Bayes in the age of intelligent machines

The success of methods based on artificial neural networks in creating intelligent machines seems like it might pose a challenge to explanations of human cognition in terms of Bayesian inference. We argue that this is not the case, and that in fact these systems offer new opportunities for Bayesian modeling. Specifically, we argue that Bayesian models of cognition and artificial neural networks lie at different levels of analysis and are complementary modeling approaches, together offering a way to understand human cognition that spans these levels. We also argue that the same perspective can be applied to intelligent machines, where a Bayesian approach may be uniquely valuable in understanding the behavior of large, opaque artificial neural networks that are trained on proprietary data

Embers of Autoregression: Understanding Large Language Models Through the Problem They are Trained to Solve

The widespread adoption of large language models (LLMs) makes it important to recognize their strengths and limitations. We argue that in order to develop a holistic understanding of these systems we need to consider the problem that they were trained to solve: next-word prediction over Internet text. By recognizing the pressures that this task exerts we can make predictions about the strategies that LLMs will adopt, allowing us to reason about when they will succeed or fail. This approach - which we call the teleological approach - leads us to identify three factors that we hypothesize will influence LLM accuracy: the probability of the task to be performed, the probability of the target output, and the probability of the provided input. We predict that LLMs will achieve higher accuracy when these probabilities are high than when they are low - even in deterministic settings where probability should not matter. To test our predictions, we evaluate two LLMs (GPT-3.5 and GPT-4) on eleven tasks, and we find robust evidence that LLMs are influenced by probability in the ways that we have hypothesized. In many cases, the experiments reveal surprising failure modes. For instance, GPT-4's accuracy at decoding a simple cipher is 51% when the output is a high-probability word sequence but only 13% when it is low-probability. These results show that AI practitioners should be careful about using LLMs in low-probability situations. More broadly, we conclude that we should not evaluate LLMs as if they are humans but should instead treat them as a distinct type of system - one that has been shaped by its own particular set of pressures.Comment: 50 pages plus 11 page of references and 23 pages of appendice

Bayesian Probabilities and the Histories Algebra

We attempt a justification of a generalisation of the consistent histories programme using a notion of probability that is valid for all complete sets of history propositions. This consists of introducing Cox's axioms of probability theory and showing that our candidate notion of probability obeys them. We also give a generalisation of Bayes' theorem and comment upon how Bayesianism should be useful for the quantum gravity/cosmology programmes.Comment: 10 pages, accepted by Int. J. Theo. Phys. Feb 200

Learning Rewards from Linguistic Feedback

We explore unconstrained natural language feedback as a learning signal for artificial agents. Humans use rich and varied language to teach, yet most prior work on interactive learning from language assumes a particular form of input (e.g., commands). We propose a general framework which does not make this assumption, using aspect-based sentiment analysis to decompose feedback into sentiment about the features of a Markov decision process. We then perform an analogue of inverse reinforcement learning, regressing the sentiment on the features to infer the teacher's latent reward function. To evaluate our approach, we first collect a corpus of teaching behavior in a cooperative task where both teacher and learner are human. We implement three artificial learners: sentiment-based "literal" and "pragmatic" models, and an inference network trained end-to-end to predict latent rewards. We then repeat our initial experiment and pair them with human teachers. All three successfully learn from interactive human feedback. The sentiment models outperform the inference network, with the "pragmatic" model approaching human performance. Our work thus provides insight into the information structure of naturalistic linguistic feedback as well as methods to leverage it for reinforcement learning.Comment: 9 pages, 4 figures. AAAI '2

Dust-Gas Scaling Relations and OH Abundance in the Galactic ISM

Observations of interstellar dust are often used as a proxy for total gas column density $N_\mathrm{H}$. By comparing $\textit{Planck}$ thermal dust data (Release 1.2) and new dust reddening maps from Pan-STARRS 1 and 2MASS (Green et al. 2018), with accurate (opacity-corrected) HI column densities and newly-published OH data from the Arecibo Millennium survey and 21-SPONGE, we confirm linear correlations between dust optical depth $\tau_{353}$, reddening $E(B{-}V)$ and the total proton column density $N_\mathrm{H}$ in the range (1$-$30)$\times$10$^{20}$cm$^{-2}$, along sightlines with no molecular gas detections in emission. We derive an $N_\mathrm{H}$/$E(B{-}V)$ ratio of (9.4$\pm$1.6)$\times$10$^{21}$cm$^{-2}$mag$^{-1}$ for purely atomic sightlines at $|b|$$>$5$^{\circ}$, which is 60$\%$ higher than the canonical value of Bohlin et al. (1978). We report a $\sim$40$\%$ increase in opacity $\sigma_{353}$=$\tau_{353}$/$N_\mathrm{H}$, when moving from the low column density ($N_\mathrm{H}$$<$5$\times$10$^{20}$cm$^{-2}$) to moderate column density ($N_\mathrm{H}$$>$5$\times$10$^{20}$cm$^{-2}$) regime, and suggest that this rise is due to the evolution of dust grains in the atomic ISM. Failure to account for HI opacity can cause an additional apparent rise in $\sigma_{353}$, of the order of a further $\sim$20$\%$. We estimate molecular hydrogen column densities $N_{\mathrm{H}_{2}}$ from our derived linear relations, and hence derive the OH/H$_2$ abundance ratio of $X_\mathrm{OH}$$\sim$1$\times$10$^{-7}$ for all molecular sightlines. Our results show no evidence of systematic trends in OH abundance with $N_{\mathrm{H}_{2}}$ in the range $N_{\mathrm{H}_{2}}$$\sim$(0.1$-$10)$\times$10$^{21}$cm$^{-2}$. This suggests that OH may be used as a reliable proxy for H$_2$ in this range, which includes sightlines with both CO-dark and CO-bright gas.Comment: The revised manuscript is accepted for publication in The Astrophysical Journa

