Miracle-dz/UniFAR-FTUs huggingface dataset:
Non-Pauli errors in the three-dimensional surface code

A powerful feature of stabilizer error correcting codes is the fact that stabilizer measurement projects arbitrary errors to Pauli errors, greatly simplifying the physical error correction process as well as classical simulations of code performance. However, logical non-Clifford operations can map Pauli errors to non-Pauli (Clifford) errors, and while subsequent stabilizer measurements will project the Clifford errors back to Pauli errors the resulting distributions will possess additional correlations that depend on both the nature of the logical operation and the structure of the code. Previous work has studied these effects when applying a transversal T gate to the three-dimensional color code and shown the existence of a nonlocal “linking charge” phenomenon between membranes of intersecting errors. In this paper we generalise these results to the case of a CCZ gate in the three-dimensional surface code and ﬁnd that many aspects of the problem are much more easily understood in this setting. In particular, the emergence of linking charge is a local effect rather than a nonlocal one. We use the relative simplicity of Clifford errors in this setting to simulate their effect on the performance of a single-shot magic state preparation process and ﬁnd that their effect on the threshold is largely determined by probability of X errors occurring immediately prior to the application of the gate, after the most recent stabilizer measurement. DOI: 10.1103/PhysRevResearch.4. 043052
The co-evolution of molecular hydrogen and the grain size distribution in an isolated galaxy

Understanding the evolution of dust and molecular hydrogen (H2) is a critical aspect of galaxy evolution, as they affect star formation and the spectral energy distribution of galaxies. We use the N-body/smoothed-particle-hydrodynamics code Gadget4-Osaka to compute the evolution of dust and H2 in a suite of numerical simulations of an isolated Milky-Way-like galaxy. The evolution of the full grain size distribution (GSD) is solved by sampling the grain size on a logarithmically spaced grid with 30 bins. The evolution of a primordial chemistry network with twelve species is solved consistently with the hydrodynamic evolution of the system, including star formation, metal and energy ejections from stars into the interstellar medium through supernova feedback and stellar winds. The formation model for H2 considers the GSD and photo-dissociation through the UV radiation of young stars. We identify the processes needed for producing a sizeable amount of H2, verify that the resulting star formation law in the later stages of galaxy evolution is consistent with observations of local spirals, and show that our model manages to produce a galactic molecular gas fraction in line with observations of Milky-Way-like galaxies. We stress the importance of the co-evolution of the GSD and H2, as models assuming a fixed MRN shape for the GSD overestimate the production of H2 in regimes where the dust abundance is dominated by large grains and underestimate it in the regime where the dust is dominated by small grains, both of which are realized in simulations of dust evolution.
A Quick Repair Facility for Debugging

Modern development environments provide a widely used auto-correction facility for quickly repairing syntactic errors. Auto-correction cannot deal with semantic errors, which are much more difficult to repair. Automated program repair techniques, designed for repairing semantic errors, are not well-suited for interactive use while debugging, as they typically assume the existence of a high-quality test suite and take considerable time. To bridge the gap, we developed ROSE, a tool to suggest quick-yet-effective repairs of semantic errors during debugging. ROSE does not rely on a test suite. Instead, it assumes a debugger stopping point where a problem is observed. It asks the developer to quickly describe what is wrong, performs a light-weight fault localization to identify potential responsible locations, and uses a generate-and-validate strategy to produce and validate repairs. Finally, it presents the results so the developer can choose and make the appropriate repair. To assess its utility, we implemented a prototype of ROSE that works in the Eclipse IDE and applied it to two benchmarks, QuixBugs and Defects4J, for repair. ROSE was able to suggest correct repairs for 17 QuixBugs and 16 Defects4J errors in seconds.
Chain-level equivariant string topology: algebra versus analysis

