Sparse Autoencoders (SAEs) have emerged as a powerful framework for machine learning interpretability, enabling the unsupervised decomposition of model representations into a dictionary of abstract, human-interpretable concepts. However, we reveal a fundamental limitation: SAEs exhibit severe instability, as identical models trained on similar datasets can produce sharply different dictionaries, undermining their reliability as an interpretability tool. To address this issue, we draw inspiration from the Archetypal Analysis framework introduced by Cutler & Breiman (1994) and present Archetypal SAEs (A-SAE), wherein dictionary atoms are constrained to the data’s convex hull. This geometric anchoring significantly enhances the stability and plausibility of inferred dictionaries, and their mildly relaxed variants RA-SAEs further match state-of-the-art reconstruction abilities. To rigorously assess dictionary quality learned by SAEs, we introduce two new benchmarks that test (i) plausibility, if dictionaries recover “true” classification directions and (ii) identifiability, if dictionaries disentangle synthetic concept mixtures. Across all evaluations, RA-SAEs consistently yield more structured representations while uncovering novel, semantically meaningful concepts in large-scale vision models.

We develop an analytical framework for understanding how the learned distribution evolves during diffusion model training. Leveraging the Gaussian equivalence principle, we derived exact solutions for the gradient-flow dynamics of weights in one or two layer linear or linear convolutional denoiser settings with arbitrary data, where linear networks converge along principal components, and convolutional networks converge along Fourier modes. Remarkably, these solutions allow us to derive the generated distribution in closed-form and its KL-divergence through training. These analytical results expose a pronounced \emph{spectral bias}, i.e. for both weights and generated distributions, the convergence time of a mode follows an inverse power law of its variance. Empirical experiments on both Gaussian and natural image datasets demonstrate that the power-law spectral bias—remain robust even when using deeper or convolutional architectures. Our results underscore the importance of the data covariance in dictating the order and rate at which diffusion models learn different modes of the data, providing potential explanations of why earlier stopping could lead to incorrect details in image generative model.

Recently, optimization has become an emerging tool for neuroscientists to study neural code. In the visual system, neurons respond to images with graded and noisy responses. Image patterns eliciting highest responses are diagnostic of the coding content of the neuron. To find these patterns, we have used black-box optimizers to search a 4096d image space, leading to the evolution of images that maximize neuronal responses. Although genetic algorithm (GA) has been commonly used, there haven't been any systematic investigations to reveal the best performing optimizer or the underlying principles necessary to improve them.

Weakly Supervised Object Localization (WSOL) has increasingly attracted interests for only using image-level supervision instead of location annotations. Some common challenges for existing methods are that they cover only the most discriminative part of the object. And a substantial amount of noise in training causes ambiguities for learning in a robust manner. In this paper, we propose to address these drawbacks by Self-Paced Pyramid Adversarial Learning(SPAL). Specifically, for suppressing noise, we use self-paced learning (SPL) to training data from simple to complex and from coarse to fine. And our network divides two subnetworks: 1) coarse pyramid network(CPN), 2) fine pyramid network (FPN). In CPN, we aim to utilize pyramid adversarial erase mechanism to process the feature maps of different scale. Consequently, CPN can cover the entire object to generate initial object proposals. Then CPN builds the relevance score as pseudo labels of proposals. In FPN, object proposals and pseudo labels can be trained to locate precise object boundaries. Finally, We also propose adversarial loss function to fit our network. Detailed experimental results on the PASCAL VOC dataset demonstrate that SPAL performs promising against the state-of-the-art methods.

Cortical oscillations are central to information transfer in neural systems. Significant evidence supports the idea that coincident spike input can allow the neural threshold to be overcome and spikes to be propagated downstream in a circuit. Thus, an observation of oscillations in neural circuits would be an indication that repeated synchronous spiking may be enabling information transfer. However, for memory transfer, in which synaptic weights must be being transferred from one neural circuit (region) to another, what is the mechanism? Here, we present a synaptic transfer mechanism whose structure provides some understanding of the phenomena that have been implicated in memory transfer, including nested oscillations at various frequencies. The circuit is based on the principle of pulse-gated, graded information transfer between neural populations.