Recent work established that the infinite-width and infinite-depth limits of residual networks commute at initialization when residual branches are scaled by $1/\sqrt{depth}$. In particular, the network output converges to the same limit whether width and depth tend to infinity sequentially or jointly. We extend this commutativity result to training in linear residual networks. Under the same $1/\sqrt{depth}$ residual-branch scaling (Depth-$\mu$P) and the $\mu$P width parameterization, we prove that, for any fixed number of gradient-descent steps with gradient clipping, the network output converges in $L^2$ along every joint width--depth growth path as both width and depth tend to infinity. Consequently, the infinite-width and infinite-depth limits commute throughout any finite training horizon. Without gradient clipping, the corresponding $L^2$ convergence does not hold in general, but we establish the weaker convergence in probability.
This paper investigates developing real-world perception for active agents, proposes Gibson Environment for this purpose, and showcases a set of perceptual tasks learned therein.
F. Xia, Amir Zamir, Zhi-Yang He et al.· 2018 IEEE/CVF Conference on...· 1,069 citations· ⚡112
This publication proposes a definition and a classification of agile software development approaches and analyses ten software development methods that can be characterized as being "agile" against the defined criterion.
P. Abrahamsson, O. Salo, Jussi Ronkainen et al.· arXiv.org· 727 citations· ⚡54
The study shows that agile practices improve both informal and formal communication, but indicates that, in larger development situations involving multiple external stakeholders, a mismatch of adequate communication mechanisms can sometimes even hinder the communication.
M. Pikkarainen, Jukka Haikara, O. Salo et al.· Empirical Software Engineeri...· 401 citations· ⚡48
The results indicate that software engineering work practices are chosen opportunistically, adapted and configured to provide value under the constrains imposed by the startup context.
Nicolò Paternoster, Carmine Giardino, M. Unterkalmsteiner et al.· Information and Software Tec...· 394 citations· ⚡54
The possibility of inferring high-dimensional data inference in a model that consists of a prior and an auxiliary differentiable constraint given some additional information is considered, thereby allowing a range of potential applications in adapting models to new domains and tasks.
Alexandros Graikos, Esmeralda S. Whitammer, N. Jojic et al.· Neural Information Processin...· 316 citations· ⚡15
Learn how Google DeepMind and GovTech Singapore uses lightweight on-device Gemma models to intercept conversational scams in private chats with zero cloud data egress.