We prove that on 2-connected closed oriented manifolds, the analytic and algebraic constructions of an IBL$_\infty$ structure associated to a closed oriented manifold coincide. The corresponding structure is invariant under orientation preserving homotopy equivalences and induces on homology the involutive Lie bialgebra structure of Chas and Sullivan.
Risk Management using Model Predictive Control

Forward planning and risk management are crucial for the success of any system or business dealing with the uncertainties of the real world. Previous approaches have largely assumed that the future will be similar to the past, or used simple forecasting techniques based on ad-hoc models. Improving solutions requires better projection of future events, and necessitates robust forward planning techniques that consider forecasting inaccuracies. This work advocates risk management through optimal control theory, and proposes several techniques to combine it with time-series forecasting. Focusing on applications in foreign exchange (FX) and battery energy storage systems (BESS), the contributions of this thesis are three-fold. First, a short-term risk management system for FX dealers is described, in which the optimal risk-cost profiles are obtained through dynamic control of the dealers’ positions on the spot market. This approach is formulated as a stochastic model predictive control (SMPC) problem, incorporating elements which model client flow, transaction cost, market impact, exchange rate volatility, and fluctuations caused by macroeconomic announcements. Second, an evolutionary approach to non-linear time-series forecasting is proposed. Using context-free grammars (CFG), a template for combining different steps of feature extraction, model selection, and hyperparameter optimisation into a single forecasting program is described. Subsequently, using grammatical evolution (GE), an evolutionary search is undertaken in the grammar space to find the optimal forecaster for a specific time-series. Third, a novel measure for evaluating forecasting models, as a part of the predictive model in finite horizon optimal control applications, is proposed. Specifically, for the case of linear-quadratic time-invariant systems, a closed-form equation for the increase in cost of a discrete-time finite horizon controller (FHC) due to prediction error is derived, and it is demonstrated that this measure is a better choice for model validation compared to standard error measures. Using both synthetic and historical data, the proposed techniques were validated and benchmarked. Real-world data from Westpac Institutional Bank retail FX trades were
Narrow-line imaging of single strontium atoms in shallow optical tweezers

Single strontium atoms held in optical tweezers have so far only been imaged using the broad $^{1\hspace{-0.3ex}}S_0$-$^{1\hspace{-0.3ex}}P_1$ transition. For Yb, use of the narrow (183 kHz-wide) $^{1\hspace{-0.3ex}}S_0$-$^{3\hspace{-0.3ex}}P_1$ transition for simultaneous imaging and cooling has been demonstrated in tweezers with a magic wavelength for the imaging transition. We demonstrate high-fidelity imaging of single Sr atoms using its even narrower (7.4 kHz-wide) $^{1\hspace{-0.3ex}}S_0$ - $^{3\hspace{-0.3ex}}P_1$ transition. The atoms are trapped in \textit{non}-magic-wavelength tweezers. We detect the photons scattered during Sisyphus cooling, thus keeping the atoms near the motional ground state of the tweezer throughout imaging. The fidelity of detection is 0.9991(4) with a survival probability of 0.97(2). An atom in a tweezer can be held under imaging conditions for 79(3) seconds allowing for hundreds of images to be taken, limited mainly by background gas collisions. We detect atoms in an arrary of 36 tweezers with 813.4-nm light and trap depths of 135(20) $\mu$K. This trap depth is three times shallower than typically used for imaging on the broad $^{1\hspace{-0.3ex}}S_0$ - $^{1\hspace{-0.3ex}}P_1$ transition. Narrow-line imaging opens the possibility to even further reduce this trap depth, as long as all trap frequencies are kept larger than the imaging transition linewidth. Imaging using a narrow-linewidth transition in a non-magic-wavelength tweezer also allows for selective imaging of a given tweezer. As a demonstration, we selectively image (hide) a single tweezer from the array. This provides a useful tool for quantum error correction protocols.
NeuroMixGDP: A Neural Collapse-Inspired Random Mixup for Private Data Release

