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Over the past year, Speculative Decoding has gained popularity as a technique for accelerating Large Language Model inference. While several methods have been introduced, most struggle to deliver satisfactory performance at batch sizes typical for data centers ($\geq 8$) and often involve significant deployment complexities. In this work, we offer a theoretical explanation of how Speculative Decoding can be effectively utilized with larger batch sizes. We also introduce a method that integrates seamlessly into existing systems without additional training or the complexity of deploying a small LLM. In a continuous batching setting, we achieve a 4x increase in throughput without any latency impact for short context generation, and a 1.7-2x improvement in both latency and throughput for longer contexts., Comment: 14 pages, 7 figures

The vector valued theta series of a positive-definite even lattice is a modular form for the Weil representation of $\mathrm{SL}_2(\mathbb{Z})$. We show that the space of cusp forms for the Weil representation is generated by such functions. This gives a positive answer to Eichler's basis problem in this case. As applications we derive Waldspurger's result on the basis problem for scalar valued modular forms and give a new proof of the surjectivity of the Borcherds lift based on the analysis of local Picard groups., Comment: 43 pages; corrected a minor error in Lemma 6.5 as well as some typos

For an isotropic subgroup $H$ of a discriminant form $D$ there exists a lift from modular forms for the Weil representation of the discriminant form $H^\bot/H$ to modular forms for the Weil representation of $D$. We determine a set of discriminant forms such that all modular forms for any discriminant form are induced from the discriminant forms in this set. Furthermore for any discriminant form in this set there exist modular forms that are not induced from smaller discriminant forms., Comment: 25 pages; more detailed summary of section 4 in the introduction, some comments added to section 3

We show, using three empirical applications, that linear regression estimates which rely on the assumption of sparsity are fragile in two ways. First, we document that different choices of the regressor matrix that do not impact ordinary least squares (OLS) estimates, such as the choice of baseline category with categorical controls, can move sparsity-based estimates two standard errors or more. Second, we develop two tests of the sparsity assumption based on comparing sparsity-based estimators with OLS. The tests tend to reject the sparsity assumption in all three applications. Unless the number of regressors is comparable to or exceeds the sample size, OLS yields more robust results at little efficiency cost., Comment: 44 pages, including appendices

Monte-Carlo path tracing is a powerful technique for realistic image synthesis but suffers from high levels of noise at low sample counts, limiting its use in real-time applications. To address this, we propose a framework with end-to-end training of a sampling importance network, a latent space encoder network, and a denoiser network. Our approach uses reinforcement learning to optimize the sampling importance network, thus avoiding explicit numerically approximated gradients. Our method does not aggregate the sampled values per pixel by averaging but keeps all sampled values which are then fed into the latent space encoder. The encoder replaces handcrafted spatiotemporal heuristics by learned representations in a latent space. Finally, a neural denoiser is trained to refine the output image. Our approach increases visual quality on several challenging datasets and reduces rendering times for equal quality by a factor of 1.6x compared to the previous state-of-the-art, making it a promising solution for real-time applications., Comment: Submitted to NeurIPS. https://openreview.net/forum?id=xNyR7DXUzJ

The transformation behaviour of the vector valued theta function of a positive-definite even lattice under the metaplectic group $\mathrm{Mp}_2(\mathbb{Z})$ is described by the Weil representation. We show that the invariants of this representation are induced from $5$ fundamental invariants. As an application we give simple generating sets for Jacobi forms of singular weight., Comment: 36 pages; added some details; to appear in Commun. Contemp. Math

In context of the universal presence of defects in additively manufactured (AM) metals, efficient computational tools are required to rapidly screen AM microstructures for mechanical integrity. To this end, a deep learning approach is used to predict the elastic stress fields in images of defect-containing metal microstructures. A large dataset consisting of the stress response of 100,000 random microstructure images is generated using high-resolution Fast Fourier Transform-based finite element (FFT-FE) calculations, which is then used to train a modified U-Net style convolutional neural network (CNN) model. The trained U-Net model more accurately predicted the stress response compared to alternative CNN architectures, exceeded the accuracy of low-resolution FFT-FE calculations, and was generalizable to microstructures with complex defect geometries. The model was applied to images of real AM microstructures with severe lack of fusion defects, and predicted a strong linear increase of maximum stress as a function of pore fraction. Together, the proposed CNN offers an efficient and accurate way to predict the structural response of defect-containing AM microstructures.

We propose a method for constructing confidence intervals that account for many forms of spatial correlation. The interval has the familiar `estimator plus and minus a standard error times a critical value' form, but we propose new methods for constructing the standard error and the critical value. The standard error is constructed using population principal components from a given `worst-case' spatial covariance model. The critical value is chosen to ensure coverage in a benchmark parametric model for the spatial correlations. The method is shown to control coverage in large samples whenever the spatial correlation is weak, i.e., with average pairwise correlations that vanish as the sample size gets large. We also provide results on correct coverage in a restricted but nonparametric class of strong spatial correlations, as well as on the efficiency of the method. In a design calibrated to match economic activity in U.S. states the method outperforms previous suggestions for spatially robust inference about the population mean.

