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Large language models (LLMs) are expensive to deploy. Parameter sharing offers a possible path towards reducing their size and cost, but its effectiveness in modern LLMs remains fairly limited. In this work, we revisit "layer tying" as form of parameter sharing in Transformers, and introduce novel methods for converting existing LLMs into smaller "Recursive Transformers" that share parameters across layers, with minimal loss of performance. Here, our Recursive Transformers are efficiently initialized from standard pretrained Transformers, but only use a single block of unique layers that is then repeated multiple times in a loop. We further improve performance by introducing Relaxed Recursive Transformers that add flexibility to the layer tying constraint via depth-wise low-rank adaptation (LoRA) modules, yet still preserve the compactness of the overall model. We show that our recursive models (e.g., recursive Gemma 1B) outperform both similar-sized vanilla pretrained models (such as TinyLlama 1.1B and Pythia 1B) and knowledge distillation baselines -- and can even recover most of the performance of the original "full-size" model (e.g., Gemma 2B with no shared parameters). Finally, we propose Continuous Depth-wise Batching, a promising new inference paradigm enabled by the Recursive Transformer when paired with early exiting. In a theoretical analysis, we show that this has the potential to lead to significant (2-3x) gains in inference throughput., Comment: 48 pages, 17 figures, 17 tables

A primary challenge in large language model (LLM) development is their onerous pre-training cost. Typically, such pre-training involves optimizing a self-supervised objective (such as next-token prediction) over a large corpus. This paper explores a promising paradigm to improve LLM pre-training efficiency and quality by suitably leveraging a small language model (SLM). In particular, this paradigm relies on an SLM to both (1) provide soft labels as additional training supervision, and (2) select a small subset of valuable ("informative" and "hard") training examples. Put together, this enables an effective transfer of the SLM's predictive distribution to the LLM, while prioritizing specific regions of the training data distribution. Empirically, this leads to reduced LLM training time compared to standard training, while improving the overall quality. Theoretically, we develop a statistical framework to systematically study the utility of SLMs in enabling efficient training of high-quality LLMs. In particular, our framework characterizes how the SLM's seemingly low-quality supervision can enhance the training of a much more capable LLM. Furthermore, it also highlights the need for an adaptive utilization of such supervision, by striking a balance between the bias and variance introduced by the SLM-provided soft labels. We corroborate our theoretical framework by improving the pre-training of an LLM with 2.8B parameters by utilizing a smaller LM with 1.5B parameters on the Pile dataset.

Ultra-hot Jupiters (UHJs) are gas giant planets orbiting close to their host star, with equilibrium temperatures exceeding 2000 K, and among the most studied planets in terms of their atmospheric composition. Thanks to a new generation of ultra-stable high-resolution spectrographs, it is possible to detect the signal from the individual lines of the species in the exoplanetary atmospheres. We employed two techniques in this study. First, we used transmission spectroscopy, which involved examining the spectra around single lines of FeII. Then we carried out a set of cross-correlation studies for two UHJs: KELT-9b and KELT-20b. Both planets orbit fast-rotating stars, which resulted in the detection of the strong Rossiter-McLaughlin (RM) effect and center-to-limb variations in the transmission spectrum. These effects had to be corrected to ensure a precise analysis. Using the transmission spectroscopy method, we detected 21 single lines of FeII in the atmosphere of KELT-9b. All of the detected lines are blue-shifted, suggesting strong day-to-night side atmospheric winds. The cross-correlation method leads to the detection of the blue-shifted signal with a signal-to-noise ratio (S/N) of 13.46. Our results are in agreement with models based on non-local thermodynamical equilibrium (NLTE) effects, with a mean micro-turbulence of nu_mic = 2.73 +/- 1.5 km/s and macro-turbulence of nu_mac = 8.22 +/- 3.85 km/s. In the atmosphere of KELT-20b, we detected 17 single lines of FeII. Considering different measurements of the systemic velocity of the system, we conclude that the existence of winds in the atmosphere of KELT-20b cannot be determined conclusively. The detected signal with the cross-correlation method presents a S/N of 11.51. The results are consistent with NLTE effects, including means of nu_mic = 3.04 +/- 0.35 km/s and nu_mac = 6.76 +/- 1.17 km/s., Comment: 38 pages, 19 Figures (39 figures in Appendix), 6 tables, Accepted for publication in A&A

Recent work has shown that state space models such as Mamba are significantly worse than Transformers on recall-based tasks due to the fact that their state size is constant with respect to their input sequence length. But in practice, state space models have fairly large state sizes, and we conjecture that they should be able to perform much better at these tasks than previously reported. We investigate whether their poor copying and recall performance could be due in part to training difficulties rather than fundamental capacity constraints. Based on observations of their "attention" maps, we propose a structured initialization technique that allows state space layers to more readily mimic attention. Across a variety of architecture settings, our initialization makes it substantially easier for Mamba to learn to copy and do associative recall from scratch.

