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The latent space of diffusion model mostly still remains unexplored, despite its great success and potential in the field of generative modeling. In fact, the latent space of existing diffusion models are entangled, with a distorted mapping from its latent space to image space. To tackle this problem, we present Isometric Diffusion, equipping a diffusion model with a geometric regularizer to guide the model to learn a geometrically sound latent space of the training data manifold. This approach allows diffusion models to learn a more disentangled latent space, which enables smoother interpolation, more accurate inversion, and more precise control over attributes directly in the latent space. Our extensive experiments consisting of image interpolations, image inversions, and linear editing show the effectiveness of our method.

Deep neural networks (DNNs) continue to grow rapidly in size, making them infeasible to train on a single device. Pipeline parallelism is commonly used in existing DNN systems to support large-scale DNN training by partitioning a DNN into multiple stages, which concurrently perform DNN training for different micro-batches in a pipeline fashion. However, existing pipeline-parallel approaches only consider sequential pipeline stages and thus ignore the topology of a DNN, resulting in missed model-parallel opportunities. This paper presents graph pipeline parallelism (GPP), a new pipeline-parallel scheme that partitions a DNN into pipeline stages whose dependencies are identified by a directed acyclic graph. GPP generalizes existing sequential pipeline parallelism and preserves the inherent topology of a DNN to enable concurrent execution of computationally-independent operators, resulting in reduced memory requirement and improved GPU performance. In addition, we develop GraphPipe, a distributed system that exploits GPP strategies to enable performant and scalable DNN training. GraphPipe partitions a DNN into a graph of stages, optimizes micro-batch schedules for these stages, and parallelizes DNN training using the discovered GPP strategies. Evaluation on a variety of DNNs shows that GraphPipe outperforms existing pipeline-parallel systems such as PipeDream and Piper by up to 1.6X. GraphPipe also reduces the search time by 9-21X compared to PipeDream and Piper.

The exponential of an operator or matrix is widely used in quantum theory, but it sometimes can be a challenge to evaluate. For non-commutative operators ${\bf X}$ and ${\bf Y}$, according to the Campbell-Baker-Hausdorff-Dynkin theorem, ${\rm e}^{{\bf X}+{\bf Y}}$ is not equivalent to ${\rm e}^{\bf X}{\rm e}^{\bf Y}$, but is instead given by the well-known infinite series formula. For a Lie algebra of a basis of three operators $\{{\bf X,Y,Z}\}$, such that $[{\bf X}, {\bf Y}] = \kappa{\bf Z}$ for scalar $\kappa$ and cyclic permutations, here it is proven that ${\rm e}^{a{\bf X}+b{\bf Y}}$ is equivalent to ${\rm e}^{p{\bf Z}}{\rm e}^{q{\bf X}}{\rm e}^{-p{\bf Z}}$ for scalar $p$ and $q$. Extensions for ${\rm e}^{a{\bf X}+b{\bf Y}+c{\bf Z}}$ are also provided. This method is useful for the dynamics of atomic and molecular nuclear and electronic spins in constant and oscillatory transverse magnetic and electric fields., Comment: 6 pages,0 figures

In order to probe the transitions of a nuclear spin $s$ from one of its substate quantum numbers $m$ to another substate $m'$, the experimenter applies a magnetic field ${\bm B}_0$ in some particular direction, such along $\hat{\bm z}$, and then applies an weaker field ${\bm B}_1(t)$ that is oscillatory in time with the angular frequency $\omega$, and is normally perpendicular to ${\bm B}_0$, such as ${\bm B}_1(t)=B_1\hat{\bm x}\cos(\omega t)$. In the rotating wave approximation, ${\bm B}_1(t)=B_1[\hat{\bm x}\cos(\omega t)+\hat{\bm y}\sin(\omega t)]$. Although this problem is solved for spin $\frac{1}{2}$ in every quantum mechanics textbook, for the general spin $s$ case, its general solution has been published only for the overall probability of a transition between the states, but the time dependence of the probability of finding the nucleus in each of the substates has not previously been published. Here we present an elementary method to solve this problem exactly, and present figures for the time dependencies of the various substates states for a variety of initial substate probabilities for a variety of $s$ values. We found a new result: unlike the $s=\frac{1}{2}$ case, for which if the initial probability of finding the particle in one of the substates was 1, and the time dependence of the probabilities of each of the substates oscillates between 0 and 1, for higher spin values, the time dependencies of the probabilities finding the particle in each of its substates, which periodic, is considerably more complicated., Comment: 9 pages 8 figures