Privacy-preserving data release algorithms have gained increasing attention for their ability to protect user privacy while enabling downstream machine learning tasks. However, the utility of current popular algorithms is not always satisfactory. Mixup of raw data provides a new way of data augmentation, which can help improve utility. However, its performance drastically deteriorates when differential privacy (DP) noise is added. To address this issue, this paper draws inspiration from the recently observed Neural Collapse (NC) phenomenon, which states that the last layer features of a neural network concentrate on the vertices of a simplex as Equiangular Tight Frame (ETF). We propose a scheme to mixup the Neural Collapse features to exploit the ETF simplex structure and release noisy mixed features to enhance the utility of the released data. By using Gaussian Differential Privacy (GDP), we obtain an asymptotic rate for the optimal mixup degree. To further enhance the utility and address the label collapse issue when the mixup degree is large, we propose a Hierarchical sampling method to stratify the mixup samples on a small number of classes. This method remarkably improves utility when the number of classes is large. Extensive experiments demonstrate the effectiveness of our proposed method in protecting against attacks and improving utility. In particular, our approach shows significantly improved utility compared to directly training classification networks with DPSGD on CIFAR100 and MiniImagenet datasets, highlighting the benefits of using privacy-preserving data release. We release reproducible code in https://github.com/Lidonghao1996/NeuroMixGDP.
Majorana corner states in an attractive quantum spin Hall insulator with opposite in-plane Zeeman energy at two sublattice sites

Higher-order topological superconductors and superfluids (SFs) host lower-dimensional Majorana corner and hinge states since novel topology exhibitions on boundaries. While such topological nontrivial phases have been explored extensively, more possible schemes are necessary for engineering Majorana states. In this paper we propose Majorana corner states could be realized in a two-dimensional attractive quantum spin-Hall insulator with opposite in-plane Zeeman energy at two sublattice sites. The appropriate Zeeman field leads to the opposite Dirac mass for adjacent edges of a square sample, and naturally induce Majorana corner states. This topological phase can be characterized by Majorana edge polarizations, and it is robust against perturbations on random potentials and random phase fluctuations as long as the edge gap remains open. Our work provides a new possibility to realize a second-order topological SF in two dimensions and engineer Majorana corner states.
Improving Graph Collaborative Filtering with Neighborhood-enriched Contrastive Learning

Recently, graph collaborative filtering methods have been proposed as an effective recommendation approach, which can capture users’ preference over items by modeling the user-item interaction graphs. Despite the effectiveness, these methods suffer from data sparsity in real scenarios. In order to reduce the influence of data sparsity, contrastive learning is adopted in graph collaborative filtering for enhancing the performance. However, these methods typically construct the contrastive pairs by random sampling, which neglect the neighboring relations among users (or items) and fail to fully exploit the potential of contrastive learning for recommendation. To tackle the above issue, we propose a novel contrastive learning approach, named Neighborhood-enriched Contrastive Learning, named NCL, which explicitly incorporates the potential neighbors into contrastive pairs. Specifically, we introduce the neighbors of a user (or an item) from graph structure and semantic space respectively. For the structural neighbors on the interaction graph, we develop a novel structure-contrastive objective that regards users (or items) and their structural neighbors as positive contrastive pairs. In implementation, the representations of users (or items) and neighbors correspond to the outputs of different GNN layers. Furthermore, to excavate the potential neighbor relation in semantic space, we assume that users with similar representations are within the semantic neighborhood, and incorporate these semantic neighbors into the prototype-contrastive objective. The proposed NCL can be optimized with EM algorithm and generalized to apply to graph collaborative filtering methods. Extensive experiments on five public datasets demonstrate the effectiveness of the proposed NCL, notably with 26% and 17% performance gain over a competitive graph collaborative filtering base model on the Yelp and Amazon-book datasets, respectively. Our implementation code is available at: https://github.com/RUCAIBox/NCL.
Real World Large Scale Recommendation Systems Reproducibility and Smooth Activations