Efficient nonlinear wave mixing is of paramount importance for a wide range of applications. However, weak optical nonlinearities pose significant challenges for accessing nonlinear light-matter interaction in compact systems. Here, we experimentally study second harmonic generation in deeply subwavelength 3R-MoS2 metasurfaces (<\lambda/13 thick). Our measurements, supported by theoretical analysis, reveal a complex interplay and coupling between geometric resonances, optical extinction, and strong nonlinear susceptibility dispersion near excitons. We further demonstrate >150-fold enhancement in second harmonic signal at 740 nm driven by the A exciton resonance. Additionally, our theoretical studies predict an enhancement of more than 10^6 in second harmonic generation in <100 nm thick structures exhibiting bound states in the continuum resonance. These findings provide insight into accessing and harnessing the unprecedented 3R-MoS2 nonlinearities at a subwavelength scale, paving the way for ultracompact nonlinear photonic devices., Comment: 3 figures

Large language models exhibit a remarkable capacity for in-context learning, where they learn to solve tasks given a few examples. Recent work has shown that transformers can be trained to perform simple regression tasks in-context. This work explores the possibility of training an in-context learner for classification tasks involving spurious features. We find that the conventional approach of training in-context learners is susceptible to spurious features. Moreover, when the meta-training dataset includes instances of only one task, the conventional approach leads to task memorization and fails to produce a model that leverages context for predictions. Based on these observations, we propose a novel technique to train such a learner for a given classification task. Remarkably, this in-context learner matches and sometimes outperforms strong methods like ERM and GroupDRO. However, unlike these algorithms, it does not generalize well to other tasks. We show that it is possible to obtain an in-context learner that generalizes to unseen tasks by training on a diverse dataset of synthetic in-context learning instances.

The equilibrium properties and interminiband transitions for Hartree-interacting two-dimensional electron gas in a one-dimensional chain of planar quantum rings subjected to a transverse homogeneous magnetic field are examined theoretically and numerically. The proposed analytical models for the external modulation potential and the basis wave-function reflect the symmetry and the topology of the system allowing to get high accuracy results in comparatively short computational times. The calculated dependencies of the electronic band structure versus magnetic field show two detached minibands in the region of low energies, while higher minibands manifest multiple crossings and anticrossings. The existence of highly degenerate energy levels (referred to as miniband nodes) for certain values of magnetic field is revealed. The miniband nodes are preserved when taking into account the Coulomb interaction of the electrons. The interaction leads to an up-shift and a broadening of the minibands, as well as to a shift of the nodes toward the larger values of the magnetic field. The miniband nodes have their signature in the magnetization of the electron gas and in the interminiband transitions. The number of electrons per a unite cell of the system has a strong impact on the current density distribution, magnetization and the oscillator strength. The obtained results open new opportunities for a flexible manipulation of magneto-optical properties of future devices operating in far-infrared and THz regimes.

The Markarian Multiwavelength Data Center (MMDC) is a web-based tool designed for accessing and retrieving multiwavelength and multimessenger data from blazar observations. MMDC facilitates the construction and interactive visualization of time-resolved multi-band spectral energy distributions (SEDs) of blazars by integrating: \textit{(i)} archival data from over 80 catalogs and databases, \textit{(ii)} optical data from all-sky survey facilities such as ASAS-SN, ZTF, and Pan-STARRS, and \textit{(iii)} newly analyzed datasets in the optical/UV band from \textit{Swift}-UVOT, in the X-ray band from \textit{Swift}-XRT and NuSTAR observations, and the high-energy $\gamma$-ray band from \textit{Fermi}-LAT observations. MMDC distinguishes itself from other online platforms by the large quantity of available data. For instance, it includes data from all blazar observations by \textit{Swift} and NuSTAR, as well as the results of detailed spectral analysis in the $\gamma$-ray band during different emission states, covering the period from 2008 to 2023. Another important distinguishing feature of MMDC is its ability to enable precise, self-consistent theoretical modeling of the observed data using machine learning algorithms trained on leptonic and lepto-hadronic models, which consider the injection of particles and all relevant cooling processes. MMDC is an innovative tool which significantly enhances blazar research by providing a comprehensive framework for data accessibility, analysis, and theoretical interpretation, thereby advancing our understanding of blazar emissions and the underlying astrophysical processes., Comment: Accepted for publication in The Astronomical Journal; MMDC is available at www.mmdc.am

