Miracle-dz/UniFAR-FTUs huggingface dataset:
Learning with a Mole: Transferable latent spatial representations for navigation without reconstruction

Agents navigating in 3D environments require some form of memory, which should hold a compact and actionable representation of the history of observations useful for decision taking and planning. In most end-to-end learning approaches the representation is latent and usually does not have a clearly defined interpretation, whereas classical robotics addresses this with scene reconstruction resulting in some form of map, usually estimated with geometry and sensor models and/or learning. In this work we propose to learn an actionable representation of the scene independently of the targeted downstream task and without explicitly optimizing reconstruction. The learned representation is optimized by a blind auxiliary agent trained to navigate with it on multiple short sub episodes branching out from a waypoint and, most importantly, without any direct visual observation. We argue and show that the blindness property is important and forces the (trained) latent representation to be the only means for planning. With probing experiments we show that the learned representation optimizes navigability and not reconstruction. On downstream tasks we show that it is robust to changes in distribution, in particular the sim2real gap, which we evaluate with a real physical robot in a real office building, significantly improving performance.
Control and Readout of a 13-level Trapped Ion Qudit

To implement useful quantum algorithms which demonstrate quantum advantage, we must scale currently demonstrated quantum computers up significantly. Leading platforms such as trapped ions face physical challenges in including more information carriers. A less explored avenue for scaling up the computational space involves utilizing the rich energy level structure of a trapped ion to encode multi-level qudits rather than two-level qubits. Here we show control and single-shot readout of qudits with up to 13 computational states, using protocols which can be extended directly to manipulate qudits of up to 25 levels in our chosen information host, $^{137}\text{Ba}^{+}$. This represents more than twice as many computational states per qudit compared with prior work in trapped ions. In addition to the preparation and readout protocols we demonstrate, universal quantum computation requires other quantum logic primitives such as entangling gates. These primitives have been demonstrated for lower qudit dimensions and can be directly generalized to the higher dimensions we employ. Hence, our advance opens an avenue towards using high-dimensional qudits for large-scale quantum computation. We anticipate efficiently utilizing available energy states in a trapped ion to play a significant and complementary role in tackling the challenge in scaling up the computational space of a trapped ion quantum computer. A qudit architecture also offers other practical benefits, which include affording relaxed fault tolerance thresholds for quantum error correction, providing an avenue for efficient quantum simulation of higher spin systems, and more efficient qubit gates.
Relativistic Phase Space Diffusion of Compact Object Binaries in Stellar Clusters and Hierarchical Triples

The LIGO/Virgo detections of compact object mergers have posed a challenge for theories of binary evolution and coalescence. One promising avenue for producing mergers dynamically is through secular eccentricity oscillations driven by an external perturber, be it a tertiary companion (as in the Lidov–Kozai, LK, mechanism) or the tidal field of the stellar cluster in which the binary orbits. The simplest theoretical models of these oscillations use a “doubly averaged” (DA) approximation, averaging both over the binary’s internal Keplerian orbit and its “outer” barycentric orbit relative to the perturber. However, DA theories do not account for fluctuations of the perturbing torque on the outer orbital timescale, which are known to increase a binary’s eccentricity beyond the maximum DA value, potentially accelerating mergers. Here we reconsider the impact of these short-timescale fluctuations in the test-particle quadrupolar limit for binaries perturbed by arbitrary spherical cluster potentials (including LK as a special case), in particular including 1pN general relativistic (GR) apsidal precession of the internal orbit. Focusing on the behavior of the binary orbital elements around peak eccentricity, we discover a new effect, relativistic phase space diffusion (RPSD), in which a binary can jump to a completely new dynamical trajectory on an outer orbital timescale, violating the approximate conservation of DA integrals of motion. RPSD arises from an interplay between secular behavior at extremely high eccentricity, short-timescale fluctuations, and rapid GR precession, and can change the subsequent secular evolution dramatically. This effect occurs even in hierarchical triples, but has not been uncovered until now.
Convergence and Diversity in the Control Hierarchy

Weir has defined a hierarchy of language classes whose second member (L2) is generated by tree-adjoining grammars (TAG), linear indexed grammars (LIG), combinatory categorial grammars, and head grammars. The hierarchy is obtained using the mechanism of control, and L2 is obtained using a context-free grammar (CFG) whose derivations are controlled by another CFG. We adapt Weir’s definition of a controllable CFG (called a labeled distinguished CFG) to give a definition of controllable pushdown automata (PDAs), called labeled distinguished PDAs. This yields three new characterizations of L2 as the class of languages generated by PDAs controlling PDAs, PDAs controlling CFGs, and CFGs controlling PDAs. We show that these four formalisms are not only weakly equivalent but equivalent in a stricter sense that we call d-weak equivalence. Furthermore, using an even stricter notion of equivalence called d-strong equivalence, we make precise the intuition that a CFG controlling a CFG is a TAG, a PDA controlling a PDA is an embedded PDA, and a PDA controlling a CFG is a LIG. The fourth member of this family, a CFG controlling a PDA, does not correspond to any kind of automaton we know of, so we invent one and call it a Pushdown Adjoining Automaton (PAA).
Interest-disclosing Mechanisms for Advertising are Privacy-Exposing (not Preserving)

