Certifying Certainty and Uncertainty in Approximate Membership Query Structures

Gopinathan, Kiran; Sergey, Ilya

doi:10.1007/978-3-030-53291-8_16

Cited by 5 publications

(3 citation statements)

References 40 publications

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“…Bloom filters are a data structure supporting approximate membership queries (AMQs). Ceramist [Gopinathan and Sergey 2020] is a recent framework for verifying hash-based AMQ structures in the Coq theorem prover. Besides handling Bloom filters, Ceramist supports subtle proofs of correctness for many other AMQs.…”

Section: Related Workmentioning

confidence: 99%

“…However, Bose et al [2008] pointed out that this assumption is incorrect, and in fact the claimed upper-bound on the false-positive rate is actually a lower bound. Proving a correct bound on the false-positive rate required a substantially more complicated argument; recently, Gopinathan and Sergey [2020] mechanized a correct, but complex proof in Coq.…”

Section: Introductionmentioning

confidence: 99%

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A separation logic for negative dependence

Bao

Gaboardi

Hsu

et al. 2022

Proc. ACM Program. Lang.

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Formal reasoning about hashing-based probabilistic data structures often requires reasoning about random variables where when one variable gets larger (such as the number of elements hashed into one bucket), the others tend to be smaller (like the number of elements hashed into the other buckets). This is an example of negative dependence , a generalization of probabilistic independence that has recently found interesting applications in algorithm design and machine learning. Despite the usefulness of negative dependence for the analyses of probabilistic data structures, existing verification methods cannot establish this property for randomized programs. To fill this gap, we design LINA, a probabilistic separation logic for reasoning about negative dependence. Following recent works on probabilistic separation logic using separating conjunction to reason about the probabilistic independence of random variables, we use separating conjunction to reason about negative dependence. Our assertion logic features two separating conjunctions, one for independence and one for negative dependence. We generalize the logic of bunched implications (BI) to support multiple separating conjunctions, and provide a sound and complete proof system. Notably, the semantics for separating conjunction relies on a non-deterministic , rather than partial, operation for combining resources. By drawing on closure properties for negative dependence, our program logic supports a Frame-like rule for negative dependence and monotone operations. We demonstrate how LINA can verify probabilistic properties of hash-based data structures and balls-into-bins processes.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A separation logic for negative dependence

Bao

Gaboardi

Hsu

et al. 2022

Proc. ACM Program. Lang.

View full text Add to dashboard Cite

show abstract

“…When presented with an input, a Bloom filter can return one of two responses: 0, indicating that the input is definitely not a member of the set, or 1, indicating that the element is possibly a member of the set. False negatives do not occur, but false positives can occur with a probability that increases with the number of elements in the set and decreases with the size of the underlying data structure [23]. Bloom filters have found widespread application for membership queries in areas such as networking, databases, web caching, and architectural predictions [24].…”

Section: Bloom Filtersmentioning

confidence: 99%

Weightless Neural Networks for Efficient Edge Inference

Susskind¹,

Arora²,

Miranda³

et al. 2022

Preprint

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Weightless Neural Networks (WNNs) are a class of machine learning model which use table lookups to perform inference. This is in contrast with Deep Neural Networks (DNNs), which use multiply-accumulate operations. State-of-the-art WNN architectures have a fraction of the implementation cost of DNNs, but still lag behind them on accuracy for common image recognition tasks. Additionally, many existing WNN architectures suffer from high memory requirements. In this paper, we propose a novel WNN architecture, BTHOWeN, with key algorithmic and architectural improvements over prior work, namely counting Bloom filters, hardware-friendly hashing, and Gaussian-based nonlinear thermometer encodings to improve model accuracy and reduce area and energy consumption. BTHOWeN targets the large and growing edge computing sector by providing superior latency and energy efficiency to comparable quantized DNNs. Compared to state-of-the-art WNNs across nine classification datasets, BTHOWeN on average reduces error by more than than 40% and model size by more than 50%. We then demonstrate the viability of the BTHOWeN architecture by presenting an FPGAbased accelerator, and compare its latency and resource usage against similarly accurate quantized DNN accelerators, including Multi-Layer Perceptron (MLP) and convolutional models. The proposed BTHOWeN models consume almost 80% less energy than the MLP models, with nearly 85% reduction in latency. In our quest for efficient ML on the edge, WNNs are clearly deserving of additional attention.

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Formally Certified Approximate Model Counting

Tan,

Yang,

Soos

et al. 2024

Computer Aided Verification

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Approximate model counting is the task of approximating the number of solutions to an input Boolean formula. The state-of-the-art approximate model counter for formulas in conjunctive normal form (CNF), $$\textsf{ApproxMC}$$ ApproxMC , provides a scalable means of obtaining model counts with probably approximately correct (PAC)-style guarantees. Nevertheless, the validity of $$\textsf{ApproxMC}$$ ApproxMC ’s approximation relies on a careful theoretical analysis of its randomized algorithm and the correctness of its highly optimized implementation, especially the latter’s stateful interactions with an incremental CNF satisfiability solver capable of natively handling parity (XOR) constraints.We present the first certification framework for approximate model counting with formally verified guarantees on the quality of its output approximation. Our approach combines: (i) a static, once-off, formal proof of the algorithm’s PAC guarantee in the Isabelle/HOL proof assistant; and (ii) dynamic, per-run, verification of $$\textsf{ApproxMC}$$ ApproxMC ’s calls to an external CNF-XOR solver using proof certificates. We detail our general approach to establish a rigorous connection between these two parts of the verification, including our blueprint for turning the formalized, randomized algorithm into a verified proof checker, and our design of proof certificates for both $$\textsf{ApproxMC}$$ ApproxMC and its internal CNF-XOR solving steps. Experimentally, we show that certificate generation adds little overhead to an approximate counter implementation, and that our certificate checker is able to fully certify $$84.7\%$$ 84.7 % of instances with generated certificates when given the same time and memory limits as the counter.

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Certifying Certainty and Uncertainty in Approximate Membership Query Structures

Cited by 5 publications

References 40 publications

A separation logic for negative dependence

A separation logic for negative dependence

Weightless Neural Networks for Efficient Edge Inference

Formally Certified Approximate Model Counting

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