Toniann Pitassi
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View article: Testing Juntas and Junta Subclasses with Relative Error
Testing Juntas and Junta Subclasses with Relative Error Open
This papers considers the junta testing problem in a recently introduced ``relative error'' variant of the standard Boolean function property testing model. In relative-error testing we measure the distance from $f$ to $g$, where $f,g: \{0…
View article: Relative-Error Testing of Conjunctions and Decision Lists
Relative-Error Testing of Conjunctions and Decision Lists Open
We study the relative-error property testing model for Boolean functions that was recently introduced in the work of [X. Chen et al., 2025]. In relative-error testing, the testing algorithm gets uniform random satisfying assignments as wel…
View article: Improving Predictor Reliability with Selective Recalibration
Improving Predictor Reliability with Selective Recalibration Open
A reliable deep learning system should be able to accurately express its confidence with respect to its predictions, a quality known as calibration. One of the most effective ways to produce reliable confidence estimates with a pre-trained…
View article: Black-Box PPP Is Not Turing-Closed
Black-Box PPP Is Not Turing-Closed Open
The complexity class PPP contains all total search problems many-one reducible to the Pigeon problem, where we are given a succinct encoding of a function mapping n+1 pigeons to n holes, and must output two pigeons that collide in a hole. …
View article: Optimal Non-Adaptive Cell Probe Dictionaries and Hashing
Optimal Non-Adaptive Cell Probe Dictionaries and Hashing Open
We present a simple and provably optimal non-adaptive cell probe data structure for the static dictionary problem. Our data structure supports storing a set of n key-value pairs from [u]× [u] using s words of space and answering key lookup…
View article: Prompt Risk Control: A Rigorous Framework for Responsible Deployment of Large Language Models
Prompt Risk Control: A Rigorous Framework for Responsible Deployment of Large Language Models Open
The recent explosion in the capabilities of large language models has led to a wave of interest in how best to prompt a model to perform a given task. While it may be tempting to simply choose a prompt based on average performance on a val…
View article: Distribution-Free Statistical Dispersion Control for Societal Applications
Distribution-Free Statistical Dispersion Control for Societal Applications Open
Explicit finite-sample statistical guarantees on model performance are an important ingredient in responsible machine learning. Previous work has focused mainly on bounding either the expected loss of a predictor or the probability that an…
View article: An improved protocol for ExactlyN with more than 3 players
An improved protocol for ExactlyN with more than 3 players Open
The ExactlyN problem in the number-on-forehead (NOF) communication setting asks $k$ players, each of whom can see every input but their own, if the $k$ input numbers add up to $N$. Introduced by Chandra, Furst and Lipton in 1983, ExactlyN …
View article: Optimal Non-Adaptive Cell Probe Dictionaries and Hashing
Optimal Non-Adaptive Cell Probe Dictionaries and Hashing Open
We present a simple and provably optimal non-adaptive cell probe data structure for the static dictionary problem. Our data structure supports storing a set of n key-value pairs from [u]x[u] using s words of space and answering key lookup …
View article: On the algebraic proof complexity of Tensor Isomorphism
On the algebraic proof complexity of Tensor Isomorphism Open
The Tensor Isomorphism problem (TI) has recently emerged as having connections to multiple areas of research within complexity and beyond, but the current best upper bound is essentially the brute force algorithm. Being an algebraic proble…
View article: Stability is Stable: Connections between Replicability, Privacy, and Adaptive Generalization
Stability is Stable: Connections between Replicability, Privacy, and Adaptive Generalization Open
The notion of replicable algorithms was introduced in Impagliazzo et al. [STOC '22] to describe randomized algorithms that are stable under the resampling of their inputs. More precisely, a replicable algorithm gives the same output with h…
View article: Quantile Risk Control: A Flexible Framework for Bounding the Probability of High-Loss Predictions
Quantile Risk Control: A Flexible Framework for Bounding the Probability of High-Loss Predictions Open
Rigorous guarantees about the performance of predictive algorithms are necessary in order to ensure their responsible use. Previous work has largely focused on bounding the expected loss of a predictor, but this is not sufficient in many r…
View article: Learning versus Refutation in Noninteractive Local Differential Privacy
Learning versus Refutation in Noninteractive Local Differential Privacy Open
We study two basic statistical tasks in non-interactive local differential privacy (LDP): learning and refutation. Learning requires finding a concept that best fits an unknown target function (from labelled samples drawn from a distributi…
View article: Reproducibility in learning
Reproducibility in learning Open
We introduce the notion of a reproducible algorithm in the context of learning. A reproducible learning algorithm is resilient to variations in its samples — with high probability, it returns the exact same output when run on two samples f…
