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The multifaceted nature of experience poses a challenge to the study of consciousness. Traditional neuroscientific approaches often concentrate on isolated facets, such as perceptual awareness or the global state of consciousness and construct a theory around the relevant empirical paradigms and findings. Theories of consciousness are, therefore, often difficult to compare; indeed, there might be little overlap in the phenomena such theories aim to explain. Here, we take a different approach: starting with active inference, a first principles framework for modelling behaviour as (approximate) Bayesian inference, and building up to a minimal theory of consciousness, which emerges from the shared features of computational models derived under active inference. We review a body of work applying active inference models to the study of consciousness and argue that there is implicit in all these models a small set of theoretical commitments that point to a minimal (and testable) theory of consciousness.

SDO-FM is a foundation model using data from NASA's Solar Dynamics Observatory (SDO) spacecraft; integrating three separate instruments to encapsulate the Sun's complex physical interactions into a multi-modal embedding space. This model can be used to streamline scientific investigations involving SDO by making the enormous datasets more computationally accessible for heliophysics research and enable investigations that require instrument fusion. We discuss four key components: an ingestion pipeline to create machine learning ready datasets, the model architecture and training approach, resultant embeddings and fine-tunable models, and finally downstream fine-tuned applications. A key component of this effort has been to include subject matter specialists at each stage of development; reviewing the scientific value and providing guidance for model architecture, dataset, and training paradigm decisions. This paper marks release of our pretrained models and embedding datasets, available to the community on Hugging Face and sdofm.org.

Stochastic differential equations are ubiquitous modelling tools in physics and the sciences. In most modelling scenarios, random fluctuations driving dynamics or motion have some non-trivial temporal correlation structure, which renders the SDE non-Markovian; a phenomenon commonly known as ``colored'' noise. Thus, an important objective is to develop effective tools for mathematically and numerically studying (possibly non-Markovian) SDEs. In this report, we formalise a mathematical theory for analysing and numerically studying SDEs based on so-called `generalised coordinates of motion'. Like the theory of rough paths, we analyse SDEs pathwise for any given realisation of the noise, not solely probabilistically. Like the established theory of Markovian realisation, we realise non-Markovian SDEs as a Markov process in an extended space. Unlike the established theory of Markovian realisation however, the Markovian realisations here are accurate on short timescales and may be exact globally in time, when flows and fluctuations are analytic. This theory is exact for SDEs with analytic flows and fluctuations, and is approximate when flows and fluctuations are differentiable. It provides useful analysis tools, which we employ to solve linear SDEs with analytic fluctuations. It may also be useful for studying rougher SDEs, as these may be identified as the limit of smoother ones. This theory supplies effective, computationally straightforward methods for simulation, filtering and control of SDEs; amongst others, we re-derive generalised Bayesian filtering, a state-of-the-art method for time-series analysis. Looking forward, this report suggests that generalised coordinates have far-reaching applications throughout stochastic differential equations., Comment: 38 pages of main, 45 pages including TOC, Appendix and references

This paper describes a discrete state-space model -- and accompanying methods -- for generative modelling. This model generalises partially observed Markov decision processes to include paths as latent variables, rendering it suitable for active inference and learning in a dynamic setting. Specifically, we consider deep or hierarchical forms using the renormalisation group. The ensuing renormalising generative models (RGM) can be regarded as discrete homologues of deep convolutional neural networks or continuous state-space models in generalised coordinates of motion. By construction, these scale-invariant models can be used to learn compositionality over space and time, furnishing models of paths or orbits; i.e., events of increasing temporal depth and itinerancy. This technical note illustrates the automatic discovery, learning and deployment of RGMs using a series of applications. We start with image classification and then consider the compression and generation of movies and music. Finally, we apply the same variational principles to the learning of Atari-like games., Comment: 64 pages, 28 figures