Today, targeted online advertising relies on unique identifiers assigned to users through third-party cookies--a practice at odds with user privacy. While the web and advertising communities have proposed solutions that we refer to as interest-disclosing mechanisms, including Google's Topics API, an independent analysis of these proposals in realistic scenarios has yet to be performed. In this paper, we attempt to validate the privacy (i.e., preventing unique identification) and utility (i.e., enabling ad targeting) claims of Google's Topics proposal in the context of realistic user behavior. Through new statistical models of the distribution of user behaviors and resulting targeting topics, we analyze the capabilities of malicious advertisers observing users over time and colluding with other third parties. Our analysis shows that even in the best case, individual users' identification across sites is possible, as 0.4% of the 250k users we simulate are re-identified. These guarantees weaken further over time and when advertisers collude: 57% of users with stable interests are uniquely re-identified when their browsing activity has been observed for 15 epochs, increasing to 75% after 30 epochs. While measuring that the Topics API provides moderate utility, we also find that advertisers and publishers can abuse the Topics API to potentially assign unique identifiers to users, defeating the desired privacy guarantees. As a result, the inherent diversity of users' interests on the web is directly at odds with the privacy objectives of interest-disclosing mechanisms; we discuss how any replacement of third-party cookies may have to seek other avenues to achieve privacy for the web.
The Emergence of Essential Sparsity in Large Pre-trained Models: The Weights that Matter

Large pre-trained transformers are show-stealer in modern-day deep learning, and it becomes crucial to comprehend the parsimonious patterns that exist within them as they grow in scale. With exploding parameter counts, Lottery Ticket Hypothesis (LTH) and its variants, have lost their pragmatism in sparsifying them due to high computation and memory bottleneck of repetitive train-prune-retrain routine of iterative magnitude pruning (IMP) which worsens with increasing model size. This paper comprehensively studies induced sparse patterns across multiple large pre-trained vision and language transformers. We propose the existence of -- essential sparsity defined with a sharp dropping point beyond which the performance declines much faster w.r. t the rise of sparsity level, when we directly remove weights with the smallest magnitudes in one-shot without re-training. We also find essential sparsity to hold valid for N:M sparsity patterns as well as on modern-scale large language models (Vicuna-7B). We also present an intriguing emerging phenomenon of abrupt sparsification during the pre-training of BERT, i.e., BERT suddenly becomes heavily sparse in pre-training after certain iterations. Moreover, our observations also indicate a counter-intuitive finding that BERT trained with a larger amount of pre-training data tends to have a better ability to condense knowledge in comparatively relatively fewer parameters. Lastly, we investigate the effect of the pre-training loss on essential sparsity and discover that self-supervised learning (SSL) objectives trigger stronger emergent sparsification properties than supervised learning (SL). Our codes are available at \url{https://github.com/VITA-Group/essential_sparsity}.
Torus links $T_{2s,2t}$ and $(s,t)$-log VOA

We reveal an intimate connection between the torus link $T_{2s,2t}$ and the logarithmic $(s,t)$ VOA. We show that the singlet character of $(s,t)$-log VOA at the root of unity coincides with the Kashaev invariant and that it has a property of the quantum modularity. Also shown is that the tail of the $N$-colored Jones polynomial gives the character. Furthermore we propose a geometric method to compute the character.
U-Statistic Reduction: Higher-Order Accurate Risk Control and Statistical-Computational Trade-Off, with Application to Network Method-of-Moments

U-statistics play central roles in many statistical learning tools but face the haunting issue of scalability. Significant efforts have been devoted into accelerating computation by U-statistic reduction. However, existing results almost exclusively focus on power analysis, while little work addresses risk control accuracy -- comparatively, the latter requires distinct and much more challenging techniques. In this paper, we establish the first statistical inference procedure with provably higher-order accurate risk control for incomplete U-statistics. The sharpness of our new result enables us to reveal how risk control accuracy also trades off with speed for the first time in literature, which complements the well-known variance-speed trade-off. Our proposed general framework converts the long-standing challenge of formulating accurate statistical inference procedures for many different designs into a surprisingly routine task. This paper covers non-degenerate and degenerate U-statistics, and network moments. We conducted comprehensive numerical studies and observed results that validate our theory's sharpness. Our method also demonstrates effectiveness on real-world data applications.
OrbitN: A Symplectic Integrator for Planetary Systems Dominated by a Central Mass—Insight into Long-term Solar System Chaos