View article: Reproducibility in Learning
Reproducibility in Learning Open
We introduce the notion of a reproducible algorithm in the context of learning. A reproducible learning algorithm is resilient to variations in its samples -- with high probability, it returns the exact same output when run on two samples …
View article: Improved Generalization Guarantees in Restricted Data Models
Improved Generalization Guarantees in Restricted Data Models Open
Differential privacy is known to protect against threats to validity incurred due to adaptive, or exploratory, data analysis - even when the analyst adversarially searches for a statistical estimate that diverges from the true value of the…
View article: Tradeoffs for small-depth Frege proofs
Tradeoffs for small-depth Frege proofs Open
We study the complexity of small-depth Frege proofs and give the first tradeoffs between the size of each line and the number of lines. Existing lower bounds apply to the overall proof size -- the sum of sizes of all lines -- and do not di…
View article: Automating algebraic proof systems is NP-hard
Automating algebraic proof systems is NP-hard Open
We show that algebraic proofs are hard to find: Given an unsatisfiable CNF formula F, it is NP-hard to find a refutation of F in the Nullstellensatz, Polynomial Calculus, or Sherali-Adams proof systems in time polynomial in the size of the…
View article: Size and Depth Separation in Approximating Benign Functions with Neural Networks
Size and Depth Separation in Approximating Benign Functions with Neural Networks Open
When studying the expressive power of neural networks, a main challenge is to understand how the size and depth of the network affect its ability to approximate real functions. However, not all functions are interesting from a practical vi…
View article: Algebraic Proof Systems (Invited Talk)
Algebraic Proof Systems (Invited Talk) Open
Given a set of polynomial equations over a field F, how hard is it to prove that they are simultaneously unsolvable? In the last twenty years, algebraic proof systems for refuting such systems of equations have been extensively studied, re…
View article: On the Pseudo-Deterministic Query Complexity of NP Search Problems
On the Pseudo-Deterministic Query Complexity of NP Search Problems Open
We study pseudo-deterministic query complexity - randomized query algorithms that are required to output the same answer with high probability on all inputs. We prove Ω(√n) lower bounds on the pseudo-deterministic complexity of a large fam…
View article: On the Power and Limitations of Branch and Cut
On the Power and Limitations of Branch and Cut Open
The Stabbing Planes proof system [Paul Beame et al., 2018] was introduced to model the reasoning carried out in practical mixed integer programming solvers. As a proof system, it is powerful enough to simulate Cutting Planes and to refute …
View article: Query-to-Communication Lifting Using Low-Discrepancy Gadgets
Query-to-Communication Lifting Using Low-Discrepancy Gadgets Open
Lifting theorems are theorems that relate the query complexity of a function $f:\{0,1\}^{n}\to\{0,1\}$ to the communication complexity of the composed function $f \circ g^{n}$, for some "gadget" $g:\{0,1\}^{b}\times\{0,1\}^{b}\to\{0,1\}$. …
View article: Lifting with Simple Gadgets and Applications to Circuit and Proof Complexity
Lifting with Simple Gadgets and Applications to Circuit and Proof Complexity Open
We significantly strengthen and generalize the theorem lifting Nullstellensatz degree to monotone span program size by Pitassi and Robere (2018) so that it works for any gadget with high enough rank, in particular, for useful gadgets such …
View article: Theoretical bounds on estimation error for meta-learning
Theoretical bounds on estimation error for meta-learning Open
Machine learning models have traditionally been developed under the assumption that the training and test distributions match exactly. However, recent success in few-shot learning and related problems are encouraging signs that these model…
View article: KRW Composition Theorems via Lifting
KRW Composition Theorems via Lifting Open
One of the major open problems in complexity theory is proving super-logarithmic lower bounds on the depth of circuits (i.e., $\mathbf{P}\not\subseteq\mathbf{NC}^1$). Karchmer, Raz, and Wigderson (Computational Complexity 5(3/4), 1995) sug…
View article: Automating cutting planes is NP-hard
Automating cutting planes is NP-hard Open
We show that Cutting Planes (CP) proofs are hard to find: Given an unsatisfiable formula $F$, 1) It is NP-hard to find a CP refutation of $F$ in time polynomial in the length of the shortest such refutation; and 2)unless Gap-Hitting-Set ad…
View article: The Surprising Power of Constant Depth Algebraic Proofs
The Surprising Power of Constant Depth Algebraic Proofs Open
A major open problem in proof complexity is to prove superpolynomial lower bounds for AC0[p]-Frege proofs. This system is the analog of AC0 [p], the class of bounded depth circuits with prime modular counting gates. Despite strong lower bo…
View article: Towards a Complexity-theoretic Understanding of Restarts in SAT solvers
Towards a Complexity-theoretic Understanding of Restarts in SAT solvers Open
Restarts are a widely-used class of techniques integral to the efficiency of Conflict-Driven Clause Learning (CDCL) Boolean SAT solvers. While the utility of such policies has been well-established empirically, a theoretical explanation of…