Related papers: Natural Proofs Versus Derandomization
We give new proofs for the hardness amplification of efficiently samplable predicates and of weakly verifiable puzzles which generalize to new settings. More concretely, in the first part of the paper, we give a new proof of Yao's XOR-Lemma…
For a $k$-ary predicate $P$, a random instance of CSP$(P)$ with $n$ variables and $m$ constraints is unsatisfiable with high probability when $m \gg n$. The natural algorithmic task in this regime is \emph{refutation}: finding a proof that…
First of all we give some reasons that "natural proofs" built not a barrier to prove P $\not=$ NP using Boolean complexity. Then we investigate the approximation method for its extension to prove super-polynomial lower bounds for the…
If no optimal propositional proof system exists, we (and independently Pudl\'ak) prove that ruling out length $t$ proofs of any unprovable sentence is hard. This mapping from unprovable to hard-to-prove sentences powerfully translates facts…
Random linear codes are a workhorse in coding theory, and are used to show the existence of codes with the best known or even near-optimal trade-offs in many noise models. However, they have little structure besides linearity, and are not…
Despite their ubiquity in language generation, it remains unknown why truncation sampling heuristics like nucleus sampling are so effective. We provide a theoretical explanation for the effectiveness of the truncation sampling by proving…
We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution $D$ over $[n]$ and a property $\mathcal{P}$, the goal is to distinguish between…
Pseudorandomness has played a central role in modern cryptography, finding theoretical and practical applications to various fields of computer science. A function that generates pseudorandom strings from shorter but truly random seeds is…
Although good encryption functions are probabilistic, most symbolic models do not capture this aspect explicitly. A typical solution, recently used to prove the soundness of such models with respect to computational ones, is to explicitly…
In this paper we investigate formal verification problems for Neural Network computations. Of central importance will be various robustness and minimization problems such as: Given symbolic specifications of allowed inputs and outputs in…
Proofs (sequent calculus, natural deduction) and imperative algorithms (pseudocodes) are two well-known coexisting concepts. Then what is their relationship? Our answer is that \[ imperative\ algorithms\ =\ proofs\ with\ cuts \] This…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
This paper studies the notion of computational entropy. Using techniques from convex optimization, we investigate the following problems: (a) Can we derandomize the computational entropy? More precisely, for the computational entropy, what…
Deep neural networks learn fragile "shortcut" features, rendering them difficult to interpret (black box) and vulnerable to adversarial attacks. This paper proposes semantic features as a general architectural solution to this problem. The…
Certified robustness circumvents the fragility of defences against adversarial attacks, by endowing model predictions with guarantees of class invariance for attacks up to a calculated size. While there is value in these certifications, the…
In recent years, a number of process-based anomaly detection schemes for Industrial Control Systems were proposed. In this work, we provide the first systematic analysis of such schemes, and introduce a taxonomy of properties that are…
In traditional software programs, it is easy to trace program logic from variables back to input, apply assertion statements to block erroneous behavior, and compose programs together. Although deep learning programs have demonstrated…
The rapid development of derandomization theory, which is a fundamental area in theoretical computer science, has recently led to many surprising applications outside its initial intention. We will review some recent such developments…
The focus of this paper is on intrinsic methods to detect overfitting. By intrinsic methods, we mean methods that rely only on the model and the training data, as opposed to traditional methods (we call them extrinsic methods) that rely on…
We construct efficient data structures that are resilient against a constant fraction of adversarial noise. Our model requires that the decoder answers most queries correctly with high probability and for the remaining queries, the decoder…