Reliable studies of the long-term dynamics of planetary systems require numerical integrators that are accurate and fast. The challenge is often formidable because the chaotic nature of many systems requires relative numerical error bounds at or close to machine precision (∼10−16, double-precision arithmetic); otherwise, numerical chaos may dominate over physical chaos. Currently, the speed/accuracy demands are usually only met by symplectic integrators. For example, the most up-to-date long-term astronomical solutions for the solar system in the past (widely used in, e.g., astrochronology and high-precision geological dating) have been obtained using symplectic integrators. However, the source codes of these integrators are unavailable. Here I present the symplectic integrator orbitN (lean version 1.0) with the primary goal of generating accurate and reproducible long-term orbital solutions for near-Keplerian planetary systems (here the solar system) with a dominant mass M 0. Among other features, orbitN-1.0 includes M 0’s quadrupole moment, a lunar contribution, and post-Newtonian corrections (1PN) due to M 0 (fast symplectic implementation). To reduce numerical round-off errors, Kahan compensated summation was implemented. I use orbitN to provide insight into the effect of various processes on the long-term chaos in the solar system. Notably, 1PN corrections have the opposite effect on chaoticity/stability on a 100 Myr versus Gyr timescale. For the current application, orbitN is about as fast as or faster (factor 1.15–2.6) than comparable integrators, depending on hardware. 1 1 The orbitN source code (C) is available at http://github.com/rezeebe/orbitN. The orbitN source code (C) is available at http://github.com/rezeebe/orbitN.
Unleashing Mask: Explore the Intrinsic Out-of-Distribution Detection Capability

Out-of-distribution (OOD) detection is an indispensable aspect of secure AI when deploying machine learning models in real-world applications. Previous paradigms either explore better scoring functions or utilize the knowledge of outliers to equip the models with the ability of OOD detection. However, few of them pay attention to the intrinsic OOD detection capability of the given model. In this work, we generally discover the existence of an intermediate stage of a model trained on in-distribution (ID) data having higher OOD detection performance than that of its final stage across different settings, and further identify one critical data-level attribution to be learning with the atypical samples. Based on such insights, we propose a novel method, Unleashing Mask, which aims to restore the OOD discriminative capabilities of the well-trained model with ID data. Our method utilizes a mask to figure out the memorized atypical samples, and then finetune the model or prune it with the introduced mask to forget them. Extensive experiments and analysis demonstrate the effectiveness of our method. The code is available at: https://github.com/tmlr-group/Unleashing-Mask.
INTERACTING SYSTEM OF A 2D RIGID CYLINDER AND N POINT VORTICES: THE CASE OF ARBITRARY SMOOTH CYLINDER SHAPES

This paper basically extends the work of Shashikanth, Marsden, Burdick and Kelly [17] by showing that the Hamiltonian (Poisson bracket) structure of the dynamically interacting system of a 2-D rigid circular cylinder and N point vortices, when the vortex strengths sum to zero and the circulation around the cylinder is zero, also holds when the cylinder has arbitrary (smooth) shape. This extension is a consequence of a reciprocity relation, obtainable by an application of a classical Green’s formula, that holds for this problem. Moreover, even when the vortex strengths do not sum to zero but with the circulation around the cylinder still zero, it is shown that there is a Poisson bracket for the system which differs from the previous bracket by the inclusion of a 2-cocycle term. Finally, comparisons are made to the works of Borisov, Mamaev and Ramodanov [15], [16], [5], [4].
Coronal Magnetic Field Extrapolation and Topological Analysis of Fine-scale Structures during Solar Flare Precursors

Magnetic field plays an important role in various solar eruption phenomena. The formation and evolution of the characteristic magnetic field topology in solar eruptions are critical problems that will ultimately help us understand the origin of these eruptions in the solar source regions. With the development of advanced techniques and instruments, observations with higher resolutions in different wavelengths and fields of view have provided more quantitative information for finer structures. It is therefore essential to improve the method with which we study the magnetic field topology in the solar source regions by taking advantage of high-resolution observations. In this study, we employ a nonlinear force-free field extrapolation method based on a nonuniform grid setting for an M-class flare eruption event (SOL2015-06-22T17:39) with embedded vector magnetograms from the Solar Dynamics Observatory (SDO) and the Goode Solar Telescope (GST). The extrapolation results for which the nonuniform embedded magnetogram for the bottom boundary was employed are obtained by maintaining the native resolutions of the corresponding GST and SDO magnetograms. We compare the field line connectivity with the simultaneous GST/Hα and SDO/Atmospheric Imaging Assembly observations for these fine-scale structures, which are associated with precursor brightenings. Then we perform a topological analysis of the field line connectivity corresponding to fine-scale magnetic field structures based on the extrapolation results. The analysis results indicate that when we combine the high-resolution GST magnetogram with a larger magnetogram from the SDO, the derived magnetic field topology is consistent with a scenario of magnetic reconnection among sheared field lines across the main polarity inversion line during solar flare precursors.
The qualitative behavior at a vortex point for the Chern-Simon-Higgs equation