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, how can an agent learn such a state representation, and how can it detect when it has found one? We introduce a metric that can accomplish both objectives, without requiring access to--or knowledge of--an underlying, unobservable state space. Our metric, the $\lambda$-discrepancy, is the difference between two distinct temporal difference (TD) value estimates, each computed using TD($\lambda$) with a different value of $\lambda$. Since TD($\lambda$=0) makes an implicit Markov assumption and TD($\lambda$=1) does not, a discrepancy between these estimates is a potential indicator of a non-Markovian state representation. Indeed, we prove that the $\lambda$-discrepancy is exactly zero for all Markov decision processes and almost always non-zero for a broad class of partially observable environments. We also demonstrate empirically that, once detected, minimizing the $\lambda$-discrepancy can help with learning a memory function to mitigate the corresponding partial observability. We then train a reinforcement learning agent that simultaneously constructs two recurrent value networks with different $\lambda$ parameters and minimizes the difference between them as an auxiliary loss. The approach scales to challenging partially observable domains, where the resulting agent frequently performs significantly better (and never performs worse) than a baseline recurrent agent with only a single value network., Comment: GitHub URL: https://github.com/brownirl/lambda_discrepancy; Videos: https://lambda-discrepancy.github.io/

The Rashomon Effect, coined by Leo Breiman, describes the phenomenon that there exist many equally good predictive models for the same dataset. This phenomenon happens for many real datasets and when it does, it sparks both magic and consternation, but mostly magic. In light of the Rashomon Effect, this perspective piece proposes reshaping the way we think about machine learning, particularly for tabular data problems in the nondeterministic (noisy) setting. We address how the Rashomon Effect impacts (1) the existence of simple-yet-accurate models, (2) flexibility to address user preferences, such as fairness and monotonicity, without losing performance, (3) uncertainty in predictions, fairness, and explanations, (4) reliable variable importance, (5) algorithm choice, specifically, providing advanced knowledge of which algorithms might be suitable for a given problem, and (6) public policy. We also discuss a theory of when the Rashomon Effect occurs and why. Our goal is to illustrate how the Rashomon Effect can have a massive impact on the use of machine learning for complex problems in society.

We present a bound for value-prediction error with respect to model misspecification that is tight, including constant factors. This is a direct improvement of the "simulation lemma," a foundational result in reinforcement learning. We demonstrate that existing bounds are quite loose, becoming vacuous for large discount factors, due to the suboptimal treatment of compounding probability errors. By carefully considering this quantity on its own, instead of as a subcomponent of value error, we derive a bound that is sub-linear with respect to transition function misspecification. We then demonstrate broader applicability of this technique, improving a similar bound in the related subfield of hierarchical abstraction., Comment: 10 page (+3 appendix). Published as a conference paper at RLC 2024

At continuous phase transitions, quantum many-body systems exhibit scale-invariance and complex, emergent universal behavior. Most strikingly, at a quantum critical point, correlations decay as a power law, with exponents determined by a set of universal scaling dimensions. Experimentally probing such power-law correlations is extremely challenging, owing to the complex interplay between decoherence, the vanishing energy gap, and boundary effects. Here, we employ a Rydberg quantum simulator to adiabatically prepare critical ground states of both a one-dimensional ring and a two-dimensional square lattice. By accounting for and tuning the openness of our quantum system, which is well-captured by the introduction of a single phenomenological length scale, we are able to directly observe power-law correlations and extract the corresponding scaling dimensions. Moreover, in two dimensions, we observe a decoupling between phase transitions in the bulk and on the boundary, allowing us to identify two distinct boundary universality classes. Our work demonstrates that direct adiabatic preparation of critical states in quantum simulators can complement recent approaches to studying quantum criticality using the Kibble-Zurek mechanism or digital quantum circuits.

Recent advances in theoretical biology suggest that basal cognition and sentient behaviour are emergent properties of in vitro cell cultures and neuronal networks, respectively. Such neuronal networks spontaneously learn structured behaviours in the absence of reward or reinforcement. In this paper, we characterise this kind of self-organisation through the lens of the free energy principle, i.e., as self-evidencing. We do this by first discussing the definitions of reactive and sentient behaviour in the setting of active inference, which describes the behaviour of agents that model the consequences of their actions. We then introduce a formal account of intentional behaviour, that describes agents as driven by a preferred endpoint or goal in latent state-spaces. We then investigate these forms of (reactive, sentient, and intentional) behaviour using simulations. First, we simulate the aforementioned in vitro experiments, in which neuronal cultures spontaneously learn to play Pong, by implementing nested, free energy minimising processes. The simulations are then used to deconstruct the ensuing predictive behaviour, leading to the distinction between merely reactive, sentient, and intentional behaviour, with the latter formalised in terms of inductive planning. This distinction is further studied using simple machine learning benchmarks (navigation in a grid world and the Tower of Hanoi problem), that show how quickly and efficiently adaptive behaviour emerges under an inductive form of active inference., Comment: 33 pages, 9 figures

