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1. Non-reversible Parallel Tempering for Uncertainty Approximation in Deep Learning

   Deng, Wei; Zhang, Qian; Feng, Qi; Liang, Faming; Lin, Guang (February 2023, Thirty-seventh AAAI Conference on Artificial Intelligence)

   Parallel tempering (PT), also known as replica exchange, is the go-to workhorse for simulations of multi-modal distributions. The key to the success of PT is to adopt efficient swap schemes. The popular deterministic even-odd (DEO) scheme exploits the non-reversibility property and has successfully reduced the communication cost from O(P 2) to O(P) given sufficient many P chains. However, such an innovation largely disappears in big data problems due to the limited chains and extremely few bias-corrected swaps. To handle this issue, we generalize the DEO scheme to promote the non-reversibility and obtain an appealing communication cost O(P log P) based on the optimal window size. In addition, we also analyze the bias when we adopt stochastic gradient descent (SGD) with large and constant learning rates as exploration kernels. Such a user-friendly nature enables us to conduct large-scale uncertainty approximation tasks without much tuning costs. 

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2. Achieving linear speedup in non-iid federated bilevel learning

   Huang, M; Zhang, D; Ji, K (July 2023, International Conference on Machine Learning)

   Federated bilevel learning has received increasing attention in various emerging machine learning and communication applications. Recently, several Hessian-vector-based algorithms have been proposed to solve the federated bilevel optimization problem. However, several important properties in federated learning such as the partial client participation and the linear speedup for convergence (i.e., the convergence rate and complexity are improved linearly with respect to the number of sampled clients) in the presence of non-i.i.d.~datasets, still remain open. In this paper, we fill these gaps by proposing a new federated bilevel algorithm named FedMBO with a novel client sampling scheme in the federated hypergradient estimation. We show that FedMBO achieves a convergence rate of $$\mathcal{O}\big(\frac{1}{\sqrt{nK}}+\frac{1}{K}+\frac{\sqrt{n}}{K^{3/2}}\big)$$ on non-i.i.d.~datasets, where $$n$$ is the number of participating clients in each round, and $$K$$ is the total number of iteration. This is the first theoretical linear speedup result for non-i.i.d.~federated bilevel optimization. Extensive experiments validate our theoretical results and demonstrate the effectiveness of our proposed method. 

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3. Arithmetic Sketching

   Boneh, Dan; Boyle, Elette; Corrigan-Gibbs, Henry; Gilboa, Niv; Ishai, Yuval (January 2023, IACR International Cryptology Conference (CRYPTO))

   This paper introduces arithmetic sketching, an abstraction of a primitive that several previous works use to achieve lightweight, low-communication zero-knowledge verification of secret-shared vectors. An arithmetic sketching scheme for a language L ⊆ F^n consists of (1) a randomized linear function compressing a long input x to a short “sketch,” and (2) a small arithmetic circuit that accepts the sketch if and only if x ∈ L, up to some small error. If the language L has an arithmetic sketching scheme with short sketches, then it is possible to test membership in L using an arithmetic circuit with few multiplication gates. Since multiplications are the dominant cost in protocols for computation on secret-shared, encrypted, and committed data, arithmetic sketching schemes give rise to lightweight protocols in each of these settings. Beyond the formalization of arithmetic sketching, our contributions are: – A general framework for constructing arithmetic sketching schemes from algebraic varieties. This framework unifies schemes from prior work and gives rise to schemes for useful new languages and with improved soundness error. – The first arithmetic sketching schemes for languages of sparse vectors: vectors with bounded Hamming weight, bounded L1 norm, and vectors whose few non-zero values satisfy a given predicate. – A method for “compiling” any arithmetic sketching scheme for a language L into a low-communication malicious-secure multi-server protocol for securely testing that a client-provided secret-shared vector is in L. We also prove the first nontrivial lower bounds showing limits on the sketch size for certain languages (e.g., vectors of Hamming-weight one) and proving the non-existence of arithmetic sketching schemes for others (e.g., the language of all vectors that contain a specific value). 

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4. Probabilistic Resource-Aware Session Types

   https://doi.org/10.1145/3571259  

   Das, Ankush; Wang, Di; Hoffmann, Jan (January 2023, Proceedings of the ACM on Programming Languages)

   Session types guarantee that message-passing processes adhere to predefined communication protocols. Prior work on session types has focused on deterministic languages but many message-passing systems, such as Markov chains and randomized distributed algorithms, are probabilistic. To implement and analyze such systems, this article develops the meta theory of probabilistic session types with an application focus on automatic expected resource analysis. Probabilistic session types describe probability distributions over messages and are a conservative extension of intuitionistic (binary) session types. To send on a probabilistic channel, processes have to utilize internal randomness from a probabilistic branching or external randomness from receiving on a probabilistic channel. The analysis for expected resource bounds is smoothly integrated with the type system and is a variant of automatic amortized resource analysis. Type inference relies on linear constraint solving to automatically derive symbolic bounds for various cost metrics. The technical contributions include the meta theory that is based on a novel nested multiverse semantics and a type-reconstruction algorithm that allows flexible mixing of different sources of randomness without burdening the programmer with complex type annotations. The type system has been implemented in the language NomosPro with linear-time type checking. Experiments demonstrate that NomosPro is applicable in different domains such as cost analysis of randomized distributed algorithms, analysis of Markov chains, probabilistic analysis of amortized data structures and digital contracts. NomosPro is also shown to be scalable by (i) implementing two broadcast and a bounded retransmission protocol where messages are dropped with a fixed probability, and (ii) verifying the limiting distribution of a Markov chain with 64 states and 420 transitions. 

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5. Time-sliced quantum circuit partitioning for modular architectures

   https://doi.org/10.1145/3387902.3392617  

   Baker, Jonathan M.; Duckering, Casey; Hoover, Alexander; Chong, Frederic T. (May 2020, CF '20: Proceedings of the 17th ACM International Conference on Computing Frontiers)

   Current quantum computer designs will not scale. To scale beyond small prototypes, quantum architectures will likely adopt a modular approach with clusters of tightly connected quantum bits and sparser connections between clusters. We exploit this clustering and the statically-known control flow of quantum programs to create tractable partitioning heuristics which map quantum circuits to modular physical machines one time slice at a time. Specifically, we create optimized mappings for each time slice, accounting for the cost to move data from the previous time slice and using a tunable lookahead scheme to reduce the cost to move to future time slices. We compare our approach to a traditional statically-mapped, owner-computes model. Our results show strict improvement over the static mapping baseline. We reduce the non-local communication overhead by 89.8% in the best case and by 60.9% on average. Our techniques, unlike many exact solver methods, are computationally tractable. 

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