Cyber-physical systems (CPS) require the joint optimization of discrete cyber actions and continuous physical parameters under stringent safety logic constraints. However, existing hierarchical approaches often compromise global optimality, whereas reinforcement learning (RL) in hybrid action spaces often relies on brittle reward penalties, masking, or shielding and struggles to guarantee constraint satisfaction. We present logic-informed reinforcement learning (LIRL), which equips standard policy-gradient algorithms with projection that maps a low-dimensional latent action onto the admissible hybrid manifold defined on-the-fly by first-order logic. This guarantees feasibility of every exploratory step without penalty tuning. Experimental evaluations have been conducted across multiple scenarios, including industrial manufacturing, electric vehicle charging stations, and traffic signal control, in all of which the proposed method outperforms existing hierarchical optimization approaches. Taking a robotic reducer assembly system in industrial manufacturing as an example, LIRL achieves a 36.47\% to 44.33\% reduction at most in the combined makespan-energy objective compared to conventional industrial hierarchical scheduling methods. Meanwhile, it consistently maintains zero constraint violations and significantly surpasses state-of-the-art hybrid-action reinforcement learning baselines. Thanks to its declarative logic-based constraint formulation, the framework can be seamlessly transferred to other domains such as smart transportation and smart grid, thereby paving the way for safe and real-time optimization in large-scale CPS.

Current advances in AI and its applicability have highlighted the need to ensure its trustworthiness for legal, ethical, and even commercial reasons. Sub-symbolic machine learning algorithms, such as the LLMs, simulate reasoning but hallucinate and their decisions cannot be explained or audited (crucial aspects for trustworthiness). On the other hand, rule-based reasoners, such as Cyc, are able to provide the chain of reasoning steps but are complex and use a large number of reasoners. We propose a middle ground using s(CASP), a goal-directed constraint-based answer set programming reasoner that employs a small number of mechanisms to emulate reliable and explainable human-style commonsense reasoning. In this paper, we explain how s(CASP) supports the 16 desiderata for trustworthy AI introduced by Doug Lenat and Gary Marcus (2023), and two additional ones: inconsistency detection and the assumption of alternative worlds. To illustrate the feasibility and synergies of s(CASP), we present a range of diverse applications, including a conversational chatbot and a virtually embodied reasoner.

Neurosymbolic (NeSy) predictors combine neural perception with symbolic reasoning to solve tasks like visual reasoning. However, standard NeSy predictors assume conditional independence between the symbols they extract, thus limiting their ability to model interactions and uncertainty - often leading to overconfident predictions and poor out-of-distribution generalisation. To overcome the limitations of the independence assumption, we introduce neurosymbolic diffusion models (NeSyDMs), a new class of NeSy predictors that use discrete diffusion to model dependencies between symbols. Our approach reuses the independence assumption from NeSy predictors at each step of the diffusion process, enabling scalable learning while capturing symbol dependencies and uncertainty quantification. Across both synthetic and real-world benchmarks - including high-dimensional visual path planning and rule-based autonomous driving - NeSyDMs achieve state-of-the-art accuracy among NeSy predictors and demonstrate strong calibration.

We revisit the task of computing the span of the top $r$ singular vectors $u_1, \ldots, u_r$ of a matrix under differential privacy. We show that a simple and efficient algorithm -- based on singular value decomposition and standard perturbation mechanisms -- returns a private rank-$r$ approximation whose error depends only on the \emph{rank-$r$ coherence} of $u_1, \ldots, u_r$ and the spectral gap $σ_r - σ_{r+1}$. This resolves a question posed by Hardt and Roth~\cite{hardt2013beyond}. Our estimator outperforms the state of the art -- significantly so in some regimes. In particular, we show that in the dense setting, it achieves the same guarantees for single-spike PCA in the Wishart model as those attained by optimal non-private algorithms, whereas prior private algorithms failed to do so. In addition, we prove that (rank-$r$) coherence does not increase under Gaussian perturbations. This implies that any estimator based on the Gaussian mechanism -- including ours -- preserves the coherence of the input. We conjecture that similar behavior holds for other structured models, including planted problems in graphs. We also explore applications of coherence to graph problems. In particular, we present a differentially private algorithm for Max-Cut and other constraint satisfaction problems under low coherence assumptions.

Existing frameworks converge on the centrality of compression to intelligence but leave underspecified why this process enforces the discovery of causal structure rather than superficial statistical patterns. We introduce a two-level framework to address this gap. The Information-Theoretic Imperative (ITI) establishes that any system persisting in uncertain environments must minimize epistemic entropy through predictive compression: this is the evolutionary "why" linking survival pressure to information-processing demands. The Compression Efficiency Principle (CEP) specifies how efficient compression mechanically selects for generative, causal models through exception-accumulation dynamics, making reality alignment a consequence rather than a contingent achievement. Together, ITI and CEP define a causal chain: from survival pressure to prediction necessity, compression requirement, efficiency optimization, generative structure discovery, and ultimately reality alignment. Each link follows from physical, information-theoretic, or evolutionary constraints, implying that intelligence is the mechanically necessary outcome of persistence in structured environments. This framework yields empirically testable predictions: compression efficiency, measured as approach to the rate-distortion frontier, correlates with out-of-distribution generalization; exception-accumulation rates differentiate causal from correlational models; hierarchical systems exhibit increasing efficiency across abstraction layers; and biological systems demonstrate metabolic costs that track representational complexity. ITI and CEP thereby provide a unified account of convergence across biological, artificial, and multi-scale systems, addressing the epistemic and functional dimensions of intelligence without invoking assumptions about consciousness or subjective experience.