Exploration is a critical challenge in robotics, centered on understanding unknown environments. In this work, we focus on robots exploring structured indoor environments which are often predictable and composed of repeating patterns. Most existing approaches, such as conventional frontier approaches, have difficulty leveraging the predictability and explore with simple heuristics such as `closest first'. Recent works use deep learning techniques to predict unknown regions of the map, using these predictions for information gain calculation. However, these approaches are often sensitive to the predicted map quality or do not reason over sensor coverage. To overcome these issues, our key insight is to jointly reason over what the robot can observe and its uncertainty to calculate probabilistic information gain. We introduce MapEx, a new exploration framework that uses predicted maps to form probabilistic sensor model for information gain estimation. MapEx generates multiple predicted maps based on observed information, and takes into consideration both the computed variances of predicted maps and estimated visible area to estimate the information gain of a given viewpoint. Experiments on the real-world KTH dataset showed on average 12.4% improvement than representative map-prediction based exploration and 25.4% improvement than nearest frontier approach., Comment: 7 pages

In this study, we examine thermal conductivity and the thermal Hall effect in electron-ion plasmas relevant to hot neutron stars, white dwarfs, and binary neutron star mergers, focusing on densities found in the outer crusts of neutron stars and the interiors of white dwarfs. We consider plasma consisting of single species of ions, which could be either iron $\isotope[56]{Fe}$, carbon $\isotope[12]{C}$, helium $\isotope[4]{He}$, or hydrogen $\isotope[1]{H}$ nuclei. The temperature range explored is from the melting temperature of the solid $T\sim10^9$~K up to $10^{11}$~K. This covers both degenerate and non-degenerate electron regimes. We find that thermal conductivity increases with density and temperature for which we provide analytical scaling relations valid in different regimes. The impact of magnetic fields on thermal conductivity is also analyzed, showing anisotropy in low-density regions and the presence of the thermal Hall effect characterized by Leduc-Righi coefficient. The transition from degenerate to non-degenerate regime is characterized by a minimum ratio of thermal conductivity to temperature, which is analogous to the minimum observed already in the case of electrical conductivity.

The study of exoplanets at different evolutionary stages can shed light on their formation, migration, and evolution. The determination of exoplanet properties depends on the properties of their host stars. It is therefore important to characterise the host stars for accurate knowledge on their planets. Our final goal is to derive, in a homogeneous and accurate way, the stellar atmospheric parameters and elemental abundances of ten young TESS transiting planet-hosting GK stars followed up with the HARPS-N at TNG spectrograph within the GAPS programme. We derived stellar kinematic properties, atmospheric parameters, and abundances of 18 elements. Lithium line measurements were used as approximate age estimations. We exploited chemical abundances and their ratios to derive information on planetary composition. Elemental abundances and kinematic properties are consistent with the nearby Galactic thin disk. All targets show C/O<0.8 and 1.0

The job shop scheduling problem (JSSP) remains a significant hurdle in optimizing production processes. This challenge involves efficiently allocating jobs to a limited number of machines while minimizing factors like total processing time or job delays. While recent advancements in artificial intelligence have yielded promising solutions, such as reinforcement learning and graph neural networks, this paper explores the potential of Large Language Models (LLMs) for JSSP. We introduce the very first supervised 120k dataset specifically designed to train LLMs for JSSP. Surprisingly, our findings demonstrate that LLM-based scheduling can achieve performance comparable to other neural approaches. Furthermore, we propose a sampling method that enhances the effectiveness of LLMs in tackling JSSP.

We investigate the influence of the helical compactification of spatial dimension on the local properties of the vacuum state for a charged scalar field with general curvature coupling parameter. A general background geometry is considered with rotational symmetry in the subspace with the coordinates appearing in the helical periodicity condition. It is shown that by a coordinate transformation the problem is reduced to the problem with standard quasiperiodicity condition in the same local geometry and with the effective compactification radius determined by the length of the compact dimension and the helicity parameter. As an application of the general procedure we have considered locally de Sitter spacetime with a helical compact dimension. By using the Hadamard function for the Bunch-Davies vacuum state, the vacuum expectation values of the field squared, current density, and energy-momentum tensor are studied. The topological contributions are explicitly separated and their asymptotics are described at early and late stages of cosmological expansion. An important difference, compared to the problem with quasiperiodic conditions, is the appearance of the nonzero off-diagonal component of the energy-momentum tensor and of the component of the current density along the uncompact dimension., Comment: 13 pages

We study the bulk viscosity of moderately hot and dense, neutrino-transparent color superconducting quark matter arising from weak-interaction-driven direct URCA processes. The quark matter is modeled using the Nambu--Jona-Lasinio model improved to account for vector and 't Hooft interactions as well as antisymmetric pairing among the red/green up and down quarks. The unpaired excitations are the strange quarks and the blue up or down quarks. We compute the relaxation rates associated with $d$ and $s$-quark decay and electron capture processes on $u$ quark for blue color. The resulting bulk viscosity for density oscillations in the 1--10\,kHz range shows a resonant peak at $T\sim 5\,\MeV$, and the damping time may drop below 10 ms. This is short enough to affect the postmerger evolution and is very similar to the damping predicted in nuclear matter., Comment: v2: 6 pages + 4 figures main text, 2 pages + 2 figures supplemental material. Matches version published in Phys. Rev. D. Letters