Real world recommendation systems influence a constantly growing set of domains. With deep networks, that now drive such systems, recommendations have been more relevant to the user's interests and tasks. However, they may not always be reproducible even if produced by the same system for the same user, recommendation sequence, request, or query. This problem received almost no attention in academic publications, but is, in fact, very realistic and critical in real production systems. We consider reproducibility of real large scale deep models, whose predictions determine such recommendations. We demonstrate that the celebrated Rectified Linear Unit (ReLU) activation, used in deep models, can be a major contributor to irreproducibility. We propose the use of smooth activations to improve recommendation reproducibility. We describe a novel family of smooth activations; Smooth ReLU (SmeLU), designed to improve reproducibility with mathematical simplicity, with potentially cheaper implementation. SmeLU is a member of a wider family of smooth activations. While other techniques that improve reproducibility in real systems usually come at accuracy costs, smooth activations not only improve reproducibility, but can even give accuracy gains. We report metrics from real systems in which we were able to productionalize SmeLU with substantial reproducibility gains and better accuracy-reproducibility trade-offs. These include click-through-rate (CTR) prediction systems, content, and application recommendation systems.
Mixing and Shifting: Exploiting Global and Local Dependencies in Vision MLPs

Token-mixing multi-layer perceptron (MLP) models have shown competitive performance in computer vision tasks with a simple architecture and relatively small computational cost. Their success in maintaining computation efficiency is mainly attributed to avoiding the use of self-attention that is often computationally heavy, yet this is at the expense of not being able to mix tokens both globally and locally. In this paper, to exploit both global and local dependencies without self-attention, we present Mix-Shift-MLP (MS-MLP) which makes the size of the local receptive field used for mixing increase with respect to the amount of spatial shifting. In addition to conventional mixing and shifting techniques, MS-MLP mixes both neighboring and distant tokens from fine- to coarse-grained levels and then gathers them via a shifting operation. This directly contributes to the interactions between global and local tokens. Being simple to implement, MS-MLP achieves competitive performance in multiple vision benchmarks. For example, an MS-MLP with 85 million parameters achieves 83.8% top-1 classification accuracy on ImageNet-1K. Moreover, by combining MS-MLP with state-of-the-art Vision Transformers such as the Swin Transformer, we show MS-MLP achieves further improvements on three different model scales, e.g., by 0.5% on ImageNet-1K classification with Swin-B. The code is available at: https://github.com/JegZheng/MS-MLP.
BiFSMN: Binary Neural Network for Keyword Spotting

The deep neural networks, such as the Deep-FSMN, have been widely studied for keyword spotting (KWS) applications. However, computational resources for these networks are significantly constrained since they usually run on-call on edge devices. In this paper, we present BiFSMN, an accurate and extreme-efficient binary neural network for KWS. We first construct a High-frequency Enhancement Distillation scheme for the binarization-aware training, which emphasizes the high-frequency information from the full-precision network's representation that is more crucial for the optimization of the binarized network. Then, to allow the instant and adaptive accuracy-efficiency trade-offs at runtime, we also propose a Thinnable Binarization Architecture to further liberate the acceleration potential of the binarized network from the topology perspective. Moreover, we implement a Fast Bitwise Computation Kernel for BiFSMN on ARMv8 devices which fully utilizes registers and increases instruction throughput to push the limit of deployment efficiency. Extensive experiments show that BiFSMN outperforms existing binarization methods by convincing margins on various datasets and is even comparable with the full-precision counterpart (e.g., less than 3% drop on Speech Commands V1-12). We highlight that benefiting from the thinnable architecture and the optimized 1-bit implementation, BiFSMN can achieve an impressive 22.3x speedup and 15.5x storage-saving on real-world edge hardware.
What Do They Capture? - A Structural Analysis of Pre-Trained Language Models for Source Code

