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Despite increasing recognition of the importance of high-quality school leadership, we know remarkably little about principal skill development. Using administrative data from Tennessee, Oregon, and New York City, we estimate the returns to principal experience as measured by student outcomes, teacher hiring and retention patterns, and teacher and supervisor ratings of principals. The typical principal leads a school for only 3-5 years and leaves the principalship after 6-7 years. We find little evidence that school performance improves as principals gain experience, despite substantial improvement in supervisor ratings. Our results suggest that strategies intended to increase principal retention are unlikely to improve school outcomes absent more comprehensive efforts to strengthen the link between principal skill development and student and school outcomes.

Reinforcement learning from human feedback (RLHF), which aligns a diffusion model with input prompt, has become a crucial step in building reliable generative AI models. Most works in this area use a discrete-time formulation, which is prone to induced errors, and often not applicable to models with higher-order/black-box solvers. The objective of this study is to develop a disciplined approach to fine-tune diffusion models using continuous-time RL, formulated as a stochastic control problem with a reward function that aligns the end result (terminal state) with input prompt. The key idea is to treat score matching as controls or actions, and thereby making connections to policy optimization and regularization in continuous-time RL. To carry out this idea, we lay out a new policy optimization framework for continuous-time RL, and illustrate its potential in enhancing the value networks design space via leveraging the structural property of diffusion models. We validate the advantages of our method by experiments in downstream tasks of fine-tuning large-scale Text2Image models of Stable Diffusion v1.5., Comment: arXiv admin note: text overlap with arXiv:2409.08400

In this paper, we introduce **harmonic loss** as an alternative to the standard cross-entropy loss for training neural networks and large language models (LLMs). Harmonic loss enables improved interpretability and faster convergence, owing to its scale invariance and finite convergence point by design, which can be interpreted as a class center. We first validate the performance of harmonic models across algorithmic, vision, and language datasets. Through extensive experiments, we demonstrate that models trained with harmonic loss outperform standard models by: (a) enhancing interpretability, (b) requiring less data for generalization, and (c) reducing grokking. Moreover, we compare a GPT-2 model trained with harmonic loss to the standard GPT-2, illustrating that the harmonic model develops more interpretable representations. Looking forward, we believe harmonic loss has the potential to become a valuable tool in domains with limited data availability or in high-stakes applications where interpretability and reliability are paramount, paving the way for more robust and efficient neural network models., Comment: 12 pages, 7 figures; The first two authors contributed equally

The use of structured light to drive highly nonlinear processes in matter not only enables imprinting spatially-resolved properties onto short-wavelength radiation, but also opens alternative avenues for exploring the dynamics of nonlinear laser-matter interactions. In this work, we experimentally and theoretically explore the unique properties of driving high-order harmonic generation (HHG) with Hermite-Gaussian beams. HHG driven by Laguerre-Gauss modes results in harmonics that inherit the azimuthal Laguerre-Gauss modal structure, with their topological charge scaling according to orbital angular momentum conservation. In contrast, when HHG is driven by Hermite-Gauss beams, the harmonic modes do not show a direct correspondence to the driving modal profile. Our experimental measurements using HG$_{01}$ and HG$_{11}$ modes, which are in excellent agreement with our numerical simulations, show that the lobes of the Hermite-Gauss driving beams effectively produce a set of separate phase-locked harmonic beamlets which can interfere downstream. This self-interference, which can be adjusted through the relative position between the gas target and the driving beam focus, can be exploited for precision extreme-ultraviolet interferometry. We demonstrate a simple application to calibrate the dispersion of an extreme-ultraviolet diffraction grating. In addition, we show through simulations that the array of harmonic beamlets can be used as an illumination source for single-shot extreme-ultraviolet ptychography., Comment: 14 pages, 8 figures

