A fault-tolerant quantum computer must decode and correct errors faster than they appear. The faster errors can be corrected, the more time the computer can do useful work. The Union-Find (UF) decoder is promising with an average time complexity slightly higher than $O(d^3)$. We report a distributed version of the UF decoder that exploits parallel computing resources for further speedup. Using an FPGA-based implementation, we empirically show that this distributed UF decoder has a sublinear average time complexity with regard to $d$, given $O(d^3)$ parallel computing resources. The decoding time per measurement round decreases as $d$ increases, a first time for a quantum error decoder. The implementation employs a scalable architecture called Helios that organizes parallel computing resources into a hybrid tree-grid structure. We are able to implement $d$ up to 21 with a Xilinx VCU129 FPGA, for which an average decoding time is 11.5 ns per measurement round under phenomenological noise of 0.1\%, significantly faster than any existing decoder implementation. Since the decoding time per measurement round of Helios decreases with $d$, Helios can decode a surface code of arbitrarily large $d$ without a growing backlog.
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Consider a mechanism that cannot observe how many players there are directly, but instead must rely on their self-reports to know how many are participating. Suppose the players can create new identities to report to the auctioneer at some cost $c$. The usual mechanism design paradigm is equivalent to implicitly assuming that $c$ is infinity for all players, while the usual Sybil attacks literature is that it is zero or finite for one player (the attacker) and infinity for everyone else (the 'honest' players). The false-name proof literature largely assumes the cost to be 0. We consider a model with variable costs that unifies these disparate streams. A paradigmatic normal form game can be extended into a Sybil game by having the action space by the product of the feasible set of identities to create action where each player chooses how many players to present as in the game and their actions in the original normal form game. A mechanism is (dominant) false-name proof if it is (dominant) incentive-compatible for all the players to self-report as at most one identity. We study mechanisms proposed in the literature motivated by settings where anonymity and self-identification are the norms, and show conditions under which they are not Sybil-proof. We characterize a class of dominant Sybil-proof mechanisms for reward sharing and show that they achieve the efficiency upper bound. We consider the extension when agents can credibly commit to the strategy of their sybils and show how this can break mechanisms that would otherwise be false-name proof.
Classifiers based on deep neural networks have been recently challenged by Adversarial Attack, where the widely existing vulnerability has invoked the research in defending them from potential threats. Given a vulnerable classifier, existing defense methods are mostly white-box and often require re-training the victim under modified loss functions/training regimes. While the model/data/training specifics of the victim are usually unavailable to the user, re-training is unappealing, if not impossible for reasons such as limited computational resources. To this end, we propose a new black-box defense framework. It can turn any pre-trained classifier into a resilient one with little knowledge of the model specifics. This is achieved by new joint Bayesian treatments on the clean data, the adversarial examples and the classifier, for maximizing their joint probability. It is further equipped with a new post-train strategy which keeps the victim intact. We name our framework Bayesian Boundary Correction (BBC). BBC is a general and flexible framework that can easily adapt to different data types. We instantiate BBC for image classification and skeleton-based human activity recognition, for both static and dynamic data. Exhaustive evaluation shows that BBC has superior robustness and can enhance robustness without severely hurting the clean accuracy, compared with existing defense methods.
Large language models (LLMs) have demonstrated remarkable capabilities out of box for a wide range of applications, yet accuracy still remains a major growth area, especially in mission-critical domains such as biomedicine. An effective method to calibrate the confidence level on LLM responses is essential to automatically detect errors and facilitate human-in-the-loop verification. An important source of calibration signals stems from expert-stipulated programmatic supervision, which is often available at low cost but has its own limitations such as noise and coverage. In this paper, we introduce a Pareto optimal self-supervision framework that can leverage available programmatic supervision to systematically calibrate LLM responses by producing a risk score for every response, without any additional manual efforts. This is accomplished by learning a harmonizer model to align LLM output with other available supervision sources, which would assign higher risk scores to more uncertain LLM responses and facilitate error correction. Experiments on standard relation extraction tasks in biomedical and general domains demonstrate the promise of this approach, with our proposed risk scores highly correlated with the real error rate of LLMs. For the most uncertain test instances, dynamic prompting based on our proposed risk scores results in significant accuracy improvement for off-the-shelf LLMs, boosting GPT-3 results past state-of-the-art (SOTA) weak supervision and GPT-4 results past SOTA supervised results on challenging evaluation datasets.
Community detection is a crucial task in network analysis that can be significantly improved by incorporating subject-level information, i.e. covariates. However, current methods often struggle with selecting tuning parameters and analyzing low-degree nodes. In this paper, we introduce a novel method that addresses these challenges by constructing network-adjusted covariates, which leverage the network connections and covariates with a unique weight to each node based on the node's degree. Spectral clustering on network-adjusted covariates yields an exact recovery of community labels under certain conditions, which is tuning-free and computationally efficient. We present novel theoretical results about the strong consistency of our method under degree-corrected stochastic blockmodels with covariates, even in the presence of mis-specification and sparse communities with bounded degrees. Additionally, we establish a general lower bound for the community detection problem when both network and covariates are present, and it shows our method is optimal up to a constant factor. Our method outperforms existing approaches in simulations and a LastFM app user network, and provides interpretable community structures in a statistics publication citation network where $30\%$ of nodes are isolated.
