Calibrating Generative Models: The Probabilistic Chomsky-Schützenberger Hierarchy

A probabilistic Chomsky–Schützenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into the regular languages, using analytic tools adapted from the classical setting we show there is no collapse in the probabilistic hierarchy: more distributions become definable at each level. We also address related issues such as closure under probabilistic conditioning

On the instrumental value of hypothetical and counterfactual thought.

People often engage in “offline simulation”, considering what would happen if they performed certain actions in the future, or had performed different actions in the past. Prior research shows that these simulations are biased towards actions a person considers to be good—i.e., likely to pay off. We ask whether, and why, this bias might be adaptive. Through computational experiments we compare five agents who differ only in the way they engage in offline simulation, across a variety of different environment types. Broadly speaking, our experiments reveal that simulating actions one already regards as good does in fact confer an advantage in downstream decision making, although this general pattern interacts with features of the environment in important ways. We contrast this bias with alternatives such as simulating actions whose outcomes are instead uncertain

Logics of Imprecise Comparative Probability

This paper studies connections between two alternatives to the standard probability calculus for representing and reasoning about uncertainty: imprecise probability andcomparative probability. The goal is to identify complete logics for reasoning about uncertainty in a comparative probabilistic language whose semantics is given in terms of imprecise probability. Comparative probability operators are interpreted as quantifying over a set of probability measures. Modal and dynamic operators are added for reasoning about epistemic possibility and updating sets of probability measures

Indicative Conditionals and Dynamic Epistemic Logic

Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal semantics and dynamic epistemic logic in this area can be of mutual benefit. In one direction, we show how concepts and tools from modal logic and dynamic epistemic logic can be used to give a simple, complete axiomatization of Yalcin's [16] semantic consequence relation for a language with epistemic modals and indicative conditionals. In the other direction, the formal semantics for indicative conditionals due to Kolodny and MacFarlane [9] gives rise to a new dynamic operator that is very natural from the point of view of dynamic epistemic logic, allowing succinct expression of dependence (as in dependence logic) or supervenience statements. We prove decidability for the logic with epistemic modals and Kolodny and MacFarlane's indicative conditional via a full and faithful computable translation from their logic to the modal logic K45.Comment: In Proceedings TARK 2017, arXiv:1707.0825

Neural-Symbolic Learning and Reasoning: Contributions and Challenges

The goal of neural-symbolic computation is to integrate robust connectionist learning and sound symbolic reasoning. With the recent advances in connectionist learning, in particular deep neural networks, forms of representation learning have emerged. However, such representations have not become useful for reasoning. Results from neural-symbolic computation have shown to offer powerful alternatives for knowledge representation, learning and reasoning in neural computation. This paper recalls the main contributions and discusses key challenges for neural-symbolic integration which have been identified at a recent Dagstuhl seminar

A Dynamic Logic for Information Evaluation in Intelligence

In the field of human intelligence, officers use an alphanumeric scale, known as the Admiralty System, to rate the credibility of messages and the reliability of their sources (NATO AJP-2.1, 2016). During this evaluation, they are expected to estimate the credibility and reliability dimensions independently of each other (NATO STANAG, 2003). However, empirical results show that officers perceive these dimensions as strongly correlated (Baker et al., 1968). More precisely, they consider credibility as playing the leading role over reliability, the importance of which is only secondary (Samet, 1975). In this paper, we present a formal evaluative procedure, called L(intel), in line with these findings. We adapt dynamic belief revision to make credibility the main dimension of evaluation and introduce dynamic operators to update credibility ratings with the source's reliability. In addition to being empirically sound, we show that L(intel) provides an effective procedure to classify intelligence messages along the descriptive taxonomy presented in Icard (2023)

Power laws in microrheology experiments on living cells: comparative analysis and modelling

We compare and synthesize the results of two microrheological experiments on the cytoskeleton of single cells. In the first one, the creep function J(t) of a cell stretched between two glass plates is measured after applying a constant force step. In the second one, a micrometric bead specifically bound to transmembrane receptors is driven by an oscillating optical trap, and the viscoelastic coefficient $G_e(\omega)$ is retrieved. Both $J(t)$ and $G_e(\omega)$ exhibit power law behavior: $J(t)= A(t/t_0)^\alpha$ and $\bar G_e(\omega)\bar = G_0 (\omega/\omega_0)^\alpha$, with the same exponent $\alpha\approx 0.2$. This power law behavior is very robust ; $\alpha$ is distributed over a narrow range, and shows almost no dependance on the cell type, on the nature of the protein complex which transmits the mechanical stress, nor on the typical length scale of the experiment. On the contrary, the prefactors $A_0$ and $G_0$appear very sensitive to these parameters. Whereas the exponents $\alpha$ are normally distributed over the cell population, the prefactors $A_0$ and $G_0$ follow a log-normal repartition. These results are compared with other data published in the litterature. We propose a global interpretation, based on a semi-phenomenological model, which involves a broad distribution of relaxation times in the system. The model predicts the power law behavior and the statistical repartition of the mechanical parameters, as experimentally observed for the cells. Moreover, it leads to an estimate of the largest response time in the cytoskeletal network: $\tau_m \approx 1000$ s.Comment: 47 pages, 14 figures // v2: PDF file is now Acrobat Reader 4 (and up) compatible // v3: Minor typos corrected - The presentation of the model have been substantially rewritten (p. 17-18), in order to give more details - Enhanced description of protocols // v4: Minor corrections in the text : the immersion angles are estimated and not measured // v5: Minor typos corrected. Two references were clarifie