Kernel ridge regression (KRR) has recently attracted renewed interest due to its potential for explaining the transient effects, such as double descent, that emerge during neural network training. In this work, we study how the alignment between the target function and the kernel affects the performance of the KRR. We focus on the truncated KRR (TKRR) which utilizes an additional parameter that controls the spectral truncation of the kernel matrix. We show that for polynomial alignment, there is an over-aligned regime, in which TKRR can achieve a faster rate than what is achievable by full KRR. The rate of TKRR can improve all the way to the parametric rate, while that of full KRR is capped at a sub-optimal value. This shows that target alignemnt can be better leveraged by utilizing spectral truncation in kernel methods. We also consider the bandlimited alignment setting and show that the regularization surface of TKRR can exhibit transient effects including multiple descent and non-monotonic behavior. Our results show that there is a strong and quantifable relation between the shape of the alignment spectrum and the generalization performance of kernel methods, both in terms of rates and in finite samples.

Offline reinforcement learning (RL) has achieved significant advances in domains such as robotic control, autonomous driving, and medical decision-making. Most existing methods primarily focus on training policies that maximize cumulative returns from a given dataset. However, many real-world applications require precise control over policy performance levels, rather than simply pursuing the best possible return. Reinforcement learning via supervised learning (RvS) frames offline RL as a sequence modeling task, enabling the extraction of diverse policies by conditioning on different desired returns. Yet, existing RvS-based transformers, such as Decision Transformer (DT), struggle to reliably align the actual achieved returns with specified target returns, especially when interpolating within underrepresented returns or extrapolating beyond the dataset. To address this limitation, we propose Doctor, a novel approach that Double Checks the Transformer with target alignment for Offline RL. Doctor integrates the strengths of supervised learning (SL) and temporal difference (TD) learning by jointly optimizing the action prediction and value estimation. During inference, Doctor introduces a double-check mechanism: actions are first sampled around the desired target returns and then validated with value functions. This ensures more accurate alignment between predicted actions and desired target returns. We evaluate Doctor on the D4RL and EpiCare benchmarks, demonstrating aligned control yields stronger performance and tunable expertise, showing its effectiveness in a wide range of tasks.

Kernel ridge regression (KRR) has recently attracted renewed interest due to its potential for explaining the transient effects, such as double descent, that emerge during neural network training. In this work, we study how the alignment between the target function and the kernel affects the performance of the KRR. We focus on the truncated KRR (TKRR) which utilizes an additional parameter that controls the spectral truncation of the kernel matrix. We show that for polynomial alignment, there is an over-aligned regime, in which TKRR can achieve a faster rate than what is achievable by full KRR. The rate of TKRR can improve all the way to the parametric rate, while that of full KRR is capped at a sub-optimal value.

Designing a useful feature map for a quantum kernel is a critical task when attempting to achieve an advantage over classical machine learning models. The choice of circuit architecture, i.e. how feature-dependent gates should be interwoven with other gates is a relatively unexplored problem and becomes very important when using a model of quantum kernels called Quantum Embedding Kernels (QEK). We study and categorize various architectural patterns in QEKs and show that existing architectural styles do not behave as the literature supposes. We also produce a novel alternative architecture based on the old ones and show that it performs equally well while containing fewer gates than its older counterparts.

Kernel ridge regression (KRR) has recently attracted renewed interest due to its potential for explaining the transient effects, such as double descent, that emerge during neural network training. In this work, we study how the alignment between the target function and the kernel affects the performance of the KRR. We focus on the truncated KRR (TKRR) which utilizes an additional parameter that controls the spectral truncation of the kernel matrix. We show that for polynomial alignment, there is an \emph{over-aligned} regime, in which TKRR can achieve a faster rate than what is achievable by full KRR. The rate of TKRR can improve all the way to the parametric rate, while that of full KRR is capped at a sub-optimal value. This shows that target alignemnt can be better leveraged by utilizing spectral truncation in kernel methods. We also consider the bandlimited alignment setting and show that the regularization surface of TKRR can exhibit transient effects including multiple descent and non-monotonic behavior. Our results show that there is a strong and quantifable relation between the shape of the \emph{alignment spectrum} and the generalization performance of kernel methods, both in terms of rates and in finite samples.

With the advent of kernel methods, automating the task of specifying a suitable kernel has become increasingly important. In this context, the Multiple Kernel Learning (MKL) problem of finding a combination of pre-specified base kernels that is suitable for the task at hand has received significant attention from researchers. In this paper we show that Multiple Kernel Learning can be framed as a standard binary classification problem with additional constraints that ensure the positive definiteness of the learned kernel. Framing MKL in this way has the distinct advantage that it makes it easy to leverage the extensive research in binary classification to develop better performing and more scalable MKL algorithms that are conceptually simpler, and, arguably, more accessible to practitioners. Experiments on nine data sets from different domains show that, despite its simplicity, the proposed technique compares favorably with current leading MKL approaches.