Modern reinforcement learning has been conditioned by at least three dogmas. The first is the environment spotlight, which refers to our tendency to focus on modeling environments rather than agents. The second is our treatment of learning as finding the solution to a task, rather than adaptation. The third is the reward hypothesis, which states that all goals and purposes can be well thought of as maximization of a reward signal. These three dogmas shape much of what we think of as the science of reinforcement learning. While each of the dogmas have played an important role in developing the field, it is time we bring them to the surface and reflect on whether they belong as basic ingredients of our scientific paradigm. In order to realize the potential of reinforcement learning as a canonical frame for researching intelligent agents, we suggest that it is time we shed dogmas one and two entirely, and embrace a nuanced approach to the third., Comment: RLC 2024

We consider plane symmetric gravitational fields within the framework of General Relativity in (D+1)-dimensional spacetime. Two classes of vacuum solutions correspond to higher-dimensional generalizations of the Rindler and Taub spacetimes. The general solutions are presented for a positive and negative cosmological constant as the only source of the gravity. Matching conditions on a planar boundary between two regions with distinct plane symmetric metric tensors are discussed. An example is considered with Rindler and Taub geometries in neighboring half-spaces. As another example, we discuss a finite thickness cosmological constant slab embedded into the Minkowski, Rindler and Taub spacetimes. The corresponding surface energy-momentum tensor is found required for matching the exterior and interior geometries., Comment: 12 pages

Machine learning (ML) plays an important role in quantum chemistry, providing fast-to-evaluate predictive models for various properties of molecules. However, most existing ML models for molecular electronic properties use density functional theory (DFT) databases as ground truth in training, and their prediction accuracy cannot surpass that of DFT. In this work, we developed a unified ML method for electronic structures of organic molecules using the gold-standard CCSD(T) calculations as training data. Tested on hydrocarbon molecules, our model outperforms DFT with the widely-used hybrid and double hybrid functionals in computational costs and prediction accuracy of various quantum chemical properties. As case studies, we apply the model to aromatic compounds and semiconducting polymers on both ground state and excited state properties, demonstrating its accuracy and generalization capability to complex systems that are hard to calculate using CCSD(T)-level methods.

In the realm of web agent research, achieving both generalization and accuracy remains a challenging problem. Due to high variance in website structure, existing approaches often fail. Moreover, existing fine-tuning and in-context learning techniques fail to generalize across multiple websites. We introduce Wilbur, an approach that uses a differentiable ranking model and a novel instruction synthesis technique to optimally populate a black-box large language model's prompt with task demonstrations from previous runs. To maximize end-to-end success rates, we also propose an intelligent backtracking mechanism that learns and recovers from its mistakes. Finally, we show that our ranking model can be trained on data from a generative auto-curriculum which samples representative goals from an LLM, runs the agent, and automatically evaluates it, with no manual annotation. Wilbur achieves state-of-the-art results on the WebVoyager benchmark, beating text-only models by 8% overall, and up to 36% on certain websites. On the same benchmark, Wilbur is within 5% of a strong multi-modal model despite only receiving textual inputs, and further analysis reveals a substantial number of failures are due to engineering challenges of operating the web.

We investigate vacuum expectation value of the energy-momentum tensor for a massive Dirac field in flat spacetime with a toroidal subspace of a general dimension. Quasiperiodicity conditions with arbitrary phases are imposed on the field operator along compact dimensions. These phases are interpreted in terms of magnetic fluxes enclosed by compact dimensions. The equation of state in the uncompact subspace is of the cosmological constant type. It is shown that, in addition to the diagonal components, the vacuum energy-momentum tensor has nonzero off-diagonal components. In special cases of twisted (antiperiodic) and untwisted (periodic) fields the off diagonal components vanish. For untwisted fields the vacuum energy density is positive and the energy-momentum tensor obeys the strong energy condition. For general values of the phases in the periodicity conditions the energy density and stresses can be either positive or negative. The numerical results are given for a Kaluza-Klein type model with two extra dimensions., Comment: 12 pages, 5 figures

The main issues of the spectral theory of Dirac operators are presented, namely: transformation operators, asymptotics of eigenvalues and eigenfunctions, description of symmetric and self-adjoint operators in Hilbert space, expansion in eigenfunctions, uniqueness theorems in inverse problems, constructive solution of inverse problems, description of isospectral operators, and some other questions. This book is aimed at specialists in spectral theory and graduate students of mathematics at universities., Comment: This book is based on our published articles, we have reused that articles as part of some chapters

