Sample-wise learning curves plot performance versus training set size. They are useful for studying scaling laws and speeding up hyperparameter tuning and model selection. Learning curves are often assumed to be well-behaved: monotone (i.e.

The hippocampus supports spatial navigation by encoding cognitive maps through collective place cell activity. We model the place cell population as non-negative spatial embeddings derived from the spectral decomposition of multi-step random walk transition kernels.

Conformal prediction has been explored as a general and efficient way to provide uncertainty quantification for time series. However, current methods struggle to handle time series data with change points -- sudden shifts in the underlying data-generating process. In this paper, we propose a novel Conformal Prediction for Time-series with Change points (CPTC) algorithm, addressing this gap by integrating a model to predict the underlying state with online conformal prediction to model uncertainties in non-stationary time series. We prove CPTC's validity and improved adaptivity in the time series setting under minimum assumptions, and demonstrate CPTC's practical effectiveness on 6 synthetic and real-world datasets, showing improved validity and adaptivity compared to state-of-the-art baselines.

Behavior cloning has shown promise for robot manipulation, but real-world demonstrations are costly to acquire at scale. While simulated data offers a scalable alternative, particularly with advances in automated demonstration generation, transferring policies to the real world is hampered by various simulation and real domain gaps. In this work, we propose a unified sim-and-real co-training framework for learning generalizable manipulation policies that primarily leverages simulation and only requires a few real-world demonstrations. Central to our approach is learning a domain-invariant, task-relevant feature space. Our key insight is that aligning the joint distributions of observations and their corresponding actions across domains provides a richer signal than aligning observations (marginals) alone. We achieve this by embedding an Optimal Transport (OT)-inspired loss within the co-training framework, and extend this to an Unbalanced OT framework to handle the imbalance between abundant simulation data and limited real-world examples. We validate our method on challenging manipulation tasks, showing it can leverage abundant simulation data to achieve up to a 30% improvement in the real-world success rate and even generalize to scenarios seen only in simulation.

A challenge in human-AI decision-making is to balance three factors: the correctness of predictions, the cost of knowledge and reasoning complexity, and the confidence about whether to abstain from automated answers or escalate to human experts. In this work, we present a cascaded LLM decision framework that adaptively delegates tasks across multiple tiers of expertise - a base model for initial candidate answers, a more capable and knowledgeable (but costlier) large model, and a human expert for when the model cascade abstains.

Generative modeling of non-negative, discrete data, such as symbolic music, remains challenging due to two persistent limitations in existing methods. First, most approaches rely on modeling continuous embeddings, which are not wellsuited for inherently discrete data distributions.

Protein structure prediction models are now capable of generating accurate 3D structural hypotheses from sequence alone. However, they routinely fail to capture the conformational diversity of dynamic biomolecular complexes, often requiring heuristic MSA subsampling approaches for generating alternative states. In parallel, cryo-electron microscopy (cryo-EM) has emerged as a powerful tool for imaging near-native structural heterogeneity, but is challenged by arduous pipelines to transform raw experimental data into atomic models. Here, we bridge the gap between these modalities, combining cryo-EM density maps with the rich sequence and biophysical priors learned by protein structure prediction models. Our method, CryoBoltz, guides the sampling trajectory of a pretrained biomolecular structure prediction model using both global and local structural constraints derived from density maps, driving predictions towards conformational states consistent with the experimental data. We demonstrate that this flexible yet powerful inferencetime approach allows us to build atomic models into heterogeneous cryo-EM maps across a variety of dynamic biomolecular systems including transporters and antibodies.

Large language models (LLMs) are now pivotal in real-world applications. Model editing has emerged as a promising paradigm for efficiently modifying LLMs without full retraining. However, current editing approaches face significant limitations due to parameter drift, which stems from inconsistencies between newly edited knowledge and the model's existing knowledge. In sequential editing scenarios, cumulative drifts progressively lead to model collapse characterized by general capability degradation and balance between acquiring new knowledge and catastrophic forgetting of existing knowledge. Drawing inspiration from the hippocampal trisynaptic circuit for continual memorizing and forgetting, we propose a Hippocampal-like Sequential Editing (HSE) framework that designs the unlearning of obsolete knowledge, domain-specific knowledge update separation and replay for edited knowledge. Specifically, the HSE framework designs three core mechanisms: (1) Machine unlearning selectively erases outdated knowledge to facilitate integration of new information, (2) Fisher information matrix-guided parameter updates prevents cross-domain knowledge interference, and (3) Parameter replay consolidates long-term editing memory through lightweight and global replay of editing data in a parametric form. Theoretical analysis demonstrates that HSE achieves smaller generalization error bounds, more stable convergence and higher computational efficiency.

This paper introduces the Quotient Bayesian Learning Rule, an extension of natural-gradient Bayesian updates to probability models that fall outside the exponential family. Building on the observation that many heavy-tailed and otherwise non-exponential distributions arise as marginals of minimal exponential families, we prove that such marginals inherit a unique Fisher-Rao information geometry via the quotient-manifold construction. Exploiting this geometry, we derive the Quotient Natural Gradient algorithm, which takes steepest-descent steps in the well-structured covering space, thereby guaranteeing parameterization-invariant optimization in the target space. Empirical results on the Student-t distribution confirm that our method converges more rapidly and attains higher-quality solutions than previous variants of the Bayesian Learning Rule.

Understanding causal relationships in multivariate time series is crucial in many scenarios, such as those dealing with financial or neurological data.