The separate tasks of denoising, conditional expectation and manifold learning can often be posed in a common setting of finding the conditional expectations arising from a product of two random variables. This paper focuses on this more general problem and describes an operator theoretic approach to estimating the conditional expectation. Kernel integral operators are used as a compactification tool, to set up the estimation problem as a linear inverse problem in a reproducing kernel Hilbert space. This equation is shown to have solutions that are stable to numerical approximation, thus guaranteeing the convergence of data-driven implementations. The overall technique is easy to implement, and their successful application to some real-world problems are also shown.
We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded domains. A number of challenges are encountered when discretizing these equations. The first comes from the heterogeneous kernel singularity in the fractional integral operator. The second comes from the dense discrete operator with its quadratic growth in memory footprint and arithmetic operations. An additional challenge comes from the need to handle volume conditions-the generalization of classical local boundary conditions to the nonlocal setting. Satisfying these conditions requires that the effect of the whole domain, including both the interior and exterior regions, can be computed on every interior point in the discretization. Performed directly, this would result in quadratic complexity. To address these challenges, we propose a strategy that decomposes the stiffness matrix into three components. The first is a sparse matrix that handles the singular near-field separately and is computed by adapting singular quadrature techniques available for the homogeneous case to the case of spatially variable order. The second component handles the remaining smooth part of the near-field as well as the far field and is approximated by a hierarchical $\mathcal{H}^{2}$ matrix that maintains linear complexity in storage and operations. The third component handles the effect of the global mesh at every node and is written as a weighted mass matrix whose density is computed by a fast-multipole type method. The resulting algorithm has therefore overall linear space and time complexity. Analysis of the consistency of the stiffness matrix is provided and numerical experiments are conducted to illustrate the convergence and performance of the proposed algorithm.
The lower bound on the decoding error probability for the optimal code given a signal-to-noise ratio and a code rate are investigated in this letter for the reconfigurable intelligent surface (RIS) communication system over a Rician fading channel at the short blocklength regime, which is the key characteristic of ultra-reliable low-latency communications (URLLC) to meet the need for strict adherence to quality of service (QoS) requirements. Sphere packing technique is used to derive our main results. The Wald sequential t-test lemma and the Gaussian-Chebyshev quadrature are the main tools to obtain the closed-form expression for the lower bound. Numerical results are provided to validate our results and demonstrate the tightness of our results compared to the Polyanskiy-Poor-Verdu (PPV) bound.
Theoretical studies on transfer learning or domain adaptation have so far focused on situations with a known hypothesis class or model; however in practice, some amount of model selection is usually involved, often appearing under the umbrella term of hyperparameter-tuning: for example, one may think of the problem of tuning for the right neural network architecture towards a target task, while leveraging data from a related source task. Now, in addition to the usual tradeoffs on approximation vs estimation errors involved in model selection, this problem brings in a new complexity term, namely, the transfer distance between source and target distributions, which is known to vary with the choice of hypothesis class. We present a first study of this problem, focusing on classification; in particular, the analysis reveals some remarkable phenomena: adaptive rates, i.e., those achievable with no distributional information, can be arbitrarily slower than oracle rates, i.e., when given knowledge on distances.
The fidelity of quantum programs in the NISQ era is limited by high levels of device noise. To increase the fidelity of quantum programs running on NISQ devices, a variety of optimizations have been proposed. These include mapping passes, routing passes, scheduling methods and standalone optimisations which are usually incorporated into a transpiler as passes. Popular transpilers such as those proposed by Qiskit, Cirq and Cambridge Quantum Computing make use of these extensively. However, choosing the right set of transpiler passes and the right configuration for each pass is a challenging problem. Transpilers often make critical decisions using heuristics since the ideal choices are impossible to identify without knowing the target application outcome. Further, the transpiler also makes simplifying assumptions about device noise that often do not hold in the real world. As a result, we often see effects where the fidelity of a target application decreases despite using state-of-the-art optimisations. To overcome this challenge, we propose OPTRAN, a framework for Choosing an Optimal Pass Set for Quantum Transpilation. OPTRAN uses classically simulable quantum circuits composed entirely of Clifford gates, that resemble the target application, to estimate how different passes interact with each other in the context of the target application. OPTRAN then uses this information to choose the optimal combination of passes that maximizes the target application's fidelity when run on the actual device. Our experiments on IBM machines show that OPTRAN improves fidelity by 87.66% of the maximum possible limit over the baseline used by IBM Qiskit. We also propose low-cost variants of OPTRAN, called OPTRAN-E-3 and OPTRAN-E-1 that improve fidelity by 78.33% and 76.66% of the maximum permissible limit over the baseline at a 58.33% and 69.44% reduction in cost compared to OPTRAN respectively.
The Q-learning algorithm is known to be affected by the maximization bias, i.e. the systematic overestimation of action values, an important issue that has recently received renewed attention. Double Q-learning has been proposed as an efficient algorithm to mitigate this bias. However, this comes at the price of an underestimation of action values, in addition to increased memory requirements and a slower convergence. In this paper, we introduce a new way to address the maximization bias in the form of a "self-correcting algorithm" for approximating the maximum of an expected value. Our method balances the overestimation of the single estimator used in conventional Q-learning and the underestimation of the double estimator used in Double Q-learning. Applying this strategy to Q-learning results in Self-correcting Q-learning. We show theoretically that this new algorithm enjoys the same convergence guarantees as Q-learning while being more accurate. Empirically, it performs better than Double Q-learning in domains with rewards of high variance, and it even attains faster convergence than Q-learning in domains with rewards of zero or low variance. These advantages transfer to a Deep Q Network implementation that we call Self-correcting DQN and which outperforms regular DQN and Double DQN on several tasks in the Atari 2600 domain.
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