This paper concerns structure learning or discovery of discrete generative models. It focuses on Bayesian model selection and the assimilation of training data or content, with a special emphasis on the order in which data are ingested. A key move - in the ensuing schemes - is to place priors on the selection of models, based upon expected free energy. In this setting, expected free energy reduces to a constrained mutual information, where the constraints inherit from priors over outcomes (i.e., preferred outcomes). The resulting scheme is first used to perform image classification on the MNIST dataset to illustrate the basic idea, and then tested on a more challenging problem of discovering models with dynamics, using a simple sprite-based visual disentanglement paradigm and the Tower of Hanoi (cf., blocks world) problem. In these examples, generative models are constructed autodidactically to recover (i.e., disentangle) the factorial structure of latent states - and their characteristic paths or dynamics.

The Rashomon set is the set of models that perform approximately equally well on a given dataset, and the Rashomon ratio is the fraction of all models in a given hypothesis space that are in the Rashomon set. Rashomon ratios are often large for tabular datasets in criminal justice, healthcare, lending, education, and in other areas, which has practical implications about whether simpler models can attain the same level of accuracy as more complex models. An open question is why Rashomon ratios often tend to be large. In this work, we propose and study a mechanism of the data generation process, coupled with choices usually made by the analyst during the learning process, that determines the size of the Rashomon ratio. Specifically, we demonstrate that noisier datasets lead to larger Rashomon ratios through the way that practitioners train models. Additionally, we introduce a measure called pattern diversity, which captures the average difference in predictions between distinct classification patterns in the Rashomon set, and motivate why it tends to increase with label noise. Our results explain a key aspect of why simpler models often tend to perform as well as black box models on complex, noisier datasets., Comment: NeurIPS 2023

We extend the method for constructing symmetry operators of higher order for two-dimensional quantum Hamiltonians by Kalnins, Kress and Miller (2010). This expansion method expresses the integral in a finite power series in terms of lower degree integrals so as to exhibit it as a first-order differential operators. One advantage of this approach is that it does not require the a priori knowledge of the explicit eigenfunctions of the Hamiltonian nor the action of their raising and lowering operators as in their recurrence approach (2011). We obtain insight into the two-dimensional Hamiltonians of radial oscillator type with general second-order differential operators for the angular variable. We then re-examine the Hamiltonian of Tremblay, Turbiner and Winternitz (2009) as well as a deformation discovered by Post, Vinet and Zhedanov (2011) which possesses reflection operators. We will extend the analysis to spaces of constant curvature. We present explicit formulas for the integrals and the symmetry algebra, the Casimir invariant and oscillator realisations with finite-dimensional irreps which fill a gap in the literature., Comment: 28 pages

This paper introduces a variational formulation of natural selection, paying special attention to the nature of "things" and the way that different "kinds" of "things" are individuated from - and influence - each other. We use the Bayesian mechanics of particular partitions to understand how slow phylogenetic processes constrain - and are constrained by - fast, phenotypic processes. The main result is a formulation of adaptive fitness as a path integral of phenotypic fitness. Paths of least action, at the phenotypic and phylogenetic scales, can then be read as inference and learning processes, respectively. In this view, a phenotype actively infers the state of its econiche under a generative model, whose parameters are learned via natural (bayesian model selection). The ensuing variational synthesis features some unexpected aspects. Perhaps the most notable is that it is not possible to describe or model a population of conspecifics per se. Rather, it is necessary to consider populations - and nested meta-populations - of different natural kinds that influence each other. This paper is limited to a description of the mathematical apparatus and accompanying ideas. Subsequent work will use these methods for simulations and numerical analyses - and identify points of contact with related mathematical formulations of evolution.