Finding correspondences between images is a fundamental problem in computer vision. In this paper, we show that correspondence emerges in image diffusion models without any explicit supervision. We propose a simple strategy to extract this implicit knowledge out of diffusion networks as image features, namely DIffusion FeaTures (DIFT), and use them to establish correspondences between real images. Without any additional fine-tuning or supervision on the task-specific data or annotations, DIFT is able to outperform both weakly-supervised methods and competitive off-the-shelf features in identifying semantic, geometric, and temporal correspondences. Particularly for semantic correspondence, DIFT from Stable Diffusion is able to outperform DINO and OpenCLIP by 19 and 14 accuracy points respectively on the challenging SPair-71k benchmark. It even outperforms the state-of-the-art supervised methods on 9 out of 18 categories while remaining on par for the overall performance.

What can be learned about causality and experimentation from passive data? This question is salient given recent successes of passively-trained language models in interactive domains such as tool use. Passive learning is inherently limited. However, we show that purely passive learning can in fact allow an agent to learn generalizable strategies for determining and using causal structures, as long as the agent can intervene at test time. We formally illustrate that, under certain assumptions, learning a strategy of first experimenting, then seeking goals, can allow generalization from passive learning in principle.

The blooming progress made in deep learning-based image restoration has been largely attributed to the availability of high-quality, large-scale datasets and advanced network structures. However, optimization functions such as L1 and L2 are still de facto. In this study, we propose to investigate new optimization functions to improve image restoration performance. Our key insight is that "random weight network can be acted as a constraint for training better image restoration networks". However, not all random weight networks are suitable as constraints.

Suppose we have a non-zero solution θ which is a stationary point of f(θ,t) at t-th step and SGD finds θt = θ at t-th step. Theorem 2.2 of Shapiro and Wardi [9] told us that the learning rate should be small enough for convergence. Obviously, we have η < in practice. As ηt = ηt+1 does not hold, SGD cannot converging to any non-zero stationary point. The proof is now complete.

Most recurrent neural networks (RNNs) do not include a fundamental constraint of real neural circuits: Dale's Law, which implies that neurons must be excitatory (E) or inhibitory (I). Dale's Law is generally absent from RNNs because simply partitioning a standard network's units into E and I populations impairs learning. However, here we extend a recent feedforward bio-inspired EI network architecture, named Dale's ANNs, to recurrent networks, and demonstrate that good performance is possible while respecting Dale's Law. This begs the question: What makes some forms of EI network learn poorly and others learn well? And, why does the simple approach of incorporating Dale's Law impair learning? Historically the answer was thought to be the sign constraints on EI network parameters, and this was a motivation behind Dale's ANNs. However, here we show the spectral properties of the recurrent weight matrix at initialisation are more impactful on network performance than sign constraints. We find that simple EI partitioning results in a singular value distribution that is multimodal and dispersed, whereas standard RNNs have an unimodal, more clustered singular value distribution, as do recurrent Dale's ANNs. We also show that the spectral properties and performance of partitioned EI networks are worse for small networks with fewer I units, and we present normalised SVD entropy as a measure of spectrum pathology that correlates with performance.