As emerging deep neural network (DNN) models continue to grow in size, using large GPU clusters to train DNNs is becoming an essential requirement to achieving acceptable training times. In this paper, we consider the case where future increases in cluster size will cause the global batch size that can be used to train models to reach a fundamental limit: beyond a certain point, larger global batch sizes cause sample efficiency to degrade, increasing overall time to accuracy. As a result, to achieve further improvements in training performance, we must instead consider "strong scaling" strategies that hold the global batch size constant and allocate smaller batches to each GPU. Unfortunately, this makes it significantly more difficult to use cluster resources efficiently. We present DeepPool, a system that addresses this efficiency challenge through two key ideas. First, burst parallelism allocates large numbers of GPUs to foreground jobs in bursts to exploit the unevenness in parallelism across layers. Second, GPU multiplexing prioritizes throughput for foreground training jobs, while packing in background training jobs to reclaim underutilized GPU resources, thereby improving cluster-wide utilization. Together, these two ideas enable DeepPool to deliver a 1.2 - 2.3x improvement in total cluster throughput over standard data parallelism with a single task when the cluster scale is large., Comment: MLSys'22

Improvement in the optoelectronic performance of halide perovskite semiconductors requires the identification and suppression of non-radiative carrier trapping processes. The iodine interstitial has been established as a deep level defect, and implicated as an active recombination centre. We analyse the quantum mechanics of carrier trapping. Fast and irreversible electron capture by the neutral iodine interstitial is found. The effective Huang-Rhys factor exceeds 300, indicative of the strong electron-phonon coupling that is possible in soft semiconductors. The accepting phonon mode has a frequency of 53 cm$^{-1}$ and has an associated electron capture coefficient of 10$^{-10}$cm$^3$s$^{-1}$. The inverse participation ratio is used to quantify the localisation of phonon modes associated with the transition. We infer that suppression of octahedral rotations is an important factor to enhance defect tolerance.

The thermodynamic limit of photovoltaic efficiency for a single-junction solar cell can be readily predicted using the bandgap of the active light absorbing material. Such an approach overlooks the energy loss due to non-radiative electron-hole processes. We propose a practical ab initio procedure to determine the maximum efficiency of a thin-film solar cell that takes into account both radiative and non-radiative recombination. The required input includes the frequency-dependent optical absorption coefficient, as well as the capture cross-sections and equilibrium populations of point defects. For kesterite-structured Cu$_2$ZnSnS$_4$, the radiative limit is reached for a film thickness of around 2.6 micrometer, where the efficiency gain due to light absorption is counterbalanced by losses due to the increase in recombination current., Comment: 5 pages; 3 figures

Various thin-film I$_2$-II-IV-VI$_4$ photovoltaic absorbers derived from kesterite Cu$_2$ZnSn(S,Se)$_4$ have been synthesized, characterized, and theoretically investigated in the past few years. The availability of this homogeneous materials dataset is an opportunity to examine trends in their defect properties and identify criteria to find new defect-tolerant materials in this vast chemical space. We find that substitutions on the Zn site lead to a smooth decrease in band tailing as the ionic radius of the substituting cation increases. Unfortunately, this substitution strategy does not ensure the suppression of deeper defects and non-radiative recombination. Trends across the full dataset suggest that Gaussian and Urbach band tails in kesterite-inspired semiconductors are two separate phenomena caused by two different antisite defect types. Deep Urbach tails are correlated with the calculated band gap narrowing caused by the (2I$_\mathrm{II}$+IV$_\mathrm{II}$) defect cluster. Shallow Gaussian tails are correlated with the energy difference between the kesterite and stannite polymorphs, which points to the role of (I$_\mathrm{II}$+II$_\mathrm{I}$) defect clusters involving Group IB and Group IIB atoms swapping across \textit{different} cation planes. This finding can explain why \textit{in-plane} cation disorder and band tailing are uncorrelated in kesterites. Our results provide quantitative criteria for discovering new kesterite-inspired photovoltaic materials with low band tailing.

