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Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by enriching a…
Reward shaping is an effective technique for incorporating domain knowledge into reinforcement learning (RL). Existing approaches such as potential-based reward shaping normally make full use of a given shaping reward function. However,…
The reward signal plays a central role in defining the desired behaviors of agents in reinforcement learning (RL). Rewards collected from realistic environments could be perturbed, corrupted, or noisy due to an adversary, sensor error, or…
Reward machines (RMs) provide a structured way to specify non-Markovian rewards in reinforcement learning (RL), thereby improving both expressiveness and programmability. Viewed more broadly, they separate what is known about the…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
In unified field theories with more than four dimensions, the form of the equations of physics in spacetime depends in general on the choice of coordinates in higher dimensions. The reason is that the group of coordinate transformations in…
In physics the value of a theory is measured by its agreement with experimental data. But how should the physics community gauge the value of an emerging theory that has not been tested experimentally as of yet? With no reality check, a…
First, this paper broaches the definition of science and the epistemic yield of tenets and approaches: phenomenological (descriptive only), well-founded (solid first principles, conducive to deep understanding), provisional (falsifiable if…
The discovery of cosmic acceleration has triggered a consistent body of theoretical work aimed at modeling its phenomenology and understanding its fundamental physical nature. In recent years, a powerful formalism that accomplishes both…
The analysis of theory-confirmation generally takes the deductive form: show that a theory in conjunction with physical data and auxiliary hypotheses yield a prediction about phenomena; verify the prediction; provide a quantitative measure…
Reward shaping is a technique in reinforcement learning that addresses the sparse-reward problem by providing more frequent and informative rewards. We introduce a self-adaptive and highly efficient reward shaping mechanism that…
Reinforcement learning with verifiable rewards (RLVR) has been a main driver of recent breakthroughs in large reasoning models. Yet it remains a mystery how rewards based solely on final outcomes can help overcome the long-horizon barrier…
We argue that models in which an observable variation of the fine structure constant is explained by motion of a cosmic scalar field, are not stable under renormalization, and require massive fine tuning that cannot be explained by any…
In continuing tasks, average-reward reinforcement learning may be a more appropriate problem formulation than the more common discounted reward formulation. As usual, learning an optimal policy in this setting typically requires a large…
A common approach to solving physical reasoning tasks is to train a value learner on example tasks. A limitation of such an approach is that it requires learning about object dynamics solely from reward values assigned to the final state of…
In this paper, we combine task-dependent reward shaping and task-independent proto-value functions to obtain reward dependent proto-value functions (RPVFs). In constructing the RPVFs we are making use of the immediate rewards which are…
A new formulation of what may be called the "fundamental theorem of the theory of relativity" is presented and proved in (3+1)-space-time, based on the full classification of special transformations and the corresponding velocity addition…
Science education at all levels is currently undergoing dramatic changes to its curricula and developing assessments for these new curricula is paramount. We have used the basis of many of these new changes (scientific practices,…
Physical reasoning is a core aspect of intelligence in animals and humans. A central question is what model should be used as a basis for reasoning. Existing work considered models ranging from intuitive physics and physical simulators to…
In this paper we present an invariant formulation of special relativity, i.e., the ''true transformations relativity.'' It deals either with true tensor quantities (when no basis has been introduced) or equivalently with coordinate- based…