Defects introduced to the surface of Bi(111) break the translational symmetry and modify the surface states locally. We present a theoretical and experimental study of the 2D defects on the surface of Bi(111) and the states that they induce. Bi crystals cleaved in ultrahigh vacuum (UHV) at low temperature (110 K) and the resulting ion-etched surface are investigated by low-energy electron diffraction (LEED), X-ray photoelectron spectroscopy, ultraviolet photoelectron spectroscopy (UPS), and scanning tunneling microscopy (STM) as well as spectroscopy (STS) techniques in combination with density functional theory (DFT) calculations. STS measurements of cleaved Bi(111) reveal that a commonly observed bilayer step edge has a lower density of states (DOS) around the Fermi level as compared to the atomic-flat terrace. Following ion bombardment, the Bi(111) surface reveals anomalous behavior at both 110 and 300 K: Surface periodicity is observed by LEED, and a significant increase in the number of bilayer step edges and energetically unfavorable monolayer steps is observed by STM. It is suggested that the newly exposed monolayer steps and the type A bilayer step edges result in an increase to the surface Fermi density as evidenced by UPS measurements and the Kohn-Sham DOS. These states appear to be thermodynamically stable under UHV conditions., Comment: 10 pages, 7 figures. See publisher's website for Supporting Information

Next-generation heat-assisted magnetic recording (HAMR) relies on fast, localized heating of the magnetic medium during the write process. Au plasmonic near-field transducers are an attractive solution to this challenge, but increased thermal stability of Au films is required to improve long-term reliability. This work compares the effect of nanoscale Al, AlOx, and Ta capping films on Au thin films with Ti or Ta adhesion layers for use in HAMR and other high-temperature plasmonic applications. Thermal stability is investigated using a bespoke laser dewetting system, and SEM and AFM are extensively used to interrogate the resulting dewet areas. The most effective capping layers are found to be 0.5-1 nm of Al or AlOx, which can eliminate dewetting under certain conditions. Even one monolayer of AlOx is shown to be highly effective in reducing dewetting. In the case of thicker capping layers of Ta and AlOx, the Au film can easily dewet underneath, leaving an intact capping layer. It is concluded that thinner capping layers are most effective against dewetting as the Au cannot dewet without breaking them and pulling them apart during the dewetting process. A simple model based on energetics considerations is developed, which explains how thinner capping layers can more effectively protect the metal from pore or fissure creation. The model provides some convenient guidelines for choosing both the substrate and capping layer, for a given metal, to maximize the resistance to laser-induced damage., Comment: 14 pages, 12 figures, 3 tables. See publisher's website for Supporting Information

Transition-metal phthalocyanine molecules have attracted considerable interest in the context of spintronics device development due to their amenability to diverse bonding regimes and their intrinsic magnetism. The latter is highly influenced by the quantum fluctuations that arise at the inevitable metal-molecule interface in a device architecture. In this study, we have systematically investigated the dynamical screening effects in phthalocyanine molecules hosting a series of transition-metal ions (Ti, V, Cr, Mn, Fe, Co, and Ni) in contact with the Cu(111) surface. Using comprehensive density functional theory plus Anderson's Impurity Model calculations, we show that the orbital-dependent hybridization and electron correlation together result in strong charge and spin fluctuations. While the instantaneous spin moments of the transition-metal ions are near atomic-like, we find that screening gives rise to considerable lowering or even quenching of these. Our results highlight the importance of quantum fluctuations in metal-contacted molecular devices, which may influence the results obtained from theoretical or experimental probes, depending on their possibly material-dependent characteristic sampling time-scales., Comment: 10 pages, 5 figures, 1 table. See publisher website for Supporting Information

We show that the spin-s square-lattice Heisenberg model has exact many-body scars. These scars are simple valence-bond solids with exactly zero energy, and they exist in even-by-even systems and ladders of width 2. Ladders have additional scars corresponding to injecting one or two magnons on top of a parent valence-bond solid scar. These scars have a remarkably simple physical origin based only the angular momentum algebra and cancellations from spin-antialignment within a valence bond. Our comprehensive exact diagonalization calculations suggest that our valence-bond solids exhaust all exact eigenstates in the Heisenberg model except for few-magnon states near the top of the spectrum. Our scars are interesting because they are not part of a tower, have area-law entanglement, break translation symmetry, and exist for Heisenberg models of all spin., Comment: 8 pages, 7 figures

