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We examine the implicit bias of mirror flow in least squares error regression with wide and shallow neural networks. For a broad class of potential functions, we show that mirror flow exhibits lazy training and has the same implicit bias as ordinary gradient flow when the network width tends to infinity. For univariate ReLU networks, we characterize this bias through a variational problem in function space. Our analysis includes prior results for ordinary gradient flow as a special case and lifts limitations which required either an intractable adjustment of the training data or networks with skip connections. We further introduce scaled potentials and show that for these, mirror flow still exhibits lazy training but is not in the kernel regime. For univariate networks with absolute value activations, we show that mirror flow with scaled potentials induces a rich class of biases, which generally cannot be captured by an RKHS norm. A takeaway is that whereas the parameter initialization determines how strongly the curvature of the learned function is penalized at different locations of the input space, the scaled potential determines how the different magnitudes of the curvature are penalized. 

We examine the implicit bias of mirror flow in least squares error regression with wide and shallow neural networks. For a broad class of potential functions, we show that mirror flow exhibits lazy training and has the same implicit bias as ordinary gradient flow when the network width tends to infinity. For univariate ReLU networks, we characterize this bias through a variational problem in function space. Our analysis includes prior results for ordinary gradient flow as a special case and lifts limitations which required either an intractable adjustment of the training data or networks with skip connections. We further introduce scaled potentials and show that for these, mirror flow still exhibits lazy training but is not in the kernel regime. For univariate networks with absolute value activations, we show that mirror flow with scaled potentials induces a rich class of biases, which generally cannot be captured by an RKHS norm. A takeaway is that whereas the parameter initialization determines how strongly the curvature of the learned function is penalized at different locations of the input space, the scaled potential determines how the different magnitudes of the curvature are penalized. 

Tuning the molecular architecture of block copolymer blends is a powerful strategy to optimize their performance in pressure-sensitive adhesive (PSA) formulations. 

Superparamagnetic tunnel junctions (sMTJs) are emerging as promising components for stochastic units in neuromorphic computing owing to their tunable random switching behavior. Conventional MTJ control methods, such as spin-transfer torque (STT) and spin–orbit torque (SOT), often require substantial power. Here, we introduce the voltage-controlled exchange coupling (VCEC) mechanism, enabling the switching between antiparallel and parallel states in sMTJs with an ultralow power consumption of only 40 nW, approximately 2 orders of magnitude lower than conventional STT-based sMTJs. This mechanism yields a sigmoid-shaped output response, making it ideally suited to neuromorphic computing applications. Furthermore, we validate the feasibility of integrating VCEC with SOT current control, offering an additional dimension for magnetic state manipulation. This work marks the first practical demonstration of the VCEC effect in sMTJs, highlighting its potential as a low-power control solution for probabilistic bits in advanced computing systems. 

Abstract Magnetic particle imaging (MPI) is a tracer-based tomographic imaging technique utilized in applications such as lung perfusion imaging, cancer diagnosis, stem cell tracking, etc. The goal of translating MPI to clinical use has prompted studies on further improving the spatial-temporal resolutions of MPI through various methods, including image reconstruction algorithm, scanning trajectory design, magnetic field profile design, and tracer design. Iron oxide magnetic nanoparticles (MNPs) are favored for MPI and magnetic resonance imaging (MRI) over other materials due to their high biocompatibility, low cost, and ease of preparation and surface modification. For core–shell MNPs, the tracers’ magnetic core size and non-magnetic coating layer characteristics can significantly affect MPI signals through dynamic magnetization relaxations. Most works to date have assumed an ensemble of MNP tracers with identical sizes, ignoring that artificially synthesized MNPs typically follow a log-normal size distribution, which can deviate theoretical results from experimental data. In this work, we first characterize the size distributions of four commercially available iron oxide MNP products and then model the collective magnetic responses of these MNPs for MPI applications. For an ensemble of MNP tracers with size standard deviations ofσ, we applied a stochastic Langevin model to study the effect of size distribution on MPI imaging performance. Under an alternating magnetic field (AMF), i.e., the excitation field in MPI, we collected the time domain dynamic magnetizations (M-t curves), magnetization-field hysteresis loops (M-H curves), point-spread functions (PSFs), and higher harmonics from these MNP tracers. The intrinsic MPI spatial resolution, which is related to the full width at half maximum (FWHM) of the PSF profile, along with the higher harmonics, serve as metrics to provide insights into how the size distribution of MNP tracers affects MPI performance. 

One-dimensional metal halide perovskites are among the most promising candidate materials for optoelectronic devices. However, the heterogeneity and fast degradation of perovskite nanowires (NWs) and nanorods (NRs) synthesized using conventional approaches impose a bottleneck for their optoelectronic applications. Recently, all-inorganic perovskite CsPbBr3 NRs with tailored dimensions, crafted using an amphiphilic bottlebrush-like block copolymer (BBCP) as nanoreactors, have demonstrated enhanced stabilities. Herein, we report the electronic investigation into these template-grown CsPbBr3 NRs using dielectric force microscopy (DFM), a contactless, nondestructive imaging technique. All freshly prepared CsPbBr3 NRs exhibited ambipolar behaviors for up to two months after sample synthesis. A transition from ambipolar to p-type behaviors occurred after two months, and nearly all NRs completed the transition within two weeks. Moreover, template-grown CsPbBr3 NRs displayed better nanoscale electronic homogeneity compared to their conventional counterparts. The improved electronic uniformity and nanoscale homogeneity place the template-grown CsPbBr3 NRs in a unique advantageous position for optoelectronic applications. 

Persistent homology (PH) is a method for generating topology-inspired representations of data. Empirical studies that investigate the properties of PH, such as its sensitivity to perturbations or ability to detect a feature of interest, commonly rely on training and testing an additional model on the basis of the PH representation. To gain more intrinsic insights about PH, independently of the choice of such a model, we propose a novel methodology based on the pull-back geometry that a PH encoding induces on the data manifold. The spectrum and eigenvectors of the induced metric help to identify the most and least significant information captured by PH. Furthermore, the pull-back norm of tangent vectors provides insights about the sensitivity of PH to a given perturbation, or its potential to detect a given feature of interest, and in turn its ability to solve a given classification or regression problem. Experimentally, the insights gained through our methodology align well with the existing knowledge about PH. Moreover, we show that the pull-back norm correlates with the performance on downstream tasks, and can therefore guide the choice of a suitable PH encoding.