Consider a set of shuffled observations drawn from a fixed probability distribution over some instance domain. What enables learning of inductive generalizations which proceed from such a set of observations? The scenario is worthwhile because it epistemically characterizes most of machine learning. This kind of learning from observations is also inverse and ill-posed. What reduces the non-uniqueness of its result and, thus, its problematic epistemic justification, which stems from a one-to-many relation between the observations and many learnable generalizations? The paper (...) argues that this role belongs to any complexity regularization which satisfies Norton’s Material Theory of Induction (MTI) by localizing the inductive risk to facts in the given domain. A prime example of the localization is the Lottery Ticket Hypothesis (LTH) about overparameterized neural networks. The explanation of MTI’s role in complexity regularization of neural networks is provided by analyzing the stability of Empirical Risk Minimization (ERM), an inductive rule that controls the learning process and leads to an inductive generalization on the given set of observations. In cases where ERM might become asymptotically unstable, making the justification of the generalization by uniform convergence unavailable, LTH and MTI can be used to define a local stability. A priori, overparameterized neural networks are such cases and the combination of LTH and MTI can block ERM’s trivialization caused by equalizing the strengths of its inductive support for risk minimization. We bring closer the investigation of generalization in artificial neural networks and the study of inductive inference and show the division of labor between MTI and the optimality justifications (developed by Gerhard Schurz) in machine learning. (shrink)

Despite an increasing role of machine learning in science, there is a lack of results on limits of empirical exploration aided by machine learning. In this paper, we construct one such limit by proving undecidability of learnability of state spaces of physical systems. We characterize state spaces as binary hypothesis classes of the computable Probably Approximately Correct learning framework. This leads to identifying the first limit for learnability of state spaces in the agnostic setting. Further, using the fact that finiteness (...) of the combinatorial dimension of hypothesis classes is undecidable, we derive undecidability for learnability of state spaces as well. Throughout the paper, we try to connect our formal results with modern neural networks. This allows us to bring the limits close to the current practice and make a first step in connecting scientific exploration aided by machine learning with results from learning theory. (shrink)

As our epistemic ambitions grow, the common and scientific endeavours are becoming increasingly dependent on Machine Learning (ML). The field rests on a single experimental paradigm, which consists of splitting the available data into a training and testing set and using the latter to measure how well the trained ML model generalises to unseen samples. If the model reaches acceptable accuracy, an a posteriori contract comes into effect between humans and the model, supposedly allowing its deployment to target environments. Yet (...) the latter part of the contract depends on human inductive predictions or generalisations, which infer a uniformity between the trained ML model and the targets. The paper asks how we justify the contract between human and machine learning. It is argued that the justification becomes a pressing issue when we use ML to reach ‘elsewheres’ in space and time or deploy ML models in non-benign environments. The paper argues that the only viable version of the contract can be based on optimality (instead of on reliability which cannot be justified without circularity) and aligns this position with Schurz’s optimality justification. It is shown that when dealing with inaccessible/unstable ground-truths (‘elsewheres’ and non-benign targets), the optimality justification undergoes a slight change, which should reflect critically on our epistemic ambitions. Therefore, the study of ML robustness should involve not only heuristics that lead to acceptable accuracies on testing sets. The justification of human inductive predictions or generalisations about the uniformity between ML models and targets should be included as well. Without it, the assumptions about inductive risk minimisation in ML are not addressed in full. (shrink)

The paper proposes a synthesis between human scientists and artificial representation learning models as a way of augmenting epistemic warrants of realist theories against various anti-realist attempts. Towards this end, the paper fleshes out unconceived alternatives not as a critique of scientific realism but rather a reinforcement, as it rejects the retrospective interpretations of scientific progress, which brought about the problem of alternatives in the first place. By utilising adversarial machine learning, the synthesis explores possibility spaces of available evidence for (...) unconceived alternatives providing modal knowledge of what is possible therein. As a result, the epistemic warrant of synthesised realist theories should emerge bolstered as the underdetermination by available evidence gets reduced. While shifting the realist commitment away from theoretical artefacts towards modalities of the possibility spaces, the synthesis comes out as a kind of perspectival modelling. (shrink)

Procedural justifications of democracy emphasize inclusiveness and respect and by doing so come into conflict with instrumental justifications that depend on voters’ competence. This conflict raises questions about jury theorems and makes their standing in democratic theory contested. We show that a type of no-regret learning called meta-induction can help to satisfy the competence assumption without excluding voters or diverse opinion leaders on an a priori basis. Meta-induction assigns weights to opinion leaders based on their past predictive performance to determine (...) the level of their inclusion in recommendations for voters. The weighting minimizes the difference between the performance of meta-induction and the best opinion leader in hindsight. The difference represents the regret of meta-induction whose minimization ensures that the recommendations are optimal in supporting voters’ competence. Meta-induction has optimal truth-tracking properties that support voters’ competence even if it is targeted by mis/disinformation and should be considered a tool for supporting democracy in hyper-plurality. (shrink)

We ask how to use machine learning to expand observability, which presently depends on human learning that informs conceivability. The issue is engaged by considering the question of correspondence between conceived observability counterfactuals and observable, yet so far unobserved or unconceived, states of affairs. A possible answer lies in importing out of reference frame content which could provide means for conceiving further observability counterfactuals. They allow us to define high-fidelity observability, increasing the level of correspondence in question. To achieve high-fidelity (...) observability, we propose to use generative machine learning models as the providers of the out of reference frame content. From an applied point of view, such a role of generative machine learning models shows an emerging dimension of human-machine cooperation. (shrink)

The environmental costs and energy constraints have become emerging issues for the future development of Machine Learning (ML) and Artificial Intelligence (AI). So far, the discussion on environmental impacts of ML/AI lacks a perspective reaching beyond quantitative measurements of the energy-related research costs. Building on the foundations laid down by Schwartz et al., 2019 in the GreenAI initiative, our argument considers two interlinked phenomena, the gratuitous generalisation capability and the future where ML/AI performs the majority of quantifiable inductive inferences. The (...) gratuitous generalisation capability refers to a discrepancy between the cognitive demands of a task to be accomplished and the performance (accuracy) of a used ML/AI model. If the latter exceeds the former because the model was optimised to achieve the best possible accuracy, it becomes inefficient and its operation harmful to the environment. The future dominated by the non-anthropic induction describes a use of ML/AI so all-pervasive that most of the inductive inferences become furnished by ML/AI generalisations. The paper argues that the present debate deserves an expansion connecting the environmental costs of research and ineffective ML/AI uses (the issue of gratuitous generalisation capability) with the (near) future marked by the all-pervasive Human-Artificial Intelligence Nexus. (shrink)