We introduce an attention-based fermionic neural network (FNN) to variationally solve the problem of two-dimensional Coulomb electron gas in magnetic fields, a canonical platform for fractional quantum Hall (FQH) liquids, Wigner crystals and other unconventional electron states. Working directly with the full Hilbert space of $N$ electrons confined to a disk, our FNN consistently attains energies lower than LL-projected exact diagonalization (ED) and learns the ground state wavefunction to high accuracy. In low LL mixing regime, our FNN reveals microscopic features in the short-distance behavior of FQH wavefunction beyond the Laughlin ansatz. For moderate and strong LL mixing parameters, the FNN outperforms ED significantly. Moreover, a phase transition from FQH liquid to a crystal state is found at strong LL mixing. Our study demonstrates unprecedented power and universality of FNN based variational method for solving strong-coupling many-body problems with topological order and electron fractionalization., Comment: Main: 10 pages, 5 figures. SM: 6 pages, 3 figures

Loop-based boson samplers interfere photons in the time degree of freedom using a sequence of delay lines. Since they require few hardware components while also allowing for long-range entanglement, they are strong candidates for demonstrating quantum advantage beyond the reach of classical emulation. We propose a method to exploit this loop-based structure to more efficiently simulate such systems. Our algorithm exploits a causal-cone argument to decompose the circuit into smaller effective components that can each be simulated sequentially by calling a state vector simulator as a subroutine. To quantify the complexity of our approach, we develop a new lattice path formalism that allows us to efficiently characterize the state space that must be tracked during the simulation. In addition, we develop a heuristic method that allows us to predict the expected average and worst-case memory requirements of running these simulations. We use these methods to compare the simulation complexity of different families of loop-based interferometers, allowing us to quantify the potential for quantum advantage of single-photon Boson Sampling in loop-based architectures., Comment: 27 pages, 15 figures. This version: added a reference to the companion git repository, fixed a bibliographic omission

Optically-addressable spin qubits form the foundation of a new generation of emerging nanoscale sensors. The engineering of these sensors has mainly focused on solid-state systems such as the nitrogen-vacancy (NV) center in diamond. However, NVs are restricted in their ability to interface with biomolecules due to their bulky diamond host. Meanwhile, fluorescent proteins have become the gold standard in bioimaging, as they are genetically encodable and easily integrated with biomolecules. While fluorescent proteins have been suggested to possess a metastable triplet state, they have not been investigated as qubit sensors. Here, we realize an optically-addressable spin qubit in the Enhanced Yellow Fluorescent Protein (EYFP) enabled by a novel spin-readout technique. A near-infrared laser pulse allows for triggered readout of the triplet state with up to 44% spin contrast. Using coherent microwave control of the EYFP spin at liquid-nitrogen temperatures, we measure a spin-lattice relaxation time of $(141 \pm 5)\, \mathrm{\mu s}$, a $(16 \pm 2)\, \mathrm{\mu s}$ coherence time under Carr-Purcell-Meiboom-Gill (CPMG) decoupling, and a predicted oscillating (AC) magnetic field sensitivity with an upper bound of $183 \, \mathrm{fT}\, \mathrm{mol}^{1/2}\, \mathrm{Hz}^{-1/2}$. We express the qubit in mammalian cells, maintaining contrast and coherent control despite the complex intracellular environment. Finally, we demonstrate optically-detected magnetic resonance at room temperature in aqueous solution with contrast up to 3%, and measure a static (DC) field sensitivity with an upper bound of $93 \, \mathrm{pT}\, \mathrm{mol}^{1/2}\, \mathrm{Hz}^{-1/2}$. Our results establish fluorescent proteins as a powerful new qubit sensor platform and pave the way for applications in the life sciences that are out of reach for solid-state technologies.

