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Transformers have been successfully applied to sequential, auto-regressive tasks despite being feedforward networks. Unlike recurrent neural networks, Transformers use attention to capture temporal relations while processing input tokens in…
The $3$SUM-Indexing problem was introduced as a data structure version of the $3$SUM problem, with the goal of proving strong conditional lower bounds for static data structures via reductions. Ideally, the conjectured hardness of…
A notorious open question in circuit complexity is whether Boolean operations of arbitrary arity can efficiently be expressed using modular counting gates only. H{\aa}stad's celebrated switching lemma yields exponential lower bounds for the…
We consider maximization of stochastic monotone continuous submodular functions (CSF) with a diminishing return property. Existing algorithms only guarantee the performance \textit{in expectation}, and do not bound the probability of…
In the permutation inversion problem, the task is to find the preimage of some challenge value, given oracle access to the permutation. This is a fundamental problem in query complexity, and appears in many contexts, particularly…
Solving inverse problems with iterative algorithms is popular, especially for large data. Due to time constraints, the number of possible iterations is usually limited, potentially affecting the achievable accuracy. Given an error one is…
This paper is devoted to the extension of the regret lower bound beyond ergodic Markov decision processes (MDPs) in the problem dependent setting. While the regret lower bound for ergodic MDPs is well-known and reached by tractable…
How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational…
Various algorithms in reinforcement learning exhibit dramatic variability in their convergence rates and ultimate accuracy as a function of the problem structure. Such instance-specific behavior is not captured by existing global minimax…
We consider the problem of learning optimal solutions of a partially known linear optimization problem and recovering its underlying cost function where a set of past decisions and the feasible set are known. We develop a new framework,…
By considering an unreliable oracle in a query-based model of quantum learning, we present a tradeoff relation between the oracle's reliability and the reusability of quantum state of the input data. The tradeoff relation manifests as the…
We propose $\textit{iterative inversion}$ -- an algorithm for learning an inverse function without input-output pairs, but only with samples from the desired output distribution and access to the forward function. The key challenge is a…
We obtain a query lower bound for quantum algorithms solving the phase estimation problem. Our analysis generalizes existing lower bound approaches to the case where the oracle Q is given by controlled powers Q^p of Q, as it is for example…
Given a sequence of tokens, such as words, the task of next-token prediction is to predict the next-token conditional probability distribution. Decoder-only transformers have become effective models for this task, but their properties are…
Many problems in machine learning are naturally expressed in the language of undirected graphical models. Here, we propose black-box learning and inference algorithms for undirected models that optimize a variational approximation to the…
First order methods endowed with global convergence guarantees operate using global lower bounds on the objective. The tightening of the bounds has been shown to increase both the theoretical guarantees and the practical performance. In…
We prove essentially optimal fine-grained lower bounds on the gap between a data structure and a partially retroactive version of the same data structure. Precisely, assuming any one of three standard conjectures, we describe a problem that…
In unitary property testing a quantum algorithm, also known as a tester, is given query access to a black-box unitary and has to decide whether it satisfies some property. We propose a new technique for proving lower bounds on the quantum…
Obtaining a non-trivial (super-linear) lower bound for computation of the Fourier transform in the linear circuit model has been a long standing open problem for over 40 years. An early result by Morgenstern from 1973, provides an $\Omega(n…
In this paper, we study the problem of regret minimization for episodic Reinforcement Learning (RL) both in the model-free and the model-based setting. We focus on learning with general function classes and general model classes, and we…