High redshift blazars are among the most powerful non-explosive sources in the Universe and play a crucial role in understanding the evolution of relativistic jets. To understand these bright objects, we performed a detailed investigation of the multiwavelength properties of 79 $\gamma$-ray blazars with redshifts ranging from z = 2.0 to 2.5, using data from Fermi LAT, Swift XRT/UVOT, and NuSTAR observations. In the $\gamma$-ray band, the spectral analysis revealed a wide range of flux and photon indices, from $5.32 \times 10^{-10}$ to $3.40 \times 10^{-7}$ photons cm$^{-2}$ s$^{-1}$ and from 1.66 to 3.15, respectively, highlighting the diverse nature of these sources. The detailed temporal analysis showed that flaring activities were observed in 31 sources. Sources such as 4C+71.07, PKS 1329-049, and 4C+01.02, demonstrated significant increase in the $\gamma$-ray luminosity and flux variations, reaching peak luminosity exceeding $10^{50}$ erg s$^{-1}$. The temporal analysis extended to X-ray and optical/UV bands, showed clear flux changes in some sources in different observations. The time-averaged properties of high redshift blazars were derived through modeling the spectral energy distributions with a one-zone leptonic scenario, assuming the emission region is within the broad-line region (BLR) and the X-ray and $\gamma$-ray emissions are due to inverse Compton scattering of synchrotron and BLR-reflected photons. This modeling allowed us to constrain the emitting particle distribution, estimate the magnetic field inside the jet, and evaluate the jet luminosity, which is discussed in comparison with the disk luminosity derived from fitting the excess in the UV band., Comment: Accepted for publication in MNRAS

We have studied possible applications of a particular pseudo-differential algebra in singular analysis for the construction of fundamental solutions and Green's functions of a certain class of elliptic partial differential operators. The pseudo-differential algebra considered in the present work, comprises degenerate partial differential operators on stretched cones which can be locally described as Fuchs type differential operators in appropriate polar coordinates. We present a general approach for the explicit construction of their parametrices, which is based on the concept of an asymptotic parametrix, introduced in \cite{FHS16}. For some selected partial differential operators, we demonstrate the feasibility of our approach by an explicit calculation of fundamental solutions and Green's functions from the corresponding parametrices. In our approach, the Green's functions are given in separable form, which generalizes the Laplace expansion of the Green's function of the Laplace operator in three dimensions. As a concrete application in quantum scattering theory, we construct a fundamental solution of a single-particle Hamilton operator with singular Coulomb potential.

We present the characterisation of the two transiting planets around HD 152843 (TOI 2319, TIC 349488688) using an intensive campaign of HARPS-N radial velocities, and two sectors of TESS data. These data reveal a unique and fascinating system: HD 152843 b and c have near equal masses of around 9 M$_\oplus$ but differing radii of $3.05 \pm 0.11$ R$_\oplus$ and $5.94^{+0.18}_{-0.16}$ R$_\oplus$ , respectively, and orbital periods of $11.62071^{+9.6e-05}_{-0.000106}$ days and $19.502104^{+7.4e-05}_{-8.5e-05}$ days. This indicates that HD 152843 c is in the lowest fifth percentile in density of the known exoplanet population, and has the longest orbital period among these low density planets. Further, HD 152843 c's radius places it in the Saturn valley, the observed lack of planets larger than Neptune, but smaller than Saturn. The orbital periods of these planets indicate they are near a 5:3 mean motion resonance, indicating the possibility of transit timing variations, and hints at the possibility of interaction with a third planet at some point in the evolution of this system. Further, the brightness of the host star and the low density of HD 152843 c make it a key target for atmospheric characterisation., Comment: Submitted for review to the Monthly Notices of the Royal Astronomical Society. 13 pages, 16 figures

Is the population of close-in planets orbiting M dwarfs sculpted by thermally driven escape or is it a direct outcome of the planet formation process? A number of recent empirical results strongly suggest the latter. However, the unique architecture of the TOI-1266 system presents a challenge to models of planet formation and atmospheric escape given its seemingly "inverted" architecture of a large sub-Neptune ($P_b=10.9$ days, $R_{p,b}=2.62\pm 0.11\, \mathrm{R}_{\oplus}$) orbiting interior to that of the system's smaller planet ($P_c=18.8$ days, $R_{p,c}=2.13\pm 0.12\, \mathrm{R}_{\oplus}$). Here we present revised planetary radii based on new TESS and diffuser-assisted ground-based transit observations, and characterize both planetary masses using a set of 145 radial velocity measurements from HARPS-N ($M_{p,b}=4.23\pm 0.69\, \mathrm{M}_{\oplus}, M_{p,c}=2.88\pm 0.80\, \mathrm{M}_{\oplus}$). Our analysis also reveals a third planet candidate ($P_d=32.3$ days, $M_{p,d}\sin{i} = 4.59^{+0.96}_{-0.94}\, \mathrm{M}_{\oplus}$), which if real, would form a chain of near 5:3 period ratios, although the system is likely not in a mean motion resonance. Our results indicate that TOI-1266 b and c are among the lowest density sub-Neptunes around M dwarfs and likely exhibit distinct bulk compositions of a gas-enveloped terrestrial ($X_{\mathrm{env},b}=5.5\pm 0.7$%) and a water-rich world (WMF$_c=59\pm 14$%), which is supported by hydrodynamic escape models. If distinct bulk compositions are confirmed through atmospheric characterization, the system's unique architecture would represent an interesting test case of inside-out sub-Neptune formation at pebble traps., Comment: Accepted for publication in MNRAS. 21 pages. Our spectroscopic time series are included in the arXiv source files as table6.csv

