Towards Disentangled Preference Optimization Dynamics Beyond Likelihood Displacement

Preference optimization is widely used to align large language models (LLMs) with human preferences. However, many margin-based objectives suppress the chosen response along with the rejected one, a phenomenon known as likelihood displacement, and no general mechanism currently prevents this across objectives. We bridge this gap by presenting a unified \emph{incentive-score decomposition} of preference optimization, revealing that diverse objectives share identical local update directions and differ only in their scalar weighting coefficients. Building on this decomposition, by analyzing the dynamics of the chosen/rejected likelihoods, we identify the \emph{disentanglement band} (DB), a simple, testable condition that characterizes when training can avoid likelihood displacement by realizing the preferred pathway: suppressing the loser while maintaining the winner, possibly after an initial transient. Leveraging the DB, we propose a plug-and-play \emph{reward calibration} (RC) that adaptively rebalances chosen versus rejected updates to satisfy the DB and mitigate likelihood displacement, without redesigning the base objective. Empirical results show that RC steers training toward more disentangled dynamics and often improves downstream performance across a range of objectives. Our code is available at https://github.com/IceyWuu/DisentangledPreferenceOptimization.

EEG-Based Multimodal Learning via Hyperbolic Mixture-of-Curvature Experts

Electroencephalography (EEG)-based multimodal learning integrates brain signals with complementary modalities to improve mental state assessment, providing great clinical potential. The effectiveness of such paradigms largely depends on the representation learning on heterogeneous modalities. For EEG-based paradigms, one promising approach is to leverage their hierarchical structures, as recent studies have shown that both EEG and associated modalities (e.g., facial expressions) exhibit hierarchical structures reflecting complex cognitive processes. However, Euclidean embeddings struggle to represent these hierarchical structures due to their flat geometry, while hyperbolic spaces, with their exponential growth property, are naturally suited for them. In this work, we propose EEG-MoCE, a novel hyperbolic mixture-of-curvature experts framework designed for multimodal neurotechnology. EEG-MoCE assigns each modality to an expert in a learnable-curvature hyperbolic space, enabling adaptive modeling of its intrinsic geometry. A curvature-aware fusion strategy then dynamically weights experts, emphasizing modalities with richer hierarchical information. Extensive experiments on benchmark datasets demonstrate that EEG-MoCE achieves state-of-the-art performance, including emotion recognition, sleep staging, and cognitive assessment.

One-Step Score-Based Density Ratio Estimation

Density ratio estimation (DRE) is a useful tool for quantifying discrepancies between probability distributions, but existing approaches often involve a trade-off between estimation quality and computational efficiency. Classical direct DRE methods are usually efficient at inference time, yet their performance can seriously deteriorate when the discrepancy between distributions is large. In contrast, score-based DRE methods often yield more accurate estimates in such settings, but they typically require considerable repeated function evaluations and numerical integration. We propose One-step Score-based Density Ratio Estimation (OS-DRE), a partly analytic and solver-free framework designed to combine these complementary advantages. OS-DRE decomposes the time score into spatial and temporal components, representing the latter with an analytic radial basis function (RBF) frame. This formulation converts the otherwise intractable temporal integral into a closed-form weighted sum, thereby removing the need for numerical solvers and enabling DRE with only one function evaluation. We further analyze approximation conditions for the analytic frame, and establish approximation error bounds for both finitely and infinitely smooth temporal kernels, grounding the framework in existing approximation theory. Experiments across density estimation, continual Kullback-Leibler and mutual information estimation, and near out-of-distribution detection demonstrate that OS-DRE offers a favorable balance between estimation quality and inference efficiency.

Nonconvex Latent Optimally Partitioned Block-Sparse Recovery via Log-Sum and Minimax Concave Penalties

We propose two nonconvex regularization methods, LogLOP-l2/l1 and AdaLOP-l2/l1, for recovering block-sparse signals with unknown block partitions. These methods address the underestimation bias of existing convex approaches by extending log-sum penalty and the Minimax Concave Penalty (MCP) to the block-sparse domain via novel variational formulations. Unlike Generalized Moreau Enhancement (GME) and Bayesian methods dependent on the squared-error data fidelity term, our proposed methods are compatible with a broad range of data fidelity terms. We develop efficient Alternating Direction Method of Multipliers (ADMM)-based algorithms for these formulations that exhibit stable empirical convergence. Numerical experiments on synthetic data, angular power spectrum estimation, and denoising of nanopore currents demonstrate that our methods outperform state-of-the-art baselines in estimation accuracy.

Structured Unitary Tensor Network Representations for Circuit-Efficient Quantum Data Encoding

Encoding classical data into quantum states is a central bottleneck in quantum machine learning: many widely used encodings are circuit-inefficient, requiring deep circuits and substantial quantum resources, which limits scalability on quantum hardware. In this work, we propose TNQE, a circuit-efficient quantum data encoding framework built on structured unitary tensor network (TN) representations. TNQE first represents each classical input via a TN decomposition and then compiles the resulting tensor cores into an encoding circuit through two complementary core-to-circuit strategies. To make this compilation trainable while respecting the unitary nature of quantum operations, we introduce a unitary-aware constraint that parameterizes TN cores as learnable block unitaries, enabling them to be directly optimized and directly encoded as quantum operators. The proposed TNQE framework enables explicit control over circuit depth and qubit resources, allowing the construction of shallow, resource-efficient circuits. Across a range of benchmarks, TNQE achieves encoding circuits as shallow as $0.04\times$ the depth of amplitude encoding, while naturally scaling to high-resolution images ($256 \times 256$) and demonstrating practical feasibility on real quantum hardware.