Exfoliation and stacking of two-dimensional (2D) van der Waals (vdW) crystals have created unprecedented opportunities in the discovery of quantum phases. A major obstacle to the advancement of this field is the limited spectroscopic access due to a mismatch in sample sizes (1 - 10 micrometer) and wavelengths (0.1 - 1 millimeter) of electromagnetic radiation relevant to their low-energy excitations. Here, we introduce a new member of the 2D vdW material family: a terahertz (THz) emitter. We show intense and broadband THz generation from the vdW ferroelectric semiconductor NbOI2 with optical rectification efficiency over one-order-of-magnitude higher than that of the current standard THz emitter, ZnTe. The NbOI2 THz emitter can be easily integrated into vdW heterostructures for on-chip near-field THz spectroscopy of a target vdW material/device. Our approach provides a general spectroscopic tool for the rapidly expanding field of 2D vdW materials and quantum matter., Comment: 18 pages, 3 figures, 15 pages of Supplementary Information

In recent years, imitation learning from large-scale human demonstrations has emerged as a promising paradigm for training robot policies. However, the burden of collecting large quantities of human demonstrations is significant in terms of collection time and the need for access to expert operators. We introduce a new data collection paradigm, RoboCrowd, which distributes the workload by utilizing crowdsourcing principles and incentive design. RoboCrowd helps enable scalable data collection and facilitates more efficient learning of robot policies. We build RoboCrowd on top of ALOHA (Zhao et al. 2023) -- a bimanual platform that supports data collection via puppeteering -- to explore the design space for crowdsourcing in-person demonstrations in a public environment. We propose three classes of incentive mechanisms to appeal to users' varying sources of motivation for interacting with the system: material rewards, intrinsic interest, and social comparison. We instantiate these incentives through tasks that include physical rewards, engaging or challenging manipulations, as well as gamification elements such as a leaderboard. We conduct a large-scale, two-week field experiment in which the platform is situated in a university cafe. We observe significant engagement with the system -- over 200 individuals independently volunteered to provide a total of over 800 interaction episodes. Our findings validate the proposed incentives as mechanisms for shaping users' data quantity and quality. Further, we demonstrate that the crowdsourced data can serve as useful pre-training data for policies fine-tuned on expert demonstrations -- boosting performance up to 20% compared to when this data is not available. These results suggest the potential for RoboCrowd to reduce the burden of robot data collection by carefully implementing crowdsourcing and incentive design principles., Comment: 21 pages, 25 figures

Quantum resistance is vital for emerging cryptographic systems as quantum technologies continue to advance towards large-scale, fault-tolerant quantum computers. Resistance may be offered by quantum key distribution (QKD), which provides information-theoretic security using quantum states of photons, but may be limited by transmission loss at long distances. An alternative approach uses classical means and is conjectured to be resistant to quantum attacks, so-called post-quantum cryptography (PQC), but it is yet to be rigorously proven, and its current implementations are computationally expensive. To overcome the security and performance challenges present in each, here we develop hybrid protocols by which QKD and PQC inter-operate within a joint quantum-classical network. In particular, we consider different hybrid designs that may offer enhanced speed and/or security over the individual performance of either approach. Furthermore, we present a method for analyzing the security of hybrid protocols in key distribution networks. Our hybrid approach paves the way for joint quantum-classical communication networks, which leverage the advantages of both QKD and PQC and can be tailored to the requirements of various practical networks., Comment: 6 pages, 3 figures, including extra supplementary materials

The rapid advancement of quantum technologies calls for the design and deployment of quantum-safe cryptographic protocols and communication networks. There are two primary approaches to achieving quantum-resistant security: quantum key distribution (QKD) and post-quantum cryptography (PQC). While each offers unique advantages, both have drawbacks in practical implementation. In this work, we introduce the pros and cons of these protocols and explore how they can be combined to achieve a higher level of security and/or improved performance in key distribution. We hope our discussion inspires further research into the design of hybrid cryptographic protocols for quantum-classical communication networks., Comment: 4 pages, a blue print paper, Submission for IEEE 2024 IEEE Workshop on Quantum IntelLigence, Learning & Security (QUILLS), https://sites.google.com/pitt.edu/quills/home