Defects influence the properties and functionality of all crystalline materials. For instance, point defects participate in electronic (e.g. carrier generation and recombination) and optical (e.g. absorption and emission) processes critical to solar energy conversion. Solid-state diffusion, mediated by the transport of charged defects, is used for electrochemical energy storage. First-principles calculations of defects based on density functional theory have been widely used to complement, and even validate, experimental observations. In this `quick-start guide', we discuss the best practice in how to calculate the formation energy of point defects in crystalline materials and analysis techniques appropriate to probe changes in structure and properties relevant across energy technologies., Comment: 6 pages, 4 figures, and 1 table

Halide perovskites exhibit slow rates of non-radiative electron-hole recombination upon illumination. Chu et al. [Sci. Adv. 6 7, eaaw7453 (2020)] use the results of first-principles simulations to argue that this arises from the nature of the crystal vibrations and leads to a breakdown of Shockley-Read-Hall theory. We highlight flaws in their methodology and analysis of carrier capture by point defects in crystalline semiconductors., Comment: 3 pages, 1 table

The Shockley-Queisser (SQ) limit provides a convenient metric for predicting light-to-electricity conversion efficiency of a solar cell based on the band gap of the light-absorbing layer. In reality, few materials approach this radiative limit. We develop a formalism and a computational method to predict the maximum photovoltaic efficiency of imperfect crystals from first principles. Our scheme includes equilibrium populations of native defects, their carrier-capture coefficients, and the associated recombination rates. When applied to kesterite solar cells, we reveal an intrinsic limit of 20% for $\mathrm{Cu_2ZnSnSe_4}$, which falls far below the SQ limit of 32%. The effects of atomic substitution and extrinsic doping are studied, leading to pathways for enhanced efficiency of 31%. This approach can be applied to support targeted-materials selection for future solar-energy technologies., Comment: 12 pages, 8 figures, 2 tables

Lattice vibrations of point defects are essential for understanding non-radiative electron and hole capture in semiconductors as they govern properties including persistent photoconductivity and Shockley-Read-Hall recombination rate. Although the harmonic approximation is sufficient to describe a defect with small lattice relaxation, for cases of large lattice relaxation it is likely to break down. We describe a first-principles procedure to account for anharmonic carrier capture and apply it to the important case of the \textit{DX} center in GaAs. This is a system where the harmonic approximation grossly fails. Our treatment of the anharmonic Morse-like potentials accurately describes the observed electron capture barrier, predicting the absence of quantum tunnelling at low temperature, and a high hole capture rate that is independent of temperature. The model also explains the origin of the composition-invariant electron emission barrier. These results highlight an important shortcoming of the standard approach for describing point defect ionization that is accompanied by large lattice relaxation, where charge transfer occurs far from the equilibrium configuration.

The flat band has attracted a lot of attention because it gives rise to many exotic phases, as recently demonstrated in magic angle twisted bilayer graphene. Here, based on first-principles calculations, we identify a metal-insulator transition in boron triangular Kagome lattice with a spin-polarized flat band at 2/3-filling. This phase transition is accompanied by the formation of a Wigner crystal, which is driven by Fermi surface nesting effect and thereby strong electron-phonon interactions, keeping ferromagnetism. Our calculation results suggest that boron triangular Kagome lattices with partially filled flat bands may open a new playground for many exotic quantum phases in two-dimensional systems, such as Winger crystallization and fractional quantum Hall states.