In this paper, we study the qualitative behavior at a vortex blow-up point for Chern-Simon-Higgs equation. Roughly speaking, we will establish an energy identity at a each such point, i.e. the local mass is the sum of the bubbles. Moreover, we prove that either there is only one bubble which is a singular bubble or there are more than two bubbles which contains no singular bubble. Meanwhile, we prove that the energies of these bubbles must satisfy a quadratic polynomial which can be used to prove the simple blow-up property when the multiplicity is small. As is well known, for many Liouville type system, Pohozaev type identity is a quadratic polynomial corresponding to energies which can be used directly to compute the local mass at a blow-up point. The difficulty here is that, besides the energy's integration, there is a additional term in the Pohozaev type identity of Chern-Simon-Higgs equation. We need some more detailed and delicated analysis to deal with it.
CUE: An Uncertainty Interpretation Framework for Text Classifiers Built on Pre-Trained Language Models

Text classifiers built on Pre-trained Language Models (PLMs) have achieved remarkable progress in various tasks including sentiment analysis, natural language inference, and question-answering. However, the occurrence of uncertain predictions by these classifiers poses a challenge to their reliability when deployed in practical applications. Much effort has been devoted to designing various probes in order to understand what PLMs capture. But few studies have delved into factors influencing PLM-based classifiers' predictive uncertainty. In this paper, we propose a novel framework, called CUE, which aims to interpret uncertainties inherent in the predictions of PLM-based models. In particular, we first map PLM-encoded representations to a latent space via a variational auto-encoder. We then generate text representations by perturbing the latent space which causes fluctuation in predictive uncertainty. By comparing the difference in predictive uncertainty between the perturbed and the original text representations, we are able to identify the latent dimensions responsible for uncertainty and subsequently trace back to the input features that contribute to such uncertainty. Our extensive experiments on four benchmark datasets encompassing linguistic acceptability classification, emotion classification, and natural language inference show the feasibility of our proposed framework. Our source code is available at: https://github.com/lijiazheng99/CUE.
Entropic covariance models

In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance matrix or its inverse. Another approach considers linear restrictions on the matrix logarithm of the covariance matrix. In this paper, we present a general framework for linear restrictions on different transformations of the covariance matrix, including the mentioned examples. Our proposed estimation method solves a convex problem and yields an M-estimator, allowing for relatively straightforward asymptotic and finite sample analysis. After developing the general theory, we focus on modelling correlation matrices and on sparsity. Our geometric insights allow to extend various recent results in covariance matrix modelling. This includes providing unrestricted parametrizations of the space of correlation matrices, which is alternative to a recent result utilizing the matrix logarithm.
Few Shot Rationale Generation using Self-Training with Dual Teachers

Self-rationalizing models that also generate a free-text explanation for their predicted labels are an important tool to build trustworthy AI applications. Since generating explanations for annotated labels is a laborious and costly pro cess, recent models rely on large pretrained language models (PLMs) as their backbone and few-shot learning. In this work we explore a self-training approach leveraging both labeled and unlabeled data to further improve few-shot models, under the assumption that neither human written rationales nor annotated task labels are available at scale. We introduce a novel dual-teacher learning framework, which learns two specialized teacher models for task prediction and rationalization using self-training and distills their knowledge into a multi-tasking student model that can jointly generate the task label and rationale. Furthermore, we formulate a new loss function, Masked Label Regularization (MLR) which promotes explanations to be strongly conditioned on predicted labels. Evaluation on three public datasets demonstrate that the proposed methods are effective in modeling task labels and generating faithful rationales.
Abundances in planetary nebulae: NGC 6886

ISO and IUE spectra of the round-shaped planetary nebula NGC 6886 are combined with spectra in the visual wavelength region taken from the literature to obtain a complete, extinction corrected spectrum from ultraviolet to infrared wavelengths. The characteristics of the nebula and its central star are determined by various methods including photoionization modeling using C. The results of the modeling are checked against the observational data and compared to those derived from a more classical abundance determination approach. The abundances determined are found to differ substantially from earlier results although the observations used are essentially the same, except for the inclusion of the ISO results. The reasons for this difference are discussed. Finally, the main results are interpreted in terms of the evolutionary stage of NGC 6886 and its central star.