The information-theoretical inequality in Kaufmann et al. (2016) provides a systematic way to prove

Specifically, to reach a desirable solution on the target domain, we design a surrogate loss mimicking target classification.

The rationale generator and the predictor are trained jointly to optimize the prediction performance.

Bayesian optimization has become widely popular across various experimental sciences due to its favorable attributes: it can handle noisy data, perform well with relatively small datasets, and provide adaptive suggestions for sequential experimentation. While still in its infancy, Bayesian optimization has recently gained traction in bioprocess engineering. However, experimentation with biological systems is highly complex and the resulting experimental uncertainty requires specific extensions to classical Bayesian optimization. Moreover, current literature often targets readers with a strong statistical background, limiting its accessibility for practitioners. In light of these developments, this review has two aims: first, to provide an intuitive and practical introduction to Bayesian optimization; and second, to outline promising application areas and open algorithmic challenges, thereby highlighting opportunities for future research in machine learning.

We establish non-asymptotic bounds on the finite-sample behavior of generalized first-order iterative algorithms -- including gradient-based optimization methods and approximate message passing (AMP) -- with Gaussian data matrices and full-memory, non-separable nonlinearities. The central result constructs an explicit coupling between the iterates of a generalized first-order method and a conditionally Gaussian process whose covariance evolves deterministically via a finite-dimensional state evolution recursion. This coupling yields tight, dimension-free bounds under mild Lipschitz and moment-matching conditions. Our analysis departs from classical inductive AMP proofs by employing a direct comparison between the generalized first-order method and the conditionally Gaussian comparison process. This approach provides a unified derivation of AMP theory for Gaussian matrices without relying on separability or asymptotics. A complementary lower bound on the Wasserstein distance demonstrates the sharpness of our upper bounds.

Sharpness-Aware Minimization (SAM) has been proven to be an effective optimization technique for improving generalization in overparameterized models. While prior works have explored the implicit regularization of SAM in simple two-core scale-invariant settings, its behavior in more general tensorized or scale-invariant models remains underexplored. In this work, we leverage scale-invariance to analyze the norm dynamics of SAM in general tensorized models. We introduce the notion of \emph{Norm Deviation} as a global measure of core norm imbalance, and derive its evolution under SAM using gradient flow analysis. We show that SAM's implicit control of Norm Deviation is governed by the covariance between core norms and their gradient magnitudes. Motivated by these findings, we propose a simple yet effective method, \emph{Deviation-Aware Scaling (DAS)}, which explicitly mimics this regularization behavior by scaling core norms in a data-adaptive manner. Our experiments across tensor completion, noisy training, model compression, and parameter-efficient fine-tuning confirm that DAS achieves competitive or improved performance over SAM, while offering reduced computational overhead.

The increasing congestion of Low Earth Orbit (LEO) poses persistent challenges to the efficient deployment and safe operation of Earth observation satellites. Mission planners must now account not only for mission-specific requirements but also for the increasing collision risk with active satellites and space debris. This work presents a reinforcement learning framework using the Advantage Actor-Critic (A2C) algorithm to optimize satellite orbital parameters for precise terrestrial coverage within predefined surface radii. By formulating the problem as a Markov Decision Process (MDP) within a custom OpenAI Gymnasium environment, our method simulates orbital dynamics using classical Keplerian elements. The agent progressively learns to adjust five of the orbital parameters - semi-major axis, eccentricity, inclination, right ascension of ascending node, and the argument of perigee-to achieve targeted terrestrial coverage. Comparative evaluation against Proximal Policy Optimization (PPO) demonstrates A2C's superior performance, achieving 5.8x higher cumulative rewards (10.0 vs 9.263025) while converging in 31.5x fewer timesteps (2,000 vs 63,000). The A2C agent consistently meets mission objectives across diverse target coordinates while maintaining computational efficiency suitable for real-time mission planning applications. Key contributions include: (1) a TLE-based orbital simulation environment incorporating physics constraints, (2) validation of actor-critic methods' superiority over trust region approaches in continuous orbital control, and (3) demonstration of rapid convergence enabling adaptive satellite deployment. This approach establishes reinforcement learning as a computationally efficient alternative for scalable and intelligent LEO mission planning.

We present a native three-qubit entangling gate that exploits engineered interactions to realize control-control-target and control-target-target operations in a single coherent step. Unlike conventional decompositions into multiple two-qubit gates, our hybrid optimization approach selectively amplifies desired interactions while suppressing unwanted couplings, yielding robust performance across the computational subspace and beyond. The new gate can be classified as a cross-resonance gate. We show it can be utilized in several ways, for example, in GHZ triplet state preparation, Toffoli-class logic demonstrations with many-body interactions, and in implementing a controlled-ZZ gate. The latter maps the parity of two data qubits directly onto a measurement qubit, enabling faster and higher-fidelity stabilizer measurements in surface-code quantum error correction. In all these examples, we show that the three-qubit gate performance remains robust across Hilbert space sizes, as confirmed by testing under increasing total excitation numbers. This work lays the foundation for co-designing circuit architectures and control protocols that leverage native multiqubit interactions as core elements of next-generation superconducting quantum processors.