Sparse autoencoders have recently produced dictionaries of high-dimensional vectors corresponding to the universe of concepts represented by large language models. We find that this concept universe has interesting structure at three levels: 1) The "atomic" small-scale structure contains "crystals" whose faces are parallelograms or trapezoids, generalizing well-known examples such as (man-woman-king-queen). We find that the quality of such parallelograms and associated function vectors improves greatly when projecting out global distractor directions such as word length, which is efficiently done with linear discriminant analysis. 2) The "brain" intermediate-scale structure has significant spatial modularity; for example, math and code features form a "lobe" akin to functional lobes seen in neural fMRI images. We quantify the spatial locality of these lobes with multiple metrics and find that clusters of co-occurring features, at coarse enough scale, also cluster together spatially far more than one would expect if feature geometry were random. 3) The "galaxy" scale large-scale structure of the feature point cloud is not isotropic, but instead has a power law of eigenvalues with steepest slope in middle layers. We also quantify how the clustering entropy depends on the layer., Comment: 13 pages, 12 figures

Motivated by interpretability and reliability, we investigate how neural networks represent knowledge during graph learning, We find hints of universality, where equivalent representations are learned across a range of model sizes (from $10^2$ to $10^9$ parameters) and contexts (MLP toy models, LLM in-context learning and LLM training). We show that these attractor representations optimize generalization to unseen examples by exploiting properties of knowledge graph relations (e.g. symmetry and meta-transitivity). We find experimental support for such universality by showing that LLMs and simpler neural networks can be stitched, i.e., by stitching the first part of one model to the last part of another, mediated only by an affine or almost affine transformation. We hypothesize that this dynamic toward simplicity and generalization is driven by "intelligence from starvation": where overfitting is minimized by pressure to minimize the use of resources that are either scarce or competed for against other tasks., Comment: 14 pages, 13 figures

Recently, numerous preference optimization algorithms have been introduced as extensions to the Direct Preference Optimization (DPO) family. While these methods have successfully aligned models with human preferences, there is a lack of understanding regarding the contributions of their additional components. Moreover, fair and consistent comparisons are scarce, making it difficult to discern which components genuinely enhance downstream performance. In this work, we propose RainbowPO, a unified framework that demystifies the effectiveness of existing DPO methods by categorizing their key components into seven broad directions. We integrate these components into a single cohesive objective, enhancing the performance of each individual element. Through extensive experiments, we demonstrate that RainbowPO outperforms existing DPO variants. Additionally, we provide insights to guide researchers in developing new DPO methods and assist practitioners in their implementations.

Though parameter shift rules have drastically improved gradient estimation methods for several types of quantum circuits, leading to improved performance in downstream tasks, so far they have not been transferable to linear optics with single photons. In this work, we derive an analytical formula for the gradients in these circuits with respect to phaseshifters via a generalized parameter shift rule, where the number of parameter shifts depends linearly on the total number of photons. Experimentally, this enables access to derivatives in photonic systems without the need for finite difference approximations. Building on this, we propose two strategies through which one can reduce the number of shifts in the expression, and hence reduce the overall sample complexity. Numerically, we show that this generalized parameter-shift rule can converge to the minimum of a cost function with fewer parameter update steps than alternative techniques. We anticipate that this method will open up new avenues to solving optimization problems with photonic systems, as well as provide new techniques for the experimental characterization and control of linear optical systems., Comment: 13 + 11 pages, 7 figures

Preference tuning is a crucial process for aligning deep generative models with human preferences. This survey offers a thorough overview of recent advancements in preference tuning and the integration of human feedback. The paper is organized into three main sections: 1) introduction and preliminaries: an introduction to reinforcement learning frameworks, preference tuning tasks, models, and datasets across various modalities: language, speech, and vision, as well as different policy approaches, 2) in-depth exploration of each preference tuning approach: a detailed analysis of the methods used in preference tuning, and 3) applications, discussion, and future directions: an exploration of the applications of preference tuning in downstream tasks, including evaluation methods for different modalities, and an outlook on future research directions. Our objective is to present the latest methodologies in preference tuning and model alignment, enhancing the understanding of this field for researchers and practitioners. We hope to encourage further engagement and innovation in this area., Comment: Survey paper

