Physical AI agents, such as robots and other embodied systems operating under tight and fluctuating resource constraints, remain far less capable than biological agents in open-ended real-world environments. This paper argues that Active Inference (AIF), grounded in the Free Energy Principle, offers a principled foundation for closing that gap. We develop this argument from first principles, following a chain from probability theory through Bayesian machine learning and variational inference to active inference and reactive message passing. From the FEP perspective, systems that maintain their structural and functional integrity over time can, under suitable assumptions, be described as minimizing variational free energy (VFE), and AIF operationalizes this by unifying perception, learning, planning, and control within a single computational objective. We show that VFE minimization is naturally realized by reactive message passing on factor graphs, where inference emerges from local, parallel computations. This realization is well matched to the constraints of physical operation, including hard deadlines, asynchronous data, fluctuating power budgets, and changing environments. Because reactive message passing is event-driven, interruptible, and locally adaptable, performance degrades gracefully under reduced resources while model structure can adjust online. We further show that, under suitable coupling and coarse-graining conditions, coupled AIF agents can be described as higher-level AIF agents, yielding a homogeneous architecture based on the same message-passing primitive across scales. Our contribution is not empirical benchmarking, but a clear theoretical and architectural case for the engineering community.

Exploring the dynamic co-evolution of multiplex graphs and nodal attributes is a compelling question in criminal and terrorism networks. This article is motivated by the study of dynamically evolving interactions among prominent terrorist organizations, considering various organizational attributes like size, ideology, leadership, and operational capacity. Statistically principled integration of multiplex graphs with nodal attributes is significantly challenging due to the need to leverage shared information within and across layers, account for uncertainty in predicting unobserved links, and capture temporal evolution of node attributes. These difficulties increase when layers are partially observed, as in terrorism networks where connections are deliberately hidden to obscure key relationships. To address these challenges, we present a principled methodological framework to integrate the multiplex graph layers and nodal attributes. The approach employs time-varying stochastic latent factor models, leveraging shared latent factors to capture graph structure and its co-evolution with node attributes. Latent factors are modeled using Gaussian processes with an infinitely wide deep neural network-based covariance function, termed neural network Gaussian processes (NN-GP). The NN-GP framework on latent factors exploits the predictive power of Bayesian deep neural network architecture while propagating uncertainty for reliability. Simulation studies highlight superior performance of the proposed approach in achieving inferential objectives. The approach, termed as dynamic joint learner, enables predictive inference (with uncertainty) of diverse unobserved dynamic relationships among prominent terrorist organizations and their organization-specific attributes, as well as clustering behavior in terms of friend-and-foe relationships, which could be informative in counter-terrorism research.

We study the role of batch size in stochastic conditional gradient methods under a $μ$-Kurdyka-Łojasiewicz ($μ$-KL) condition. Focusing on momentum-based stochastic conditional gradient algorithms (e.g., Scion), we derive a new analysis that explicitly captures the interaction between stepsize, batch size, and stochastic noise. Our study reveals a regime-dependent behavior: increasing the batch size initially improves optimization accuracy but, beyond a critical threshold, the benefits saturate and can eventually degrade performance under a fixed token budget. Notably, the theory predicts the magnitude of the optimal stepsize and aligns well with empirical practices observed in large-scale training. Leveraging these insights, we derive principled guidelines for selecting the batch size and stepsize, and propose an adaptive strategy that increases batch size and sequence length during training while preserving convergence guarantees. Experiments on NanoGPT are consistent with the theoretical predictions and illustrate the emergence of the predicted scaling regimes. Overall, our results provide a theoretical framework for understanding batch size scaling in stochastic conditional gradient methods and offer guidance for designing efficient training schedules in large-scale optimization.

The exponential mechanism is a general method to construct a randomized estimator that satisfies (ε,0)-differential privacy. Recently, Wang et al. showed that the Gibbs posterior, which is a data-dependent probability distribution that contains the Bayesian posterior, is essentially equivalent to the exponential mechanism under certain boundedness conditions on the loss function. While the exponential mechanism provides a way to build an (ε,0)-differential private algorithm, it requires boundedness of the loss function, which is quite stringent for some learning problems. In this paper, we focus on (ε,δ)-differential privacy of Gibbs posteriors with convex and Lipschitz loss functions. Our result extends the classical exponential mechanism, allowing the loss functions to have an unbounded sensitivity.

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

Recommendation and collaborative filtering systems are important in modern information and e-commerce applications. As these systems are becoming increasingly popular in the industry, their outputs could affect business decision making, introducing incentives for an adversarial party to compromise the availability or integrity of such systems. We introduce a data poisoning attack on collaborative filtering systems. We demonstrate how a powerful attacker with full knowledge of the learner can generate malicious data so as to maximize his/her malicious objectives, while at the same time mimicking normal user behavior to avoid being detected. While the complete knowledge assumption seems extreme, it enables a robust assessment of the vulnerability of collaborative filtering schemes to highly motivated attacks.

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

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

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

This paper describes InfoGAN, an information-theoretic extension to the Generative Adversarial Network that is able to learn disentangled representations in a completely unsupervised manner. InfoGAN is a generative adversarial network that also maximizes the mutual information between a small subset of the latent variables and the observation. We derive a lower bound of the mutual information objective that can be optimized efficiently. Specifically, InfoGAN successfully disentangles writing styles from digit shapes on the MNIST dataset, pose from lighting of 3D rendered images, and background digits from the central digit on the SVHN dataset. It also discovers visual concepts that include hair styles, presence/absence of eyeglasses, and emotions on the CelebA face dataset. Experiments show that InfoGAN learns interpretable representations that are competitive with representations learned by existing supervised methods. For an up-to-date version of this paper, please see https://arxiv.org/abs/1606.03657.