Text classification is a well-studied and versatile building block for many NLP applications. Yet, existing approaches require either large annotated corpora to train a model with or, when using large language models as a base, require carefully crafting the prompt as well as using a long context that can fit many examples. As a result, it is not possible for end-users to build classifiers for themselves. To address this issue, we propose a novel approach to few-shot text classification using an LLM. Rather than few-shot examples, the LLM is prompted with descriptions of the salient features of each class. These descriptions are coauthored by the user and the LLM interactively: while the user annotates each few-shot example, the LLM asks relevant questions that the user answers. Examples, questions, and answers are summarized to form the classification prompt. Our experiments show that our approach yields high accuracy classifiers, within 82% of the performance of models trained with significantly larger datasets while using only 1% of their training sets. Additionally, in a study with 30 participants, we show that end-users are able to build classifiers to suit their specific needs. The personalized classifiers show an average accuracy of 90%, which is 15% higher than the state-of-the-art approach., Comment: Accepted at EMNLP 2023 (Findings)

The dichromatic number of a digraph $D$ is the smallest $k$ such that $D$ can be partitioned into $k$ acyclic subdigraphs, and the dichromatic number of an undirected graph is the maximum dichromatic number over all its orientations. Extending a well-known result of Lov\'{a}sz, we show that the dichromatic number of the Kneser graph $KG(n,k)$ is $\Theta(n-2k+2)$ and that the dichromatic number of the Borsuk graph $BG(n+1,a)$ is $n+2$ if $a$ is large enough. We then study the list version of the dichromatic number. We show that, for any $\varepsilon>0$ and $2\leq k\leq n^{1/2-\varepsilon}$, the list dichromatic number of $KG(n,k)$ is $\Theta(n\ln n)$. This extends a recent result of Bulankina and Kupavskii on the list chromatic number of $KG(n,k)$, where the same behaviour was observed. We also show that for any $\rho>3$, $r\geq 2$ and $m\geq\ln^{\rho}r$, the list dichromatic number of the complete $r$-partite graph with $m$ vertices in each part is $\Theta(r\ln m)$, extending a classical result of Alon. Finally, we give a directed analogue of Sabidussi's theorem on the chromatic number of graph products., Comment: 15 pages

We study temporal analogues of the Unrestricted Vertex Separator problem from the static world. An $(s,z)$-temporal separator is a set of vertices whose removal disconnects vertex $s$ from vertex $z$ for every time step in a temporal graph. The $(s,z)$-Temporal Separator problem asks to find the minimum size of an $(s,z)$-temporal separator for the given temporal graph. We introduce a generalization of this problem called the $(s,z,t)$-Temporal Separator problem, where the goal is to find a smallest subset of vertices whose removal eliminates all temporal paths from $s$ to $z$ which take less than $t$ time steps. Let $\tau$ denote the number of time steps over which the temporal graph is defined (we consider discrete time steps). We characterize the set of parameters $\tau$ and $t$ when the problem is $\mathcal{NP}$-hard and when it is polynomial time solvable. Then we present a $\tau$-approximation algorithm for the $(s,z)$-Temporal Separator problem and convert it to a $\tau^2$-approximation algorithm for the $(s,z,t)$-Temporal Separator problem. We also present an inapproximability lower bound of $\Omega(\ln(n) + \ln(\tau))$ for the $(s,z,t)$-Temporal Separator problem assuming that $\mathcal{NP}\not\subset\mbox{\sc Dtime}(n^{\log\log n})$. Then we consider three special families of graphs: (1) graphs of branchwidth at most $2$, (2) graphs $G$ such that the removal of $s$ and $z$ leaves a tree, and (3) graphs of bounded pathwidth. We present polynomial-time algorithms to find a minimum $(s,z,t)$-temporal separator for (1) and (2). As for (3), we show a polynomial-time reduction from the Discrete Segment Covering problem with bounded-length segments to the $(s,z,t)$-Temporal Separator problem where the temporal graph has bounded pathwidth.