Reinforcement Learning from human feedback (RLHF) has been shown a promising direction for aligning generative models with human intent and has also been explored in recent works for alignment of diffusion generative models. In this work, we provide a rigorous treatment by formulating the task of fine-tuning diffusion models, with reward functions learned from human feedback, as an exploratory continuous-time stochastic control problem. Our key idea lies in treating the score-matching functions as controls/actions, and upon this, we develop a unified framework from a continuous-time perspective, to employ reinforcement learning (RL) algorithms in terms of improving the generation quality of diffusion models. We also develop the corresponding continuous-time RL theory for policy optimization and regularization under assumptions of stochastic different equations driven environment. Experiments on the text-to-image (T2I) generation will be reported in the accompanied paper.

Most deep learning models of multiclass arrhythmia classification are tested on fingertip photoplethysmographic (PPG) data, which has higher signal-to-noise ratios compared to smartwatch-derived PPG, and the best reported sensitivity value for premature atrial/ventricular contraction (PAC/PVC) detection is only 75%. To improve upon PAC/PVC detection sensitivity while maintaining high AF detection, we use multi-modal data which incorporates 1D PPG, accelerometers, and heart rate data as the inputs to a computationally efficient 1D bi-directional Gated Recurrent Unit (1D-Bi-GRU) model to detect three arrhythmia classes. We used motion-artifact prone smartwatch PPG data from the NIH-funded Pulsewatch clinical trial. Our multimodal model tested on 72 subjects achieved an unprecedented 83% sensitivity for PAC/PVC detection while maintaining a high accuracy of 97.31% for AF detection. These results outperformed the best state-of-the-art model by 20.81% for PAC/PVC and 2.55% for AF detection even while our model was computationally more efficient (14 times lighter and 2.7 faster).

Plasmonic near-field transducers (NFTs) play a key role in administering nanoscale heating for a number of applications ranging from medical devices to next generation data processing technology. We present a novel multi-scale approach, combining quantum many-body perturbation theory with finite-element modelling, to predict the electric and thermal material parameters of various Au-based, noble metal (M) alloys. Specifically, we focus on modelling their performance within an NFT designed to focus high-intensity, sub-diffracted light for technologies such as nanoscale etching, manipulation, sensing, and heat-assisted magnetic recording (HAMR). Elemental Au is the long-standing general-purpose NFT medium due its excellent plasmonic performance at relevant wavelengths. However, elemental Au is a soft, ductile material that tends to extrude and deform in response to extreme temperature gradients. Therefore, alloying Au with other noble metals such as Ag, Cu, Pd or Pt, has attracted considerable interest for improved mechanical and thermal robustness while reaching threshold plasmonic generation at standard optoelectronics operating wavelengths (e.g., $\approx 830$~nm) and approximate high-power NFT temperatures ($\approx 400$~K). We predict that certain Au-Ag alloys may offer improved thermal stability as whole-NFT media compared to elemental Au, alongside plasmonic figures of merit comparable to that of Au. Simulations of certain solid solution Au-Pd/Pt alloys enable us to predict significantly enhanced thermal conductivity. We predict that alloying with Pd at low concentrations $\sim 10\%$ may preserve the NFT performance of Au, while offering the benefits of improved thermal and mechanical stability., Comment: 8 pages, 4 figures, 1 table. Includes Supplemental Material with 10 tables

Finding the optimal learning rate for language model pretraining is a challenging task. This is not only because there is a complicated correlation between learning rate, batch size, number of training tokens, model size, and other hyperparameters but also because it is prohibitively expensive to perform a hyperparameter search for large language models with Billions or Trillions of parameters. Recent studies propose using small proxy models and small corpus to perform hyperparameter searches and transposing the optimal parameters to large models and large corpus. While the zero-shot transferability is theoretically and empirically proven for model size related hyperparameters, like depth and width, the zero-shot transfer from small corpus to large corpus is underexplored. In this paper, we study the correlation between optimal learning rate, batch size, and number of training tokens for the recently proposed WSD scheduler. After thousands of small experiments, we found a power-law relationship between variables and demonstrated its transferability across model sizes. Based on the observation, we propose a new learning rate scheduler, Power scheduler, that is agnostic about the number of training tokens and batch size. The experiment shows that combining the Power scheduler with Maximum Update Parameterization (muP) can consistently achieve impressive performance with one set of hyperparameters regardless of the number of training tokens, batch size, model size, and even model architecture. Our 3B dense and MoE models trained with the Power scheduler achieve comparable performance as state-of-the-art small language models. We open-source these pretrained models at https://ibm.biz/BdKhLa.

