Dendritic updates Complete versions of the dendritic update rules (summarised in Eqns (2) & (3)) are given below. This is valid in our regime where the environmental latent updates slowly compared to neural timescales. The notation we're using admits the possible presence of biases as well as the weights (though biases typically aren't used) by assuming a row of constant 1's could be added to the synaptic inputs effectively absorbing a bias into the weight matrix without loss of generality, for example wgB p(t) wgB p(t)+ bgB . Somatic updates Somatic updates rules (Eqns (4) & (5)) and are repeated here for completeness: p(t)= (t)pB(t)+(1 (t))pA(t) g(t)= (t)gB(t)+(1 (t))gA(t). Update ordering For this hierarchical network of multicompartmental neurons we must specify the order in which we perform these discrete updates to the different layers and the different compartments within these layers.

Obtaining high-quality labels is costly, whereas unlabeled covariates are often abundant, motivating semi-supervised inference methods with reliable uncertainty quantification. Prediction-powered inference (PPI) leverages a machine-learning predictor trained on a small labeled sample to improve efficiency, but it can lose efficiency under model misspecification and suffer from coverage distortions due to label reuse. We introduce Machine-Learning-Assisted Generalized Entropy Calibration (MEC), a cross-fitted, calibration-weighted variant of PPI. MEC improves efficiency by reweighting labeled samples to better align with the target population, using a principled calibration framework based on Bregman projections. This yields robustness to affine transformations of the predictor and relaxes requirements for validity by replacing conditions on raw prediction error with weaker projection-error conditions. As a result, MEC attains the semiparametric efficiency bound under weaker assumptions than existing PPI variants. Across simulations and a real-data application, MEC achieves near-nominal coverage and tighter confidence intervals than CF-PPI and vanilla PPI.

Self-supervised learning (SSL) aims to learn rich and meaningful representations without relying onhumanannotations.

A mainstream type of current self-supervised learning methods pursues a general-purpose representation that can be well transferred to downstream tasks, typically by optimizing on a given pretext task such as instance discrimination. In this work, we argue that existing pretext tasks inevitably introduce biases into the learned representation, which in turn leads to biased transfer performance on various downstream tasks. To cope with this issue, we propose Maximum Entropy Coding (MEC), a more principled objective that explicitly optimizes on the structure of the representation, so that the learned representation is less biased and thus generalizes better to unseen downstream tasks. Inspired by the principle of maximum entropy in information theory, we hypothesize that a generalizable representation should be the one that admits the maximum entropy among all plausible representations. To make the objective end-to-end trainable, we propose to leverage the minimal coding length in lossy data coding as a computationally tractable surrogate for the entropy, and further derive a scalable reformulation of the objective that allows fast computation. Extensive experiments demonstrate that MEC learns a more generalizable representation than previous methods based on specific pretext tasks. It achieves state-of-the-art performance consistently on various downstream tasks, including not only ImageNet linear probe, but also semi-supervised classification, object detection, instance segmentation, and object tracking. Interestingly, we show that existing batch-wise and feature-wise self-supervised objectives could be seen equivalent to low-order approximations of MEC. Code and pre-trained models are available at https://github.com/xinliu20/MEC.

Reinforcement learning (RL) commonly relies on scalar rewards with limited ability to express temporal, conditional, or safety-critical goals, and can lead to reward hacking. Temporal logic expressible via the more general class of $ω$-regular objectives addresses this by precisely specifying rich behavioural properties. Even still, measuring performance by a single scalar (be it reward or satisfaction probability) masks safety-performance trade-offs that arise in settings with a tolerable level of risk. We address both limitations simultaneously by combining $ω$-regular objectives with explicit constraints, allowing safety requirements and optimisation targets to be treated separately. We develop a model-based RL algorithm based on linear programming, which in the limit produces a policy maximising the probability of satisfying an $ω$-regular objective while also adhering to $ω$-regular constraints within specified thresholds. Furthermore, we establish a translation to constrained limit-average problems with optimality-preserving guarantees.

Abstract--Immersive virtual reality (VR) applications impose stringent requirements on latency, energy efficiency, and computational resources, particularly in multi-user interactive scenarios. T o address these challenges, we introduce the concept of spatial computing communications (SCC), a framework designed to meet the latency and energy demands of multi-user VR over distributed mobile edge computing (MEC) networks. SCC jointly represents the physical space, defined by users and base stations, and the virtual space, representing shared immersive environments, using a probabilistic model of user dynamics and resource requirements. The resource deployment task is then formulated as a multi-objective combinatorial optimization (MOCO) problem that simultaneously minimizes system latency and energy consumption across distributed MEC resources. T o solve this problem, we propose MO-CMPO, a multi-objective consistency model with policy optimization that integrates supervised learning and reinforcement learning (RL) fine-tuning guided by preference weights. Leveraging a sparse graph neural network (GNN), MO-CMPO efficiently generates Pareto-optimal solutions. Simulations with real-world New Radio base station datasets demonstrate that MO-CMPO achieves superior hypervolume performance and significantly lower inference latency than baseline methods. Furthermore, the analysis reveals practical deployment patterns: latency-oriented solutions favor local MEC execution to reduce transmission delay, while energy-oriented solutions minimize redundant placements to save energy.

The rising aging population has increased the importance of fall detection (FD) systems as an assistive technology, where deep learning techniques are widely applied to enhance accuracy. FD systems typically use edge devices (EDs) worn by individuals to collect real-time data, which are transmitted to a cloud center (CC) or processed locally. However, this architecture faces challenges such as a limited ED model size and data transmission latency to the CC. Mobile edge computing (MEC), which allows computations at MEC servers deployed between EDs and CC, has been explored to address these challenges. We propose a multilayer MEC (MLMEC) framework to balance accuracy and latency. The MLMEC splits the architecture into stations, each with a neural network model. If front-end equipment cannot detect falls reliably, data are transmitted to a station with more robust back-end computing. The knowledge distillation (KD) approach was employed to improve front-end detection accuracy by allowing high-power back-end stations to provide additional learning experiences, enhancing precision while reducing latency and processing loads. Simulation results demonstrate that the KD approach improved accuracy by 11.65% on the SisFall dataset and 2.78% on the FallAllD dataset. The MLMEC with KD also reduced the data latency rate by 54.15% on the FallAllD dataset and 46.67% on the SisFall dataset compared to the MLMEC without KD. In summary, the MLMEC FD system exhibits improved accuracy and reduced latency.

We thank all reviewers for thoughtful feedback! We reply separately to each reviewer. Reviewer #1: We would like to point out some of the paper's main contributions, not fully recognized in the review. Another example is our algorithm for sampling DAGs conditionally on a root-partition (Sections 3.4 Accordingly, our main innovations are algorithmic. We would like to correct that our algorithm for sampling DAGs is not "classical" (cf.