HEEGNet: Hyperbolic Embeddings for EEG

Electroencephalography (EEG)-based brain-computer interfaces facilitate direct communication with a computer, enabling promising applications in human-computer interactions. However, their utility is currently limited because EEG decoding often suffers from poor generalization due to distribution shifts across domains (e.g., subjects). Learning robust representations that capture underlying task-relevant information would mitigate these shifts and improve generalization. One promising approach is to exploit the underlying hierarchical structure in EEG, as recent studies suggest that hierarchical cognitive processes, such as visual processing, can be encoded in EEG. While many decoding methods still rely on Euclidean embeddings, recent work has begun exploring hyperbolic geometry for EEG. Hyperbolic spaces, regarded as the continuous analogue of tree structures, provide a natural geometry for representing hierarchical data. In this study, we first empirically demonstrate that EEG data exhibit hyperbolicity and show that hyperbolic embeddings improve generalization. Motivated by these findings, we propose HEEGNet, a hybrid hyperbolic network architecture to capture the hierarchical structure in EEG and learn domain-invariant hyperbolic embeddings. To this end, HEEGNet combines both Euclidean and hyperbolic encoders and employs a novel coarse-to-fine domain adaptation strategy. Extensive experiments on multiple public EEG datasets, covering visual evoked potentials, emotion recognition, and intracranial EEG, demonstrate that HEEGNet achieves state-of-the-art performance.

Calibrating Uncertainty for Zero-Shot Adversarial CLIP

CLIP delivers strong zero-shot classification but remains highly vulnerable to adversarial attacks. Previous work of adversarial fine-tuning largely focuses on matching the predicted logits between clean and adversarial examples, which overlooks uncertainty calibration and may degrade the zero-shot generalization. A common expectation in reliable uncertainty estimation is that predictive uncertainty should increase as inputs become more difficult or shift away from the training distribution. However, we frequently observe the opposite in the adversarial setting: perturbations not only degrade accuracy but also suppress uncertainty, leading to severe miscalibration and unreliable over-confidence. This overlooked phenomenon highlights a critical reliability gap beyond robustness. To bridge this gap, we propose a novel adversarial fine-tuning objective for CLIP considering both prediction accuracy and uncertainty alignments. By reparameterizing the output of CLIP as the concentration parameter of a Dirichlet distribution, we propose a unified representation that captures relative semantic structure and the magnitude of predictive confidence. Our objective aligns these distributions holistically under perturbations, moving beyond single-logit anchoring and restoring calibrated uncertainty. Experiments on multiple zero-shot classification benchmarks demonstrate that our approach effectively restores calibrated uncertainty and achieves competitive adversarial robustness while maintaining clean accuracy.

Any-Step Density Ratio Estimation via Interval-Annealed Secant Alignment

Estimating density ratios is a fundamental problem in machine learning, but existing methods often trade off accuracy for efficiency. We propose \textit{Interval-annealed Secant Alignment Density Ratio Estimation (ISA-DRE)}, a framework that enables accurate, any-step estimation without numerical integration. Instead of modeling infinitesimal tangents as in prior methods, ISA-DRE learns a global secant function, defined as the expectation of all tangents over an interval, with provably lower variance, making it more suitable for neural approximation. This is made possible by the \emph{Secant Alignment Identity}, a self-consistency condition that formally connects the secant with its underlying tangent representations. To mitigate instability during early training, we introduce \emph{Contraction Interval Annealing}, a curriculum strategy that gradually expands the alignment interval during training. This process induces a contraction mapping, which improves convergence and training stability. Empirically, ISA-DRE achieves competitive accuracy with significantly fewer function evaluations compared to prior methods, resulting in much faster inference and making it well suited for real-time and interactive applications.

Neural Bridge Processes

Learning stochastic functions from partially observed context-target pairs is a fundamental problem in probabilistic modeling. Traditional models like Gaussian Processes (GPs) face scalability issues with large datasets and assume Gaussianity, limiting their applicability. While Neural Processes (NPs) offer more flexibility, they struggle with capturing complex, multi-modal target distributions. Neural Diffusion Processes (NDPs) enhance expressivity through a learned diffusion process but rely solely on conditional signals in the denoising network, resulting in weak input coupling from an unconditional forward process and semantic mismatch at the diffusion endpoint. In this work, we propose Neural Bridge Processes (NBPs), a novel method for modeling stochastic functions where inputs x act as dynamic anchors for the entire diffusion trajectory. By reformulating the forward kernel to explicitly depend on x, NBP enforces a constrained path that strictly terminates at the supervised target. This approach not only provides stronger gradient signals but also guarantees endpoint coherence. We validate NBPs on synthetic data, EEG signal regression and image regression tasks, achieving substantial improvements over baselines. These results underscore the effectiveness of DDPM-style bridge sampling in enhancing both performance and theoretical consistency for structured prediction tasks.

QuProFS: An Evolutionary Training-free Approach to Efficient Quantum Feature Map Search

The quest for effective quantum feature maps for data encoding presents significant challenges, particularly due to the flat training landscapes and lengthy training processes associated with parameterised quantum circuits. To address these issues, we propose an evolutionary training-free quantum architecture search (QAS) framework that employs circuit-based heuristics focused on trainability, hardware robustness, generalisation ability, expressivity, complexity, and kernel-target alignment. By ranking circuit architectures with various proxies, we reduce evaluation costs and incorporate hardware-aware circuits to enhance robustness against noise. We evaluate our approach on classification tasks (using quantum support vector machine) across diverse datasets using both artificial and quantum-generated datasets. Our approach demonstrates competitive accuracy on both simulators and real quantum hardware, surpassing state-of-the-art QAS methods in terms of sampling efficiency and achieving up to a 2x speedup in architecture search runtime.