Neptune-sized planets exhibit a wide range of compositions and densities, depending onf cators related to their formation and evolution history, such as the distance from their host stars and atmospheric escape processes. They can vary from relatively low-density planets with thick hydrogen-helium atmospheres to higher-density planets with a substantial amount of water or a rocky interior with a thinner atmosphere, such as HD 95338 b, TOI-849 b and TOI-2196 b. The discovery of exoplanets in the hot-Neptune desert, a region close to the host stars with a deficit of Neptune-sized planets, provides insights into the formation and evolution of planetary systems, including the existence of this region itself. Here we show observations of the transiting planet TOI-1853 b, which has a radius of 3.46 +- 0.08 Earth radii and orbits a dwarf star every 1.24 days. This planet has a mass of 73.2 +- 2.7 Earth masses, almost twice that of any other Neptune-sized planet known so far, and a density of 9.7 +- 0.8 grams per cubic centimetre. These values place TOI-1853 b in the middle of the Neptunian desert and imply that heavy elements dominate its mass. The properties of TOI-1853 b present a puzzle for conventional theories of planetary formation and evolution, and could be the result of several proto-planet collisions or the final state of an initially high-eccentricity planet that migrated closer to its parent star., Comment: Preprint submitted to Nature. Please refer to the published version for the final parameters estimations

We compute the anisotropic electrical conductivity tensor of the inner crust of a compact star at non-zero temperature by extending a previous work on the conductivity of the outer crust. The physical scenarios, where such crust is formed, involve proto-neutron stars born in supernova explosions, binary neutron star mergers and accreting neutron stars. The temperature-density range studied covers the transition from a non-degenerate to a highly degenerate electron gas and assumes that the nuclei form a liquid, i.e., the temperature is above the melting temperature of the lattice of nuclei. The electronic transition probabilities include (a) the dynamical screening of electron-ion interaction in the hard-thermal-loop approximation for the QED plasma, (b) the correlations of the ionic component in a one-component plasma, and (c) finite nuclear size effects. The conductivity tensor is obtained from the Boltzmann kinetic equation in relaxation time approximation accounting for the anisotropies introduced by a magnetic field. The sensitivity of the results towards the matter composition of the inner crust is explored by using several compositions of the inner crust which were obtained using different nuclear interactions and methods of solving the many-body problem. The standard deviation of relaxation time and components of the conductivity tensor from the average are below $\le 10\%$ except close to crust-core transition, where non-spherical nuclear structures are expected. Our results can be used in dissipative magneto-hydrodynamics (MHD) simulations of warm compact stars., Comment: 13 pages, 13 figures, 5 tables

The Rocky Planet Search (RPS) program is dedicated to a blind radial velocity (RV) search of planets around bright stars in the Northern hemisphere, using the high-resolution echelle spectrograph HARPS-N installed on the Telescopio Nazionale Galileo (TNG). The goal of this work is to revise and update the properties of three planetary systems by analysing the HARPS-N data with state-of-the-art stellar activity mitigation tools. The stars considered are HD 99492 (83Leo B), HD 147379 (Gl617 A) and HD 190007. We employ a systematic process of data modelling, that we selected from the comparison of different approaches. We use YARARA to remove instrumental systematics from the RV, and then use SPLEAF to further mitigate the stellar noise with a multidimensional correlated noise model. We also search for transit features in the Transiting Exoplanets Survey Satellite (TESS) data of these stars. We report on the discovery of a new planet around HD 99492, namely HD 99492 c, with an orbital period of 95.2 days and a minimum mass of msin i = 17.9 M_Earth, and refine the parameters of HD 99492 b. We also update and refine the Keplerian solutions for the planets around HD 147379 and HD 190007, but do not detect additional planetary signals. We discard the transiting geometry for the planets, but stress that TESS did not exhaustively cover all the orbital phases. The addition of the HARPS-N data, and the use of advanced data analysis tools, has allowed us to present a more precise view of these three planetary systems. It demonstrates once again the importance of long observational efforts such as the RPS program. Added to the RV exoplanet sample, these planets populate two apparently distinct populations revealed by a bimodality in the planets minimum mass distribution. The separation is located between 30 and 50 M_Earth., Comment: 27 pages, 26 figures (13 in Appendix); Accepted for publication in A&A

Despite the popularity and success of deep learning, there is limited understanding of when, how, and why neural networks generalize to unseen examples. Since learning can be seen as extracting information from data, we formally study information captured by neural networks during training. Specifically, we start with viewing learning in presence of noisy labels from an information-theoretic perspective and derive a learning algorithm that limits label noise information in weights. We then define a notion of unique information that an individual sample provides to the training of a deep network, shedding some light on the behavior of neural networks on examples that are atypical, ambiguous, or belong to underrepresented subpopulations. We relate example informativeness to generalization by deriving nonvacuous generalization gap bounds. Finally, by studying knowledge distillation, we highlight the important role of data and label complexity in generalization. Overall, our findings contribute to a deeper understanding of the mechanisms underlying neural network generalization., Comment: PhD thesis