There is evidence that interface recombination in Cu2ZnSnS4 solar cells contributes to the open-circuit voltage deficit. Our hybrid density functional theory calculations suggest that electron-hole recombination at the Cu2ZnSnS4/CdS interface is caused by a deeper conduction band that slows electron extraction. In contrast, the bandgap is not narrowed for the Cu2ZnSnSe4/CdS interface, consistent with a lower open-circuit voltage deficit., Comment: 5 pages, 5 figures

The performance of kesterite thin-film solar cells is limited by a low open-circuit voltage due to defect-mediated electron-hole recombination. We calculate the non-radiative carrier-capture cross sections and Shockley-Read-Hall recombination coefficients of deep-level point defects in Cu$_2$ZnSnS$_4$ (CZTS) from first-principles. While the oxidation state of Sn is +4 in stoichiometric CZTS, inert lone pair (5$s^2$) formation lowers the oxidation state to +2. The stability of the lone pair suppresses the ionization of certain point defects, inducing charge transition levels deep in the band gap. We find large lattice distortions associated with the lone-pair defect centers due to the difference in ionic radii between Sn(II) and Sn(IV). The combination of a deep trap level and large lattice distortion facilitates efficient non-radiative carrier capture, with capture cross-sections exceeding $10^{-12}$ cm$^2$. The results highlight a connection between redox active cations and `killer' defect centres that form giant carrier traps. This lone pair effect will be relevant to other emerging photovoltaic materials containing n$s^2$ cations.

Extended defects such as stacking faults and anti-site domain boundaries can perturb the band edges in Cu$_2$ZnSnS$_4$ and Cu$_2$ZnSnSe$_4$, acting as a weak electron barrier or a source for electron capture, respectively. In order to find ways to prohibit the formation of planar defects, we investigated the effect of chemical substitution on the stability of the intrinsic stacking fault and metastable polytypes and analyze their electrical properties. Substitution of Ag for Cu makes stacking faults less stable, whereas the other substitutions (Cd and Ge) promote their formation. Ge substitution has no effect on the electron barrier of the intrinsic stacking fault, but Cd substitution reduces the barrier energy and Ag substitution makes the stacking fault electron capture. While Cd substitution stabilizes the stannite structure, chemical substitutions make the primitive-mixed CuAu (PMCA) structure less stable with respect to the ground-state kesterite structure., Comment: 5 pages, 3 figures

The efficiencies of solar cells based on kesterite Cu$_2$ZnSnS$_4$ (CZTS) and Cu$_2$ZnSnSe$_4$ (CZTSe) are limited by a low open-circuit voltage due to high rates of non-radiative electron-hole recombination. To probe the origin of this bottleneck, we calculate the band offset of CZTS(Se) with CdS, confirming a weak spike of 0.1 eV for CZTS/wurtzite-CdS and a strong spike of 0.4 eV for CZTSe/wurtzite-CdS. We also consider the effects of temperature on the band alignment, finding that increasing temperature significantly enhances the spike-type offset. We further resolve an outstanding discrepancy between measured and calculated phonon frequencies for the kesterites, and use these to estimate the upper limit of electron and hole mobilities based on optic phonon Fr\"ohlich scattering, which uncovers an intrinsic asymmetry with faster (minority carrier) electron mobility., Comment: 5 pages, 3 figures, includes supplementary material

We investigated stability and the electronic structure of extended defects including anti-site domain boundaries and stacking faults in the kesterite-structured semiconductors, Cu$_2$ZnSnS$_4$ (CZTS) and Cu$_2$ZnSnSe$_4$ (CZTSe). Our hybrid density functional theory calculations show that stacking faults in CZTS and CZTSe induce a higher conduction band edge than the bulk counterparts, and thus the stacking faults act as electron barriers. Antisite domain boundaries, however, accumulate electrons as the conduction band edge is reduced in energy, having an opposite role. An Ising model was constructed to account for the stability of stacking faults, which shows the nearest neighbour interaction is stronger in the case of the selenide., Comment: 13 pages, 2 figures