Recently, many pre-trained language models for source code have been proposed to model the context of code and serve as a basis for downstream code intelligence tasks such as code completion, code search, and code summarization. These models leverage masked pre-training and Transformer and have achieved promising results. However, currently there is still little progress regarding interpretability of existing pre-trained code models. It is not clear why these models work and what feature correlations they can capture. In this paper, we conduct a thorough structural analysis aiming to provide an interpretation of pre-trained language models for source code (e.g., CodeBERT, and GraphCodeBERT) from three distinctive perspectives: (1) attention analysis, (2) probing on the word embedding, and (3) syntax tree induction. Through comprehensive analysis, this paper reveals several insightful findings that may inspire future studies: (1) Attention aligns strongly with the syntax structure of code. (2) Pre-training language models of code can preserve the syntax structure of code in the intermediate representations of each Transformer layer. (3) The pre-trained models of code have the ability of inducing syntax trees of code. Theses findings suggest that it may be helpful to incorporate the syntax structure of code into the process of pre-training for better code representations.
Qualitative properties of solutions to a non-local free boundary problem modeling cell polarization

We consider a parabolic non-local free boundary problem that has been derived as a limit of a bulk-surface reaction-diffusion system which models cell polarization. The authors have justified the well-posedness of this problem and have further proved uniqueness of solutions and global stability of steady states. In this paper we investigate qualitative properties of the free boundary. We present necessary and sufficient conditions for the initial data that imply continuity of the support at $t = 0$. If one of these assumptions fail, then jumps of the support take place. In addition we provide a complete characterization of the jumps for a large class of initial data.
Continuous-time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations

We develop a new continuous‐time stochastic gradient descent method for optimizing over the stationary distribution of stochastic differential equation (SDE) models. The algorithm continuously updates the SDE model's parameters using an estimate for the gradient of the stationary distribution. The gradient estimate is simultaneously updated using forward propagation of the SDE state derivatives, asymptotically converging to the direction of steepest descent. We rigorously prove convergence of the online forward propagation algorithm for linear SDE models (i.e., the multidimensional Ornstein–Uhlenbeck process) and present its numerical results for nonlinear examples. The proof requires analysis of the fluctuations of the parameter evolution around the direction of steepest descent. Bounds on the fluctuations are challenging to obtain due to the online nature of the algorithm (e.g., the stationary distribution will continuously change as the parameters change). We prove bounds for the solutions of a new class of Poisson partial differential equations (PDEs), which are then used to analyze the parameter fluctuations in the algorithm. Our algorithm is applicable to a range of mathematical finance applications involving statistical calibration of SDE models and stochastic optimal control for long time horizons where ergodicity of the data and stochastic process is a suitable modeling framework. Numerical examples explore these potential applications, including learning a neural network control for high‐dimensional optimal control of SDEs and training stochastic point process models of limit order book events.
Detecting False Alarms from Automatic Static Analysis Tools: How Far are We?

Automatic static analysis tools (ASATs), such as Findbugs, have a high false alarm rate. The large number of false alarms produced poses a barrier to adoption. Researchers have proposed the use of machine learning to prune false alarms and present only actionable warnings to developers. The state-of-the-art study has identified a set of “Golden Features” based on metrics computed over the characteristics and history of the file, code, and warning. Recent studies show that machine learning using these features is extremely effective and that they achieve almost perfect performance. We perform a detailed analysis to better understand the strong performance of the “Golden Features”. We found that several studies used an experimental procedure that results in data leakage and data duplication, which are subtle issues with significant implications. Firstly, the ground-truth labels have leaked into features that measure the proportion of actionable warnings in a given context. Secondly, many warnings in the testing dataset appear in the training dataset. Next, we demonstrate limitations in the warning oracle that determines the ground-truth labels, a heuristic comparing warnings in a given revision to a reference revision in the future. We show the choice of reference revision influences the warning distribution. Moreover, the heuristic produces labels that do not agree with human oracles. Hence, the strong performance of these techniques previously seen is overoptimistic of their true performance if adopted in practice. Our results convey several lessons and provide guidelines for evaluating false alarm detectors.