We study the bulk viscosity of moderately hot and dense, neutrino-transparent relativistic $npe\mu$ matter arising from weak-interaction direct Urca processes. This work parallels our recent study of the bulk viscosity of $npe\mu$ matter with a trapped neutrino component. The nuclear matter is modeled in a relativistic density functional approach with two different parametrizations -- DDME2 (which does not allow for the low-temperature direct-Urca process at any density) and NL3 (which allows for low-temperature direct-Urca process above a low-density threshold). We compute the equilibration rates of Urca processes of neutron decay and lepton capture, as well as the rate of the muon decay, and find that the muon decay process is subdominant to the Urca processes at temperatures $T\geq 3$MeV in the case of DDME2 model and $T\geq 1$MeV in the case of NL3 model. Thus, the Urca-process-driven bulk viscosity is computed with the assumption that pure leptonic reactions are frozen. As a result the electronic and muonic Urca channels contribute to the bulk viscosity independently and at certain densities the bulk viscosity of $npe\mu$ matter shows instead of the standard one-peak (resonant) form a "flattened" shape. In the final step, we estimate the damping timescales of density oscillations by the bulk viscosity. We find that, e.g., at a typical oscillation frequency $f=1$kHz, the damping of oscillations is most efficient at temperatures $3\leq T\leq 5$MeV and densities $n_B\leq 2n_0$ where they can affect the evolution of the post-merger object., Comment: v2: 28 pages, 18 figures, matches published version. v1: 27 pages, 19 figures

Neural networks employ spurious correlations in their predictions, resulting in decreased performance when these correlations do not hold. Recent works suggest fixing pretrained representations and training a classification head that does not use spurious features. We investigate how spurious features are represented in pretrained representations and explore strategies for removing information about spurious features. Considering the Waterbirds dataset and a few pretrained representations, we find that even with full knowledge of spurious features, their removal is not straightforward due to entangled representation. To address this, we propose a linear autoencoder training method to separate the representation into core, spurious, and other features. We propose two effective spurious feature removal approaches that are applied to the encoding and significantly improve classification performance measured by worst group accuracy.

In reinforcement learning (RL), state representations are key to dealing with large or continuous state spaces. While one of the promises of deep learning algorithms is to automatically construct features well-tuned for the task they try to solve, such a representation might not emerge from end-to-end training of deep RL agents. To mitigate this issue, auxiliary objectives are often incorporated into the learning process and help shape the learnt state representation. Bootstrapping methods are today's method of choice to make these additional predictions. Yet, it is unclear which features these algorithms capture and how they relate to those from other auxiliary-task-based approaches. In this paper, we address this gap and provide a theoretical characterization of the state representation learnt by temporal difference learning (Sutton, 1988). Surprisingly, we find that this representation differs from the features learned by Monte Carlo and residual gradient algorithms for most transition structures of the environment in the policy evaluation setting. We describe the efficacy of these representations for policy evaluation, and use our theoretical analysis to design new auxiliary learning rules. We complement our theoretical results with an empirical comparison of these learning rules for different cumulant functions on classic domains such as the four-room domain (Sutton et al, 1999) and Mountain Car (Moore, 1990)., Comment: ICML 2023

We present the results of a high-cadence and high-precision radial velocity (RV) monitoring of 3 late-type dwarf stars hosting long-period giants with well-measured orbits, in order to search for short-period sub-Neptunes (SN, $M \sin i < 30$ M$_\oplus$). Building on the results and expertise of our previous studies, we carry out combined fits of our HARPS-N data with literature RVs, using MCMC analyses and Gaussian Process regression. We then use the results of our survey to estimate the frequency of sub-Neptunes in systems hosting cold-Jupiters, $f(SN|CJ)$, and compare it with the frequency around field M-dwarfs, $f(SN)$. We identify a new short-period low-mass planet orbiting GJ 328, GJ 328\,c, with $P_c = 241.8^{+1.3}_{-1.7}$ d and $M_c \sin i = 21.4^{+ 3.4}_{- 3.2}$ M$_\oplus$. We moreover identify and model the chromospheric activity signals and rotation periods of GJ 649 and GJ 849, around which no additional planet is found. Then, taking into account also planetary system around the previosuly-analyzed low-mass star BD-11 4672, we derive an estimate of the frequencies of inner planets in such systems. In particular $f(SN|CJ) = 0.25^{+0.58}_{-0.07}$ for mini-Neptunes ($10$ M$_\oplus < M \sin i < 30$ M$_\oplus$, $P < 150$ d), marginally larger than $f(SN)$. For lower-mass planets ($M \sin i < 10$ M$_\oplus$) instead $f(SN|CJ) <0.69$, compatible with $f(SN)$. In light of the newly detected mini-Neptune, we find tentative evidence of a positive correlation between the presence of those planets and that of inner low-mass planets, $f(SN|CJ) > f(SN)$. This might indicate that cold Jupiters have an opposite influence in the formation of inner sub-Neptunes around late-type dwarfs as opposed to their solar-type counterparts, boosting the formation of mini-Neptunes instead of impeding it., Comment: 21 pages, 17 figures, 8 table. Accepted by A&A