We study PAC-Bayes derandomization for smooth loss functions. Our goal is to obtain generalization bounds that hold with high probability for deterministic predictors by exploiting smoothness properties of both the loss and the predictor class. We show that passing from the Gibbs predictor to the deterministic predictor at the posterior mean has a precise cost, given by the generalization gap of the Jensen gap class. We control this class through its Rademacher complexity, leading to bounds for deterministic predictors that involve flatness quantities expressed in terms of parameter Jacobians and Hessians of the score map. The framework applies to both bounded and unbounded smooth loss functions, and we specialize the results to linear predictors and smooth neural networks. Finally, the Jacobian and Hessian quantities appearing in the theory motivate a practical regularizer. For BatchNorm networks, we compute this regularizer with respect to effective BatchNorm weights obtained by folding the BatchNorm transformation into the adjacent affine weights. Experiments on CIFAR-10 illustrate the behavior of this regularizer under different batch sizes.

Understanding how performance scales jointly with model size and data is a central problem in modern machine learning. Existing theoretical works on scaling laws typically describe generalization as a function of data or compute, often in fixed-feature or infinite-width regimes and for online SGD. Here, we instead study how generalization scales with the number of trainable parameters and the number of samples in a feature-learning model. We analyze $\ell_2$-regularized empirical test error minimization in a quadratic two-layer network in a finite-sample setting with structured data. This setting allows for an explicit characterization of the generalization error as a function of the number of samples, model width, and regularization. Our results reveal a phase diagram with distinct scaling regimes as the number of parameters varies. In particular, the generalization error follows data-dependent power laws controlled by the spectral structure of the target. We further characterize the transitions between regimes, including the onset of interpolation, and their impact on generalization.

Venezuela earthquake rescuers discover collapsed buildings were'held up by STYROFOAM' as catastrophic death toll reaches 1,430 Remains of at least 117 dogs found at California'no-kill' shelter as investigators uncover suspected burial site and 600 collars Two young sisters smile for the camera as they're arrested for stabbing mom-of-five to death in broad daylight Sun-kissed enclave named Florida's newest boomtown as telltale restaurant chain opens more stores in area Horrifying truth about'squishy dumplings': Fears as putrid fumes'sicken' mom and toys explode in children's hands... experts sound alarm on possible cancer links in new analysis Delaware senator rushed to hospital after getting into car crash while sitting in passenger's seat World's first'pregnant man' Thomas Beatie reveals astonishing full story for the first time as his daughter turns 18... and confronts a hard truth about trans teens Taylor Swift gets BOOED at Alan Jackson's final concert... as Travis Kelce ...

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A PhD student spotted the wolves going after the so-called'king of the forest' on a trail camera. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy . While reviewing footage for her PhD research, Polish Academy of Sciences ecologist Robin Wijnands spotted something pretty wild .

More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Open offices are loud and not great for productivity. Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy . I think a lot about productivity.

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Biological circuits have evolved to incorporate multiple modules that perform similar functions. In the fly olfactory circuit, both lateral inhibition (LI) and neuronal spike frequency adaptation (SFA) are thought to enhance pattern separation for odor learning. However, it remains unclear whether these mechanisms play redundant or distinct roles in this process. In this study, we present a computational model of the fly olfactory circuit to investigate odor discrimination under varying noise conditions that simulate complex environments. Our results show that LI primarily enhances odor discrimination in low and medium noise scenarios, but this benefit diminishes and may reverse under higher noise conditions. In contrast, SFA consistently improves discrimination across all noise levels. LI is preferentially engaged in low and medium noise environments, whereas SFA dominates in high noise settings. When combined, these two sparsification mechanisms enable optimal discrimination performance. This work demonstrates that seemingly redundant modules in biological circuits can, in fact, be essential for achieving optimal learning in complex contexts.

More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Just 10 weeks after conception, most fetuses move their right arm more than their left. Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy . Are you right-handed or left-handed? The answer for most of us is right. That's because nearly 90 percent of all people are right-dominant.