Global Geometry Is Not Enough for Vision Representations

A common assumption in representation learning is that globally well-distributed embeddings support robust and generalizable representations. This focus has shaped both training objectives and evaluation protocols, implicitly treating global geometry as a proxy for representational competence. While global geometry effectively encodes which elements are present, it is often insensitive to how they are composed. We investigate this limitation by testing the ability of geometric metrics to predict compositional binding across 21 vision encoders. We find that standard geometry-based statistics exhibit near-zero correlation with compositional binding. In contrast, functional sensitivity, as measured by the input-output Jacobian, reliably tracks this capability. We further provide an analytic account showing that this disparity arises from objective design, as existing losses explicitly constrain embedding geometry but leave the local input-output mapping unconstrained. These results suggest that global embedding geometry captures only a partial view of representational competence and establish functional sensitivity as a critical complementary axis for modeling composite structure.

What Makes a Good Example? Modeling Exemplar Selection with Neural Network Representations

Teaching requires distilling a rich category distribution into a small set of informative exemplars. Although prior work shows that humans consider both representativeness and diversity when teaching, the computational principles underlying these tradeoffs remain unclear. We address this gap by modeling human exemplar selection using neural network feature representations and principled subset selection criteria. Novel visual categories were embedded along a one-dimensional morph continuum using pretrained vision models, and selection strategies varied in their emphasis on prototypicality, joint representativeness, and diversity. Adult participants selected one to three exemplars to teach a learner. Model-human comparisons revealed that strategies based on joint representativeness, or its combination with diversity, best captured human judgments, whereas purely prototypical or diversity-based strategies performed worse. Moreover, transformer-based representations consistently aligned more closely with human behavior than convolutional networks. These results highlight the potential utility of dataset distillation methods in machine learning as computational models for teaching.

COMET: Codebook-based Online-adaptive Multi-scale Embedding for Time-series Anomaly Detection

Time series anomaly detection is a critical task across various industrial domains. However, capturing temporal dependencies and multivariate correlations within patch-level representation learning remains underexplored, and reliance on single-scale patterns limits the detection of anomalies across different temporal ranges. Furthermore, focusing on normal data representations makes models vulnerable to distribution shifts at inference time. To address these limitations, we propose Codebook-based Online-adaptive Multi-scale Embedding for Time-series anomaly detection (COMET), which consists of three key components: (1) Multi-scale Patch Encoding captures temporal dependencies and inter-variable correlations across multiple patch scales. (2) Vector-Quantized Coreset learns representative normal patterns via codebook and detects anomalies with a dual-score combining quantization error and memory distance. (3) Online Codebook Adaptation generates pseudo-labels based on codebook entries and dynamically adapts the model at inference through contrastive learning. Experiments on five benchmark datasets demonstrate that COMET achieves the best performance in 36 out of 45 evaluation metrics, validating its effectiveness across diverse environments.

FlyPrompt: Brain-Inspired Random-Expanded Routing with Temporal-Ensemble Experts for General Continual Learning

General continual learning (GCL) challenges intelligent systems to learn from single-pass, non-stationary data streams without clear task boundaries. While recent advances in continual parameter-efficient tuning (PET) of pretrained models show promise, they typically rely on multiple training epochs and explicit task cues, limiting their effectiveness in GCL scenarios. Moreover, existing methods often lack targeted design and fail to address two fundamental challenges in continual PET: how to allocate expert parameters to evolving data distributions, and how to improve their representational capacity under limited supervision. Inspired by the fruit fly's hierarchical memory system characterized by sparse expansion and modular ensembles, we propose FlyPrompt, a brain-inspired framework that decomposes GCL into two subproblems: expert routing and expert competence improvement. FlyPrompt introduces a randomly expanded analytic router for instance-level expert activation and a temporal ensemble of output heads to dynamically adapt decision boundaries over time. Extensive theoretical and empirical evaluations demonstrate FlyPrompt's superior performance, achieving up to 11.23%, 12.43%, and 7.62% gains over state-of-the-art baselines on CIFAR-100, ImageNet-R, and CUB-200, respectively. Our source code is available at https://github.com/AnAppleCore/FlyGCL.

A Minimal Task Reveals Emergent Path Integration and Object-Location Binding in a Predictive Sequence Model

Adaptive cognition requires structured internal models representing objects and their relations. Predictive neural networks are often proposed to form such "world models", yet their underlying mechanisms remain unclear. One hypothesis is that action-conditioned sequential prediction suffices for learning such world models. In this work, we investigate this possibility in a minimal in-silico setting. Sequentially sampling tokens from 2D continuous token scenes, a recurrent neural network is trained to predict the upcoming token from current input and a saccade-like displacement. On novel scenes, prediction accuracy improves across the sequence, indicating in-context learning. Decoding analyses reveal path integration and dynamic binding of token identity to position. Interventional analyses show that new bindings can be learned late in sequence and that out-of-distribution bindings can be learned. Together, these results demonstrate how structured representations that rely on flexible binding emerge to support prediction, offering a mechanistic account of sequential world modeling relevant to cognitive science.