Burgess et al. have recently introduced the BLOR corrective exchange-correlation functional that is, by construction, the unique simplified rotationally-invariant DFT+U functional that enforces the flat-plane condition separately on each effective orbital of a localized subspace. Detached from the Hubbard model, functionals of this type are both double-counting correction free and, when optimized in situ using appropriate error quantifiers, effectively parameter free. In this work, the extension of the BLOR functional to address many-body errors (mBLOR) is derived. The mBLOR functional is built to enforce the flat-plane condition on the entire subspace, rather than on each orbital individually. In this way inter-orbital errors are corrected on the same footing as the single-particle ones. Focusing on exact test cases with strong inter-orbital interactions, the BLOR and mBLOR functionals were benchmarked against contemporary DFT+U functionals using the total energy extensivity condition on stretched homo-nuclear p-block dimers that represent various self-interaction and static-correlation error regimes. The BLOR functional outperformed all other DFT+$U$ functionals tested, which often act to increase total-energy errors, yet it still yielded large errors in some systems. mBLOR instead yielded low energy errors across all four strongly-correlated dimers, while being constructed using only semi-local approximation ingredients. As mBLOR would not otherwise introduce a band-gap correction in the manner that is a desirable feature of DFT+U, we developed a cost-free technique to reintroduce it automatically by moving the functional's unusual explicit derivative discontinuity into the potential. With this in place, mBLOR is the only known DFT$+U$ functional that opens the bandgap of stretched neutral homo-nuclear dimers without the aid of unphysical spin-symmetry breaking., Comment: As accepted for publication in Phys. Rev. B. 22 pages, 9 figures, and 4 tables

We present the implementation of the Hubbard ($U$) and Hund ($J$) corrected Density Functional Theory (DFT+$U$+$J$) functionality in the Quickstep program, which is part of the CP2K suite. The tensorial and L\"owdin subspace representations are implemented and compared. Full analytical DFT+$U$+$J$ forces are implemented and benchmarked for the tensorial and L\"owdin representations. We also present the implementation of the recently proposed minimum-tracking linear-response method that enables the $U$ and $J$ parameters to be calculated on first principles basis without reference to the Kohn-Sham eigensystem. These implementations are benchmarked against recent results for different materials properties including DFT+$U$ band gap opening in NiO, the relative stability of various polaron distributions in TiO$_2$, the dependence of the calculated TiO$_2$ band gap on +$J$ corrections, and, finally, the role of the +$U$ and +$J$ corrections for the computed properties of a series of the hexahydrated transition metals. Our implementation provides results consistent with those already reported in the literature from comparable methods. We conclude the contribution with tests on the influence of the L\"owdin orthonormalization on the occupancies, calculated parameters, and derived properties.

This paper introduces long-context Granite code models that support effective context windows of up to 128K tokens. Our solution for scaling context length of Granite 3B/8B code models from 2K/4K to 128K consists of a light-weight continual pretraining by gradually increasing its RoPE base frequency with repository-level file packing and length-upsampled long-context data. Additionally, we also release instruction-tuned models with long-context support which are derived by further finetuning the long context base models on a mix of permissively licensed short and long-context instruction-response pairs. While comparing to the original short-context Granite code models, our long-context models achieve significant improvements on long-context tasks without any noticeable performance degradation on regular code completion benchmarks (e.g., HumanEval). We release all our long-context Granite code models under an Apache 2.0 license for both research and commercial use.

