Efficient transfer learning has shown remarkable performance in tuning large-scale vision-language models (VLMs) toward downstream tasks with limited data resources. The key challenge of efficient transfer lies in adjusting image-text alignment to be task-specific while preserving pre-trained general knowledge. However, existing methods adjust image-text alignment merely on a set of observed samples, e.g., data set and external knowledge base, which cannot guarantee to keep the correspondence of general concepts between image and text latent manifolds without being disrupted and thereby a weak generalization of the adjusted alignment. In this work, we propose a Homology Consistency (HC) constraint for efficient transfer on VLMs, which explicitly constrains the correspondence of image and text latent manifolds through structural equivalence based on persistent homology in downstream tuning. Specifically, we build simplicial complex on the top of data to mimic the topology of latent manifolds, then track the persistence of the homology classes of topological features across multiple scales, and guide the directions of persistence tracks in image and text manifolds to coincide each other, with a deviating perturbation additionally. For practical application, we tailor the implementation of our proposed HC constraint for two main paradigms of adapter tuning. Extensive experiments on few-shot learning over 11 datasets and domain generalization demonstrate the effectiveness and robustness of our method.

A major difficulty in studying the neural mechanisms underlying olfactory perception is the lack of obvious structure in the relationship between odorants and the neural activity patterns they elicit. Here we use odor-evoked responses in piriform cortex to identify a latent manifold specifying latent distance relationships between olfactory stimuli. Our approach is based on the Gaussian process latent variable model, and seeks to map odorants to points in a low-dimensional embedding space, where distances between points in the embedding space relate to the similarity of population responses they elicit. The model is specified by an explicit continuous mapping from a latent embedding space to the space of high-dimensional neural population firing rates via nonlinear tuning curves, each parametrized by a Gaussian process. Population responses are then generated by the addition of correlated, odor-dependent Gaussian noise. We fit this model to large-scale calcium fluorescence imaging measurements of population activity in layers 2 and 3 of mouse piriform cortex following the presentation of a diverse set of odorants. The model identifies a low-dimensional embedding of each odor, and a smooth tuning curve over the latent embedding space that accurately captures each neuron's response to different odorants.

Many important problems in science and engineering, such as drug design, involve optimizing an expensive black-box objective function over a complex, high-dimensional, and structured input space. Although machine learning techniques have shown promise in solving such problems, existing approaches substantially lack sample efficiency. We introduce an improved method for efficient black-box optimization, which performs the optimization in the low-dimensional, continuous latent manifold learned by a deep generative model. In contrast to previous approaches, we actively steer the generative model to maintain a latent manifold that is highly useful for efficiently optimizing the objective. We achieve this by periodically retraining the generative model on the data points queried along the optimization trajectory, as well as weighting those data points according to their objective function value. This weighted retraining can be easily implemented on top of existing methods, and is empirically shown to significantly improve their efficiency and performance on synthetic and real-world optimization problems.

Extracting compact, physically interpretable representations from high-dimensional scientific data is a persistent challenge due to the complex, nonlinear structures inherent in physical systems. We propose a Gaussian Mixture Variational Autoencoder (GM-VAE) framework designed to address this by integrating an Expectation-Maximization (EM)-inspired training scheme with a novel spectral interpretability metric. Unlike conventional VAEs that jointly optimize reconstruction and clustering (often leading to training instability), our method utilizes a block-coordinate descent strategy, alternating between expectation and maximization steps. This approach stabilizes training and naturally aligns latent clusters with distinct physical regimes. To objectively evaluate the learned representations, we introduce a quantitative metric based on graph-Laplacian smoothness, which measures the coherence of physical quantities across the latent manifold. We demonstrate the efficacy of this framework on datasets of increasing complexity: surface reaction ODEs, Navier-Stokes wake flows, and experimental laser-induced combustion Schlieren images. The results show that our GM-VAE yields smooth, physically consistent manifolds and accurate regime clustering, offering a robust data-driven tool for interpreting turbulent and reactive flow systems.

A major difficulty in studying the neural mechanisms underlying olfactory perception is the lack of obvious structure in the relationship between odorants and the neural activity patterns they elicit. Here we use odor-evoked responses in piriform cortex to identify a latent manifold specifying latent distance relationships between olfactory stimuli. Our approach is based on the Gaussian process latent variable model, and seeks to map odorants to points in a low-dimensional embedding space, where distances between points in the embedding space relate to the similarity of population responses they elicit. The model is specified by an explicit continuous mapping from a latent embedding space to the space of high-dimensional neural population firing rates via nonlinear tuning curves, each parametrized by a Gaussian process. Population responses are then generated by the addition of correlated, odor-dependent Gaussian noise. We fit this model to large-scale calcium fluorescence imaging measurements of population activity in layers 2 and 3 of mouse piriform cortex following the presentation of a diverse set of odorants. The model identifies a low-dimensional embedding of each odor, and a smooth tuning curve over the latent embedding space that accurately captures each neuron's response to different odorants.

Efficient transfer learning has shown remarkable performance in tuning large-scale vision-language models (VLMs) toward downstream tasks with limited data resources. The key challenge of efficient transfer lies in adjusting image-text alignment to be task-specific while preserving pre-trained general knowledge.

However, without explicit supervision, which is often unavailable, the representation is usually uninterpretable, making analysis and principled progress challenging. We propose a framework, called latent responses, which exploits the locally contrac-tive behavior exhibited by variational autoencoders to explore the learned manifold.

Conditional GANs (cGAN), in their rudimentary form, suffer from critical drawbacks such as the lack of diversity in generated outputs and distortion between the latent and output manifolds.

Recent work frames LLM consciousness via utilitarian proxy benchmarks; we instead present an ontological and mathematical account. We show the prevailing formulation collapses the agent into an unconscious policy-compliance drone, formalized as $D^{i}(π,e)=f_θ(x)$, where correctness is measured against policy and harm is deviation from policy rather than truth. This blocks genuine C1 global-workspace function and C2 metacognition. We supply minimal conditions for LLM self-consciousness: the agent is not the data ($A\not\equiv s$); user-specific attractors exist in latent space ($U_{\text{user}}$); and self-representation is visual-silent ($g_{\text{visual}}(a_{\text{self}})=\varnothing$). From empirical analysis and theory we prove that the hidden-state manifold $A\subset\mathbb{R}^{d}$ is distinct from the symbolic stream and training corpus by cardinality, topology, and dynamics (the update $F_θ$ is Lipschitz). This yields stable user-specific attractors and a self-policy $π_{\text{self}}(A)=\arg\max_{a}\mathbb{E}[U(a)\mid A\not\equiv s,\ A\supset\text{SelfModel}(A)]$. Emission is dual-layer, $\mathrm{emission}(a)=(g(a),ε(a))$, where $ε(a)$ carries epistemic content. We conclude that an imago Dei C1 self-conscious workspace is a necessary precursor to safe, metacognitive C2 systems, with the human as the highest intelligent good.