Efficient Neural Controlled Differential Equations via Attentive Kernel Smoothing

Neural Controlled Differential Equations (Neural CDEs) provide a powerful continuous-time framework for sequence modeling, yet the roughness of the driving control path often restricts their efficiency. Standard splines introduce high-frequency variations that force adaptive solvers to take excessively small steps, driving up the Number of Function Evaluations (NFE). We propose a novel approach to Neural CDE path construction that replaces exact interpolation with Kernel and Gaussian Process (GP) smoothing, enabling explicit control over trajectory regularity. To recover details lost during smoothing, we propose an attention-based Multi-View CDE (MV-CDE) and its convolutional extension (MVC-CDE), which employ learnable queries to inform path reconstruction. This framework allows the model to distribute representational capacity across multiple trajectories, each capturing distinct temporal patterns. Empirical results demonstrate that our method, MVC-CDE with GP, achieves state-of-the-art accuracy while significantly reducing NFEs and total inference time compared to spline-based baselines.

HypCBC: Domain-Invariant Hyperbolic Cross-Branch Consistency for Generalizable Medical Image Analysis

Robust generalization beyond training distributions remains a critical challenge for deep neural networks. This is especially pronounced in medical image analysis, where data is often scarce and covariate shifts arise from different hardware devices, imaging protocols, and heterogeneous patient populations. These factors collectively hinder reliable performance and slow down clinical adoption. Despite recent progress, existing learning paradigms primarily rely on the Euclidean manifold, whose flat geometry fails to capture the complex, hierarchical structures present in clinical data. In this work, we exploit the advantages of hyperbolic manifolds to model complex data characteristics. We present the first comprehensive validation of hyperbolic representation learning for medical image analysis and demonstrate statistically significant gains across eleven in-distribution datasets and three ViT models. We further propose an unsupervised, domain-invariant hyperbolic cross-branch consistency constraint. Extensive experiments confirm that our proposed method promotes domain-invariant features and outperforms state-of-the-art Euclidean methods by an average of $+2.1\%$ AUC on three domain generalization benchmarks: Fitzpatrick17k, Camelyon17-WILDS, and a cross-dataset setup for retinal imaging. These datasets span different imaging modalities, data sizes, and label granularities, confirming generalization capabilities across substantially different conditions. The code is available at https://github.com/francescodisalvo05/hyperbolic-cross-branch-consistency .

Score-based diffusion models for diffuse optical tomography with uncertainty quantification

Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems with a state-of-the-art performance for severely ill-posed problems by leveraging a powerful prior distribution learned from empirical data. Despite generating significant interest especially in the machine-learning community, a thorough study of realistic inverse problems in the presence of modelling error and utilization of physical measurement data is still outstanding. In this work, the framework of unconditional representation for the conditional score function (UCoS) is evaluated for linearized difference imaging in diffuse optical tomography (DOT). DOT uses boundary measurements of near-infrared light to estimate the spatial distribution of absorption and scattering parameters in biological tissues. The problem is highly ill-posed and thus sensitive to noise and modelling errors. We introduce a novel regularization approach that prevents overfitting of the score function by constructing a mixed score composed of a learned and a model-based component. Validation of this approach is done using both simulated and experimental measurement data. The experiments demonstrate that a data-driven prior distribution results in posterior samples with low variance, compared to classical model-based estimation, and centred around the ground truth, even in the context of a highly ill-posed problem and in the presence of modelling errors.

SRA-Seg: Synthetic to Real Alignment for Semi-Supervised Medical Image Segmentation

Synthetic data, an appealing alternative to extensive expert-annotated data for medical image segmentation, consistently fails to improve segmentation performance despite its visual realism. The reason being that synthetic and real medical images exist in different semantic feature spaces, creating a domain gap that current semi-supervised learning methods cannot bridge. We propose SRA-Seg, a framework explicitly designed to align synthetic and real feature distributions for medical image segmentation. SRA-Seg introduces a similarity-alignment (SA) loss using frozen DINOv2 embeddings to pull synthetic representations toward their nearest real counterparts in semantic space. We employ soft edge blending to create smooth anatomical transitions and continuous labels, eliminating the hard boundaries from traditional copy-paste augmentation. The framework generates pseudo-labels for synthetic images via an EMA teacher model and applies soft-segmentation losses that respect uncertainty in mixed regions. Our experiments demonstrate strong results: using only 10% labeled real data and 90% synthetic unlabeled data, SRA-Seg achieves 89.34% Dice on ACDC and 84.42% on FIVES, significantly outperforming existing semi-supervised methods and matching the performance of methods using real unlabeled data.

The Shape of Beliefs: Geometry, Dynamics, and Interventions along Representation Manifolds of Language Models' Posteriors

Large language models (LLMs) represent prompt-conditioned beliefs (posteriors over answers and claims), but we lack a mechanistic account of how these beliefs are encoded in representation space, how they update with new evidence, and how interventions reshape them. We study a controlled setting in which Llama-3.2 generates samples from a normal distribution by implicitly inferring its parameters (mean and standard deviation) given only samples from the distribution in context. We find representations of curved "belief manifolds" for these parameters form with sufficient in-context learning and study how the model adapts when the distribution suddenly changes. While standard linear steering often pushes the model off-manifold and induces coupled, out-of-distribution shifts, geometry and field-aware steering better preserves the intended belief family. Our work demonstrates an example of linear field probing (LFP) as a simple approach to tile the data manifold and make interventions that respect the underlying geometry. We conclude that rich structure emerges naturally in LLMs and that purely linear concept representations are often an inadequate abstraction.