We study the entire energy spectrum of an electron droplet in the lowest Landau level. By exact diagonalization calculations, we find highly excited states in the middle of the spectrum that display unexpected density distribution and pair correlation. We show that these exceptional excited states contain tightly bound electron bubbles with local filling $\nu = 1$ that form various ordered structures. Remarkably, these bubble excited states are shown to exist for both the $1/r$ Coulomb interaction and the $1/r^3$ dipole interaction. The experimental realization of bubble excited states in moir\'e materials under a magnetic field is also discussed., Comment: Main: 6 pages, 4 figures. SM: 11 pages, 6 figures

Traversability estimation in rugged, unstructured environments remains a challenging problem in field robotics. Often, the need for precise, accurate traversability estimation is in direct opposition to the limited sensing and compute capability present on affordable, small-scale mobile robots. To address this issue, we present a novel method to learn [u]ncertainty-aware [n]avigation features from high-fidelity scans of [real]-world environments (UNRealNet). This network can be deployed on-robot to predict these high-fidelity features using input from lower-quality sensors. UNRealNet predicts dense, metric-space features directly from single-frame lidar scans, thus reducing the effects of occlusion and odometry error. Our approach is label-free, and is able to produce traversability estimates that are robot-agnostic. Additionally, we can leverage UNRealNet's predictive uncertainty to both produce risk-aware traversability estimates, and refine our feature predictions over time. We find that our method outperforms traditional local mapping and inpainting baselines by up to 40%, and demonstrate its efficacy on multiple legged platforms.

Moir\'e materials provide an ideal platform for exploring quantum phases of matter. However, solving the many-electron problem in moir\'e systems is challenging due to strong correlation effects. We introduce a powerful variational representation of quantum states, many-body neural Bloch wavefunction, to solve many-electron problems in moir\'e materials accurately and efficiently. Applying our method to the semiconductor heterobilayer WSe2/WS2 , we obtain a generalized Wigner crystal at filling factor n = 1/3, a Mott insulator n = 1, and a correlated insulator with local magnetic moments and antiferromagnetic spin correlation at n = 2. Our neural network approach improves the simulation accuracy of strongly interacting moir\'e materials and paves the way for discovery of new quantum phases with variational learning principle in a unified framework.

We propose a new observable derived from a centrality-dependent scaling of transverse particle spectra. By removing the global scales of total particle number and mean transverse momentum, we isolate the shape of the spectrum. In hydrodynamic simulations, while the multiplicity and mean transverse momentum fluctuate significantly, the scaled spectrum is found to be almost constant even at an event-by-event level and after resonance decays. This universality survives when averaging over events in each centrality bin before scaling. We then investigate the presence of this scaling in experimental data from the ALICE collaboration in Pb-Pb, Xe-Xe, and p-Pb collisions. We find a remarkable universality in the experimentally observed scaled spectra at low transverse momentum, compatible with hydrodynamic predictions. The data show a minor breaking of universality at large transverse momentum and hints of evolution with the system size that are not seen in simulations. Our results motivate further theoretical and experimental investigations of this new observable to bring to light the collective and non-collective behavior encoded in the transverse particle spectrum of different collision systems., Comment: V1: 6 pages, 3 figures

We demonstrate nearly a microsecond of spin coherence in Er3+ ions doped in cerium dioxide nanocrystal hosts, despite a large gyromagnetic ratio and nanometric proximity of the spin defect to the nanocrystal surface. The long spin coherence is enabled by reducing the dopant density below the instantaneous diffusion limit in a nuclear spin-free host material, reaching the limit of a single erbium spin defect per nanocrystal. We observe a large Orbach energy in a highly symmetric cubic site, further protecting the coherence in a qubit that would otherwise rapidly decohere. Spatially correlated electron spectroscopy measurements reveal the presence of Ce3+ at the nanocrystal surface that likely acts as extraneous paramagnetic spin noise. Even with these factors, defect-embedded nanocrystal hosts show tremendous promise for quantum sensing and quantum communication applications, with multiple avenues, including core-shell fabrication, redox tuning of oxygen vacancies, and organic surfactant modification, available to further enhance their spin coherence and functionality in the future., Comment: 26 pages, 5 figures