Manifestation of classical wave delays in a fully quantized model of the scattering of a single photon

We consider a fully quantized model of spontaneous emission, scattering, and absorption, and study propagation of a single photon from an emitting atom to a detector atom both with and without an intervening scatterer. We find an exact quantum analog to the classical complex analytic signal of an electromagnetic wave scattered by a medium of charged oscillators. This quantum signal exhibits classical phase delays. We define a time of detection which, in the appropriate limits, exactly matches the predictions of a classically defined delay for light propagating through a medium of charged oscillators. The fully quantized model provides a simple, unambiguous, and causal interpretation of delays that seemingly imply speeds greater than c in the region of anomalous dispersion.Comment: 18 pages, 4 figures, revised for clarity, typos corrrecte

Evaluation of the effectiveness and cost-effectiveness of Families for Health V2 for the treatment of childhood obesity : study protocol for a randomized controlled trial

Background: Effective programs to help children manage their weight are required. Families for Health focuses on a parenting approach, designed to help parents develop their parenting skills to support lifestyle change within the family. Families for Health V1 showed sustained reductions in overweight after 2 years in a pilot evaluation, but lacks a randomized controlled trial (RCT) evidence base. Methods/design: This is a multi-center, investigator-blind RCT, with parallel economic evaluation, with a 12-month follow-up. The trial will recruit 120 families with at least one child aged 6 to 11 years who is overweight (≥91st centile BMI) or obese (≥98th centile BMI) from three localities and assigned randomly to Families for Health V2 (60 families) or the usual care control (60 families) groups. Randomization will be stratified by locality (Coventry, Warwickshire, Wolverhampton). Families for Health V2 is a family-based intervention run in a community venue. Parents/carers and children attend parallel groups for 2.5 hours weekly for 10 weeks. The usual care arm will be the usual support provided within each NHS locality. A mixed-methods evaluation will be carried out. Child and parent participants will be assessed at home visits at baseline, 3-month (post-treatment) and 12-month follow-up. The primary outcome measure is the change in the children’s BMI z-scores at 12 months from the baseline. Secondary outcome measures include changes in the children’s waist circumference, percentage body fat, physical activity, fruit/vegetable consumption and quality of life. The parents’ BMI and mental well-being, family eating/activity, parent–child relationships and parenting style will also be assessed. Economic components will encompass the measurement and valuation of service utilization, including the costs of running Families for Health and usual care, and the EuroQol EQ-5D health outcomes. Cost-effectiveness will be expressed in terms of incremental cost per quality-adjusted life year gained. A de novo decision-analytic model will estimate the lifetime cost-effectiveness of the Families for Health program. Process evaluation will document recruitment, attendance and drop-out rates, and the fidelity of Families for Health delivery. Interviews with up to 24 parents and children from each arm will investigate perceptions and changes made. Discussion: This paper describes our protocol to assess the effectiveness and cost-effectiveness of a parenting approach for managing childhood obesity and presents challenges to implementation. Trial registration: Current Controlled Trials ISRCTN4503220

Formalizing Neurath's ship:Approximate algorithms for online causal learning

Higher-level cognition depends on the ability to learn models of the world. We can characterize this at the computational level as a structure-learning problem with the goal of best identifying the prevailing causal relationships among a set of relata. However, the computational cost of performing exact Bayesian inference over causal models grows rapidly as the number of relata increases. This implies that the cognitive processes underlying causal learning must be substantially approximate. A powerful class of approximations that focuses on the sequential absorption of successive inputs is captured by the Neurath's ship metaphor in philosophy of science, where theory change is cast as a stochastic and gradual process shaped as much by people's limited willingness to abandon their current theory when considering alternatives as by the ground truth they hope to approach. Inspired by this metaphor and by algorithms for approximating Bayesian inference in machine learning, we propose an algorithmic-level model of causal structure learning under which learners represent only a single global hypothesis that they update locally as they gather evidence. We propose a related scheme for understanding how, under these limitations, learners choose informative interventions that manipulate the causal system to help elucidate its workings. We find support for our approach in the analysis of four experiments