Related papers: Solomonoff Induction Violates Nicod's Criterion
Large Language Models exhibit sycophancy: prioritizing agreeableness over correctness. Current remedies evaluate reasoning outcomes: RLHF rewards correct answers, self-correction critiques outputs. All require ground truth, which is often…
Let $p\ge 1$ and let $\boldsymbol{v} \colon \mathbb R^d \to \mathbb R^d$ be a compactly supported vector field with $\boldsymbol{v} \in L^p(\mathbb R^d)$ and $\operatorname{div} \boldsymbol{v} = 0$ (in the sense of distributions). It was…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
We show that the One-way ANOVA and Tukey-Kramer (TK) tests agree on any sample with two groups. This result is based on a simple identity connecting the Fisher-Snedecor and studentized probabilistic distributions and is proven without any…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
Let $(X_n)$ be a Markov chain on a standard borelian space $\mathbb{X}$. Any stopping time $\tau$ such that $\mathbb{E}_x\tau$ is finite for all $x\in\mathbb{X}$ induces a Markov chain in $\mathbb{X}$. In this article, we show that there is…
Strong typicality and the Markov lemma have been used in the proofs of several multiterminal source coding theorems. Since these two tools can be applied to finite alphabets only, the results proved by them are subject to the same…
We give the first agnostic, efficient, proper learning algorithm for monotone Boolean functions. Given $2^{\tilde{O}(\sqrt{n}/\varepsilon)}$ uniformly random examples of an unknown function $f:\{\pm 1\}^n \rightarrow \{\pm 1\}$, our…
Reinforcement learning algorithms typically rely on the assumption that the environment dynamics and value function can be expressed in terms of a Markovian state representation. However, when state information is only partially observable,…
We consider the problem of intruder deduction in security protocol analysis: that is, deciding whether a given message $M$ can be deduced from a set of messages $\Gamma$ under the theory of blind signatures and arbitrary convergent…
Godel's First Incompleteness Theorem is generalized to definable theories, which are not necessarily recursively enumerable, by using a couple of syntactic-semantic notions, one is the consistency of a theory with the set of all true…
Mostof the existing literature on supervised machine learning problems focuses on the case when the training data set is drawn from an i.i.d. sample. However, many practical problems are characterized by temporal dependence and strong…
Robin's criterion states that the Riemann Hypothesis (RH) is true if and only if Robin's inequality sum_{d|n}d<e^{gamma}n loglog n is satisfied for n>=5041, where gamma denotes the Euler(-Mascheroni) constant. We show by elementary methods…
Standard supervised classification trains models to imitate the exact labels provided by a perfect oracle. This imitation happens in a single pass, restricting the model to a fixed compute budget even when inputs vary in complexity.…
Traditional approaches to non-monotonic reasoning fail to satisfy a number of plausible axioms for belief revision and suffer from conceptual difficulties as well. Recent work on ranked preferential models (RPMs) promises to overcome some…
We discuss the (non)effectivity of Arslanov's completeness criterion. In particular, we show that a parameterized version, similar to the recursion theorem with parameters, fails. We also discuss the parameterized version of another…
We study connections between Natural Proofs, derandomization, and the problem of proving "weak" circuit lower bounds such as ${\sf NEXP} \not\subset {\sf TC^0}$. Natural Proofs have three properties: they are constructive (an efficient…
Tackling Natural Language Inference with a logic-based method is becoming less and less common. While this might have been counterintuitive several decades ago, nowadays it seems pretty obvious. The main reasons for such a conception are…
For obtaining causal inferences that are objective, and therefore have the best chance of revealing scientific truths, carefully designed and executed randomized experiments are generally considered to be the gold standard. Observational…
A reflection map, induced by the deterministic Skorohod problem on the nonnegative orthant, is applied to an $\mathbb{R}^n$ valued function $X$ on $[0,\infty)$ and then to $a+X$, where $a$ is a nonnegative constant vector. A question that…