correlations are responsible for multifractality in the series with current sheets. The multifractality in both time series is formally shown to be associated with an energy-cascade process using the p-model., Comment: Accepted by MNRAS

Oscillations in time-dependent 2D electronic spectra appear as evidence of quantum coherence in light-harvesting systems related to electronic-vibrational resonant interactions. Nature, however, takes place in a non-equilibrium steady-state, so the relevance of these arguments to the natural process is unclear. Here we examine the role of intramolecular vibrations in the non-equilibrium steady-state of photosynthetic dimers in the natural scenario of incoherent light excitation. It is found that vibrations resonant with the energy difference between exciton states do not increase the quantum yield nor the imaginary part of the intersite coherence that is relevant for transport compared with non-resonant vibrations in the natural non-equilibrium steady state. That is, the vibration-electronic resonance interaction does not alter energy transport under natural incoherent-light excitation conditions., Comment: 24 pages, 6 figures

The motivation for this work stems from the authors' desire to revive the study of ``fat bundles''. Recently, several new works have emerged in this field, including \cite{DV2022, cavenaghilinollohann2, ovando1, ovando2, BOCHENSKI2016131}, while the most notable reference being W. Ziller's unpublished notes on fat bundles (\cite{Ziller_fatnessrevisited}). Given these developments, it is natural to revisit this topic, recalling known facts and furnishing a new perspective to the known results, despite obtaining new ones. One uses recent advances in positive curvatures to obtain a simple and geometric classification of fat homogeneous Riemannian foliations. Although B\'erard-Bergery established a similar classification in \cite{bergeryfat}, we believe one of the novelties of this paper lies in the combination of dual foliations and Ambrose--Singer's Theorem with metric deformations: motivated by the regularization properties of Cheeger deformations and the non-metric dependence of fatness, we show that: the vertical bundle of a fat submersion is obstructed, being wholly generated by the O'Neill tensor (this is a consequence of a dual-leaf argument); we prove that any fat foliation induced by the fibers of a fiber bundle with compact structure group is \emph{twisted} (any Riemannian submersion compatible metric has dual-foliation with only one dual leaf). We also prove that if the total space of a fat Riemannian submersion has non-negative sectional curvature, then their leaves are a symmetric space. We conclude further classification results., Comment: Major changes: the title was changed to reflect the new perspective of the paper. Results were added, proofs revisited, and exposition improved. Some results contained mistakes or imprecisions in their statements. This was also fixed

The appearance of dark sunspots over the solar photosphere is not considered to be symmetric between the northern and southern hemispheres. Among the different conclusions obtained by several authors, we can point out that the North-South asymmetry is a real and systematic phenomenon and is not due to random variability. In the present work, we selected the sunspot area data of a sample of 13 solar cycles divided by hemisphere extracted from the Marshall Space Flight Centre (MSFC) database to investigate the behavior of probability distributions using an out-of-equilibrium statistical model a.k.a non-extensive statistical mechanics. Based on this statistical framework, we obtained that the non-extensive entropic parameter $q$ has a semi-sinusoidal variation with a period of $\sim$22 year (Hale cycle). Among the most important results, we can highlight that the asymmetry index $q(A)$ revealed the dominance of the northern hemisphere against the southern one. Thus, we concluded that the parameter $q(A)$ can be considered an effective measure for diagnosing long-term variations of the solar dynamo. Finally, our study opens a new approach to investigating solar variability from the nonextensive perspective., Comment: 17 pages, 2 tables and 5 figures. Submitted to Solar Physics

We study the problem of learning a linear system model from the observations of $M$ clients. The catch: Each client is observing data from a different dynamical system. This work addresses the question of how multiple clients collaboratively learn dynamical models in the presence of heterogeneity. We pose this problem as a federated learning problem and characterize the tension between achievable performance and system heterogeneity. Furthermore, our federated sample complexity result provides a constant factor improvement over the single agent setting. Finally, we describe a meta federated learning algorithm, FedSysID, that leverages existing federated algorithms at the client level.

Pairing a lexical retriever with a neural re-ranking model has set state-of-the-art performance on large-scale information retrieval datasets. This pipeline covers scenarios like question answering or navigational queries, however, for information-seeking scenarios, users often provide information on whether a document is relevant to their query in form of clicks or explicit feedback. Therefore, in this work, we explore how relevance feedback can be directly integrated into neural re-ranking models by adopting few-shot and parameter-efficient learning techniques. Specifically, we introduce a kNN approach that re-ranks documents based on their similarity with the query and the documents the user considers relevant. Further, we explore Cross-Encoder models that we pre-train using meta-learning and subsequently fine-tune for each query, training only on the feedback documents. To evaluate our different integration strategies, we transform four existing information retrieval datasets into the relevance feedback scenario. Extensive experiments demonstrate that integrating relevance feedback directly in neural re-ranking models improves their performance, and fusing lexical ranking with our best performing neural re-ranker outperforms all other methods by 5.2 nDCG@20., Comment: Accepted at EMNLP 2022

Question Answering (QA) systems are increasingly deployed in applications where they support real-world decisions. However, state-of-the-art models rely on deep neural networks, which are difficult to interpret by humans. Inherently interpretable models or post hoc explainability methods can help users to comprehend how a model arrives at its prediction and, if successful, increase their trust in the system. Furthermore, researchers can leverage these insights to develop new methods that are more accurate and less biased. In this paper, we introduce SQuARE v2, the new version of SQuARE, to provide an explainability infrastructure for comparing models based on methods such as saliency maps and graph-based explanations. While saliency maps are useful to inspect the importance of each input token for the model's prediction, graph-based explanations from external Knowledge Graphs enable the users to verify the reasoning behind the model prediction. In addition, we provide multiple adversarial attacks to compare the robustness of QA models. With these explainability methods and adversarial attacks, we aim to ease the research on trustworthy QA models. SQuARE is available on https://square.ukp-lab.de., Comment: Accepted at AACL 2022 as Demo Paper