Deterministic game-solving algorithms are conventionally analyzed in the light of their average-case complexity against a distribution of random game-trees, where leaf values are independently sampled from a fixed distribution. This simplified model enables uncluttered mathematical analysis, revealing two key properties: root value distributions asymptotically collapse to a single fixed value for finitevalued trees, and all reasonable algorithms achieve global optimality. However, these findings are artifacts of the model's design: its long criticized independence assumption strips games of structural complexity, producing trivial instances where no algorithm faces meaningful challenges. To address this limitation, we introduce a class of synthetic games generated by a probabilistic model that incrementally constructs game-trees using a fixed level-wise conditional distribution. By enforcing ancestor dependencies, a critical structural feature of real-world games, our framework generates problems with adjustable difficulty while retaining some form of analytical tractability. For several algorithms, including AlphaBeta and Scout, we derive recursive formulas characterizing their average-case complexities under this model. These allow us to rigorously compare algorithms on deep gametrees, where Monte-Carlo simulations are no longer feasible. While asymptotically, all algorithms seem to converge to identical branching factor (a result analogous to that of independence-based models), deep finite trees reveal stark differences: AlphaBeta incurs a significantly larger constant multiplicative factor compared to algorithms like Scout, leading to a substantial practical slowdown. Our framework sheds new light on classical game-solving algorithms, offering rigorous evidence and analytical tools to advance the understanding of these methods under a richer, more challenging, and yet tractable model.

Recent monocular metric depth estimation (MMDE) methods have made notable progress towards zero-shot generalization.

While deep learning has revolutionised inverse problems, its safe deployment is hindered by three primary reliability concerns: hallucinations, instabilities, and performance volatility [48]. Hallucinations manifest as high-fidelity features that are factually false; instabilities reflect heightened sensitivity to measurement noise; and performance volatility refers to significant fluctuations in reconstruction quality across the data, yielding high-fidelity results for some samples while failing on seemingly similar images. In many applications, the risk of generating realistic but unfaithful content can impede the safe deployment of AI methods for inverse problems. The choice of "hallucinate" as the Cambridge Dictionary's word of the year in 2023 illustrates this open problem [53]. The problem of AI hallucinations persists, as the Financial Times [44] highlighted that, "AI hallucinations haunt users more than job losses." A first step toward training AI methods that do not suffer from hallucinations is the assessment and identification of hallucinated outputs. Consider the inverse problem of recovering xfrom noisy measurements y " Fpx,eq, x PM1 ĂX, e PEĂY, (1.1)

Emerging neural reconstruction techniques based on tomography (e.g., NeRF, NeAT, and NeRP) have started showing unique capabilities in medical imaging. In this work, we present a novel Polychromatic neural representation (Polyner) to tackle the challenging problem of CT imaging when metallic implants exist within the human body. CT metal artifacts arise from the drastic variation of metal's attenuation coefficients at various energy levels of the X-ray spectrum, leading to a nonlinear metal effect in CT measurements. Recovering CT images from metal-affected measurements hence poses a complicated nonlinear inverse problem where empirical models adopted in previous metal artifact reduction (MAR) approaches lead to signal loss and strongly aliased reconstructions.

Tree Search (TS) is crucial to some of the most influential successes in reinforcement learning. Here, we tackle two major challenges with TS that limit its usability: distribution shift and scalability. We first discover and analyze a counter-intuitive phenomenon: action selection through TS and a pre-trained value function often leads to lower performance compared to the original pre-trained agent, even when having access to the exact state and reward in future steps. We show this is due to a distribution shift to areas where value estimates are highly inaccurate and analyze this effect using Extreme Value theory. To overcome this problem, we introduce a novel off-policy correction term that accounts for the mismatch between the pre-trained value and its corresponding TS policy by penalizing under-sampled trajectories.

Neural Information Processing Systems http://nips.cc/

How does our motor system solve the problem of anticipatory control in spite of a wide spectrum of response dynamics from different musculo-skeletal systems, transport delays as well as response latencies throughout the central nervous system? To a great extent, our highly-skilled motor responses are a result of a reactive feedback system, originating in the brain-stem and spinal cord, combined with a feed-forward anticipatory system, that is adaptively fine-tuned by sensory experience and originates in the cerebellum. Based on that interaction we design the counterfactual predictive control (CFPC) architecture, an anticipatory adaptive motor control scheme in which a feed-forward module, based on the cerebellum, steers an error feedback controller with counterfactual error signals. Those are signals that trigger reactions as actual errors would, but that do not code for any current or forthcoming errors. In order to determine the optimal learning strategy, we derive a novel learning rule for the feed-forward module that involves an eligibility trace and operates at the synaptic level. In particular, our eligibility trace provides a mechanism beyond co-incidence detection in that it convolves a history of prior synaptic inputs with error signals. In the context of cerebellar physiology, this solution implies that Purkinje cell synapses should generate eligibility traces using a forward model of the system being controlled. From an engineering perspective, CFPC provides a general-purpose anticipatory control architecture equipped with a learning rule that exploits the full dynamics of the closed-loop system.