Related papers: Certificates in Data Structures
Randomized smoothing is the dominant standard for provable defenses against adversarial examples. Nevertheless, this method has recently been proven to suffer from important information theoretic limitations. In this paper, we argue that…
[See the paper for the full abstract.] We show tight upper and lower bounds for time-space trade-offs for the $c$-Approximate Near Neighbor Search problem. For the $d$-dimensional Euclidean space and $n$-point datasets, we develop a data…
Most state-of-the-art satisfiability algorithms today are variants of the DPLL procedure augmented with clause learning. The main bottleneck for such algorithms, other than the obvious one of time, is the amount of memory used. In the field…
A learning method is self-certified if it uses all available data to simultaneously learn a predictor and certify its quality with a tight statistical certificate that is valid on unseen data. Recent work has shown that neural network…
In this paper, we give novel certificates for triangular equivalence and rank profiles. These certificates enable somebody to verify the row or column rank profiles or the whole rank profile matrix faster than recomputing them, with a…
Learned index structures aim to accelerate queries by training machine learning models to approximate the rank function associated with a database attribute. While effective in practice, their theoretical limitations are not fully…
DNA strings and their properties are widely studied since last 20 years due to its applications in DNA computing. In this area, one designs a set of DNA strings (called DNA code) which satisfies certain thermodynamic and combinatorial…
Testing whether a probability distribution is compatible with a given Bayesian network is a fundamental task in the field of causal inference, where Bayesian networks model causal relations. Here we consider the class of causal structures…
The design of large libraries of oligonucleotides having constant GC-content and satisfying Hamming distance constraints between oligonucleotides and their Watson-Crick complements is important in reducing hybridization errors in DNA…
Deep learning models are vulnerable to adversarial perturbations, raising important concerns for safety-critical deployment. Empirical defenses can achieve strong robustness in practice, but lack formal guarantees, motivating the need for…
The rule labeling heuristic aims to establish confluence of (left-)linear term rewrite systems via decreasing diagrams. We present a formalization of a confluence criterion based on the interplay of relative termination and the rule…
We develop a new technique for proving cell-probe lower bounds for static data structures. Previous lower bounds used a reduction to communication games, which was known not to be tight by counting arguments. We give the first lower bound…
We consider the verification of neural network policies for discrete-time stochastic systems with respect to reach-avoid specifications. We use a learner-verifier procedure that learns a certificate for the specification, represented as a…
Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…
Many systems contain latent variables that make their dynamics partially unidentifiable or cause distribution shifts in the observed statistics between offline and online data. However, existing control techniques often assume access to…
In safety-critical machine learning applications, it is crucial to defend models against adversarial attacks -- small modifications of the input that change the predictions. Besides rigorously studied $\ell_p$-bounded additive…
We prove that the subset sum problem has a polynomial time computable certificate of infeasibility for all $a$ weight vectors with density at most $1/(2n)$ and for almost all integer right hand sides. The certificate is branching on a…
The minimum accuracy heuristic evaluates quantum feature maps without requiring full quantum support vector machine (QSVM) training. However, the original formulation is computationally expensive, restricted to balanced datasets, and lacks…
We develop a rigorous mathematical analysis of zero-shot learning with attributes. In this setting, the goal is to label novel classes with no training data, only detectors for attributes and a description of how those attributes are…
Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more…