Full-scale quantum computers require the integration of millions of quantum bits. The promise of leveraging industrial semiconductor manufacturing to meet this requirement has fueled the pursuit of quantum computing in silicon quantum dots. However, to date, their fabrication has relied on electron-beam lithography and, with few exceptions, on academic style lift-off processes. Although these fabrication techniques offer process flexibility, they suffer from low yield and poor uniformity. An important question is whether the processing conditions developed in the manufacturing fab environment to enable high yield, throughput, and uniformity of transistors are suitable for quantum dot arrays and do not compromise the delicate qubit properties. Here, we demonstrate quantum dots hosted at a 28Si/28SiO2 interface, fabricated in a 300 mm semiconductor manufacturing facility using all-optical lithography and fully industrial processing. As a result, we achieve nanoscale gate patterns with remarkable homogeneity. The quantum dots are well-behaved in the multi-electron regime, with excellent tunnel barrier control, a crucial feature for fault-tolerant two-qubit gates. Single-spin qubit operation using magnetic resonance reveals relaxation times of over 1 s at 1 Tesla and coherence times of over 3 ms, matching the quality of silicon spin qubits reported to date. The feasibility of high-quality qubits made with fully-industrial techniques strongly enhances the prospects of a large-scale quantum computer, Comment: 23 pages, 4 figures, 12 supplementary figures

Standard inference about a scalar parameter estimated via GMM amounts to applying a t-test to a particular set of observations. If the number of observations is not very large, then moderately heavy tails can lead to poor behavior of the t-test. This is a particular problem under clustering, since the number of observations then corresponds to the number of clusters, and heterogeneity in cluster sizes induces a form of heavy tails. This paper combines extreme value theory for the smallest and largest observations with a normal approximation for the average of the remaining observations to construct a more robust alternative to the t-test. The new test is found to control size much more successfully in small samples compared to existing methods. Analytical results in the canonical inference for the mean problem demonstrate that the new test provides a refinement over the full sample t-test under more than two but less than three moments, while the bootstrapped t-test does not.

High carrier mobilities play a fundamental role for high-frequency electronics, integrated optoelectronics as well as for sensor and spintronic applications, where device performance is directly linked to the magnitude of the carrier mobility. Van der Waals heterostructures formed by graphene and hexagonal boron nitride (hBN) already outperform all known materials in terms of room temperature mobility. Here, we show that the mobility of today's best graphene/hBN devices can be surpassed by more than a factor of three by heterostructures formed by tungsten diselenide (WSe$_2$), graphene and hBN, which can have mobilities as high as 350,000 cm$^2$/(Vs) at room temperature, and resistivities as low as 15 Ohm. The resistivity of these devices shows a much weaker temperature dependence than the one of graphene on any other known substrate. The origin of this behaviour points to modified acoustic phonon bands in graphene and questions our understanding of electron-phonon scattering in van der Waals heterostructures., Comment: 15 pages, 3 figures

We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the sum of the smaller summands. If the tail is well approximated by a Pareto density, then this new approximation has substantially smaller error rates compared to the usual normal approximation for underlying distributions with finite variance and less than three moments. It can also provide an accurate approximation for some infinite variance distributions.

Transcranial focused ultrasound (tFUS) is an emerging form of non-surgical human neuromodulation that confers advantages over existing electro and electromagnetic technologies by providing a superior spatial resolution on the millimeter scale as well as the capability to target sub-cortical structures non-invasively. An examination of the pairing of tFUS and blood oxygen level dependent (BOLD) functional MRI (fMRI) in humans is presented here., Comment: EMBC 2016

A microscopic study of the individual annealed (In,Ga)As/GaAs quantum dots is done by means of high-resolution transmission electron microscopy. The Cauchy-Green strain-tensor component distribution and the chemical composition of the (In,Ga)As alloy are extracted from the microscopy images. The image processing allows for the reconstruction of the strain-induced electric-field gradients at the individual atomic columns extracting thereby the magnitude and asymmetry parameter of the nuclear quadrupole interaction. Nuclear magnetic resonance absorption spectra are analyzed for parallel and transverse mutual orientations of the electric-field gradient and a static magnetic field., Comment: 8 pages, 6 figures

Constraint satisfaction problems (CSPs) are typically solved using conventional von Neumann computing architectures. However, these architectures do not reflect the distributed nature of many of these problems and are thus ill-suited to solving them. In this paper we present a hybrid analog/digital hardware architecture specifically designed to solve such problems. We cast CSPs as networks of stereotyped multi-stable oscillatory elements that communicate using digital pulses, or events. The oscillatory elements are implemented using analog non-stochastic circuits. The non-repeating phase relations among the oscillatory elements drive the exploration of the solution space. We show that this hardware architecture can yield state-of-the-art performance on a number of CSPs under reasonable assumptions on the implementation. We present measurements from a prototype electronic chip to demonstrate that a physical implementation of the proposed architecture is robust to practical non-idealities and to validate the theory proposed., Comment: First two authors contributed equally to this work

Objective. While ultrasound is largely established for use in diagnostic imaging and heating therapies, its application for neuromodulation is relatively new and not well understood. The objective of the present study was to investigate issues related to interactions between focused acoustic beams and brain tissues to better understand possible limitations of transcranial ultrasound for neuromodulation. Approach. A computational model of transcranial focused ultrasound was constructed and validated against bench top experimental data. The models were then incrementally extended to address and investigate a number of issues related to the use of ultrasound for neuromodulation. These included the effect of variations in skull geometry and gyral anatomy, as well as the effect of transmission across multiple tissue and media layers, such as scalp, skull, CSF, and gray/white matter on ultrasound insertion behavior. In addition, a sensitivity analysis was run to characterize the influence of acoustic properties of intracranial tissues. Finally, the heating associated with ultrasonic stimulation waveforms designed for neuromodulation was modeled. Main results. Depending on factors such as acoustic frequency, the insertion behavior of a transcranial focused ultrasound beam is only subtly influenced by the geometry and acoustic properties of the underlying tissues. Significance. These issues are critical for the refinement of device design and the overall advancement of ultrasound methods for noninvasive neuromodulation., Comment: 32 pages, 14 figures, and 3 tables