The Steiner Traveling Salesman Problem (STSP) is a variant of the classical Traveling Salesman Problem. The STSP involves incorporating steiner nodes, which are extra nodes not originally part of the required visit set but that can be added to the route to enhance the overall solution and minimize the total travel cost. Given the NP-hard nature of the STSP, we propose a quantum approach to address it. Specifically, we employ quantum annealing using D-Wave's hardware to explore its potential for solving this problem. To enhance computational feasibility, we develop a preprocessing method that effectively reduces the network size. Our experimental results demonstrate that this reduction technique significantly decreases the problem complexity, making the Quadratic Unconstrained Binary Optimization formulation, the standard input for quantum annealers, better suited for existing quantum hardware. Furthermore, the results highlight the potential of quantum annealing as a promising and innovative approach for solving the STSP.

Ensemble methods for stream mining necessitate managing multiple models and updating them as data distributions evolve. Considering the calls for more sustainability, established methods are however not sufficiently considerate of ensemble members' computational expenses and instead overly focus on predictive capabilities. To address these challenges and enable green online learning, we propose heterogeneous online ensembles (HEROS). For every training step, HEROS chooses a subset of models from a pool of models initialized with diverse hyperparameter choices under resource constraints to train. We introduce a Markov decision process to theoretically capture the trade-offs between predictive performance and sustainability constraints. Based on this framework, we present different policies for choosing which models to train on incoming data. Most notably, we propose the novel $ζ$-policy, which focuses on training near-optimal models at reduced costs. Using a stochastic model, we theoretically prove that our $ζ$-policy achieves near optimal performance while using fewer resources compared to the best performing policy. In our experiments across 11 benchmark datasets, we find empiric evidence that our $ζ$-policy is a strong contribution to the state-of-the-art, demonstrating highly accurate performance, in some cases even outperforming competitors, and simultaneously being much more resource-friendly.

In this paper we present a variational algorithm for the Traveling Salesman Problem (TSP) that combines (i) a compact encoding of permutations, which reduces the qubit requirement too, (ii) an optimize-freeze-reuse strategy: where the circuit topology (``Ansatz'') is first optimized on a training instance by Simulated Annealing (SA), then ``frozen'' and re-used on novel instances, limited to a rapid re-optimization of only the circuit parameters. This pipeline eliminates costly structural research in testing, making the procedure immediately implementable on NISQ hardware. On a set of $40$ randomly generated symmetric instances that span $4 - 7$ cities, the resulting Ansatz achieves an average optimal trip sampling probability of $100\%$ for 4 city cases, $90\%$ for 5 city cases and $80\%$ for 6 city cases. With 7 cities the success rate drops markedly to an average of $\sim 20\%$, revealing the onset of scalability limitations of the proposed method. The results show robust generalization ability for moderate problem sizes and indicate how freezing the Ansatz can dramatically reduce time-to-solution without degrading solution quality. The paper also discusses scalability limitations, the impact of ``warm-start'' initialization of parameters, and prospects for extension to more complex problems, such as Vehicle Routing and Job-Shop Scheduling.

Contemporary machine learning optimizes for predictive accuracy, yet systems that achieve state of the art performance remain causally opaque: their internal representations provide no principled handle for intervention. We can retrain such models, but we cannot surgically edit specific mechanisms while holding others fixed, because learned latent variables lack causal semantics. We argue for a conceptual reorientation: intelligence is the ability to build and refine explanations, falsifiable claims about manipulable structure that specify what changes and what remains invariant under intervention. Explanations subsume prediction but demand more: causal commitments that can be independently tested and corrected at the level of mechanisms. We introduce computational explanations, mappings from observations to intervention ready causal accounts. We instantiate these explanations with Energy Structured Causal Models (ESCMs), in which mechanisms are expressed as constraints (energy functions or vector fields) rather than explicit input output maps, and interventions act by local surgery on those constraints. This shift makes internal structure manipulable at the level where explanations live: which relations must hold, which can change, and what follows when they do. We provide concrete instantiations of the structural-causal principles LAP and ICM in the ESCM context, and also argue that empirical risk minimization systematically produces fractured, entangled representations, a failure we analyze as gauge ambiguity in encoder energy pairs. Finally, we show that under mild conditions, ESCMs recover standard SCM semantics. Building on Part I's principles (LAP, ICM, CAP) and its definition of intelligence as explanation-building under criticism, this paper offers a formal language for causal reasoning in systems that aspire to understand, not merely to predict.

We propose an anytime online algorithm for the problem of learning a sequence of adversarial convex cost functions while approximately satisfying another sequence of adversarial online convex constraints. A sequential algorithm is called \emph{anytime} if it provides a non-trivial performance guarantee for any intermediate timestep $t$ without requiring prior knowledge of the length of the entire time horizon $T$. Our proposed algorithm achieves optimal performance bounds without resorting to the standard doubling trick, which has poor practical performance due to multiple restarts. Our core technical contribution is the use of time-varying Lyapunov functions to keep track of constraint violations. This must be contrasted with prior works that used a fixed Lyapunov function tuned to the known horizon length $T$. The use of time-varying Lyapunov function poses unique analytical challenges as properties, such as \emph{monotonicity}, on which the prior proofs rest, no longer hold. By introducing a new analytical technique, we show that our algorithm achieves $O(\sqrt{t})$ regret and $\tilde{O}(\sqrt{t})$ cumulative constraint violation bounds for any $t\geq 1$. We extend our results to the dynamic regret setting, achieving bounds that adapt to the path length of the comparator sequence without prior knowledge of its total length. We also present an adaptive algorithm in the optimistic setting, whose performance gracefully scales with the cumulative prediction error. We demonstrate the practical utility of our algorithm through numerical experiments involving the online shortest path problem.