Controlling the parameters' norm often yields good generalisation when training neural networks. Beyond simple intuitions, the relation between regularising parameters' norm and obtained estimators remains theoretically misunderstood. For one hidden ReLU layer networks with unidimensional data, this work shows the parameters' norm required to represent a function is given by the total variation of its second derivative, weighted by a $\sqrt{1+x^2}$ factor. Notably, this weighting factor disappears when the norm of bias terms is not regularised. The presence of this additional weighting factor is of utmost significance as it is shown to enforce the uniqueness and sparsity (in the number of kinks) of the minimal norm interpolator. Conversely, omitting the bias' norm allows for non-sparse solutions.Penalising the bias terms in the regularisation, either explicitly or implicitly, thus leads to sparse estimators.

Over the past few years, numerous computational models have been developed to solve Optimal Transport (OT) in a stochastic setting, where distributions are represented by samples and where the goal is to find the closest map to the ground truth OT map, unknown in practical settings. So far, no quantitative criterion has yet been put forward to tune the parameter of these models and select maps that best approximate the ground truth. To perform this task, we propose to leverage the Brenier formulation of OT. Theoretically, we show that this formulation guarantees that, up to sharp a distortion parameter depending on the smoothness/strong convexity and a statistical deviation term, the selected map achieves the lowest quadratic error to the ground truth. This criterion, estimated via convex optimization, enables parameter tuning and model selection among entropic regularization of OT, input convex neural networks and smooth and strongly convex nearest-Brenier (SSNB) models.We also use this criterion to question the use of OT in Domain-Adaptation (DA). In a standard DA experiment, it enables us to identify the potential that is closest to the true OT map between the source and the target. Yet, we observe that this selected potential is far from being the one that performs best for the downstream transfer classification task.

Parameter-efficient fine-tuning (PEFT) of pre-trained language models (PLMs) has emerged as a highly successful approach, with training only a small number of parameters without sacrificing performance and becoming the de-facto learning paradigm with the increasing size of PLMs. However, existing PEFT methods are not memory-efficient, because they still require caching most of the intermediate activations for the gradient calculation, akin to fine-tuning. One effective way to reduce the activation memory is to apply a reversible model, so the intermediate activations are not necessary to be cached and can be recomputed. Nevertheless, modifying a PLM to its reversible variant is not straightforward, since the reversible model has a distinct architecture from the currently released PLMs. In this paper, we first investigate what is a key factor for the success of existing PEFT methods, and realize that it's essential to preserve the PLM's starting point when initializing a PEFT method.

Efficient on-device learning requires a small memory footprint at training time to fit the tight memory constraint. Existing work solves this problem by reducing the number of trainable parameters. However, this doesn't directly translate to memory saving since the major bottleneck is the activations, not parameters.

Remote sensing imagery from systems such as Sentinel provides full coverage of the Earth's surface at around 10-meter resolution. The remote sensing community has transitioned to extensive use of deep learning models due to their high performance on benchmarks such as the UCMerced and ISPRS Vaihingen datasets. Convolutional models such as UNet and ResNet variations are commonly employed for remote sensing but typically only accept three channels, as they were developed for RGB imagery, while satellite systems provide more than ten. Recently, several transformer architectures have been proposed for remote sensing, but they have not been extensively benchmarked and are typically used on small datasets such as Salinas Valley. Meanwhile, it is becoming feasible to obtain dense spatial land-use labels for entire first-level administrative divisions of some countries. Scaling law observations suggest that substantially larger multi-spectral transformer models could provide a significant leap in remote sensing performance in these settings. In this work, we propose ChromaFormer, a family of multi-spectral transformer models, which we evaluate across orders of magnitude differences in model parameters to assess their performance and scaling effectiveness on a densely labeled imagery dataset of Flanders, Belgium, covering more than 13,500 km^2 and containing 15 classes. We propose a novel multi-spectral attention strategy and demonstrate its effectiveness through ablations. Furthermore, we show that models many orders of magnitude larger than conventional architectures, such as UNet, lead to substantial accuracy improvements: a UNet++ model with 23M parameters achieves less than 65% accuracy, while a multi-spectral transformer with 655M parameters achieves over 95% accuracy on the Biological Valuation Map of Flanders.

The single contribution of the paper which is relevant in practice is an alternative derivation of an existing method (Expectation Maximization for learning SPN weights). While this is an interesting result, I think that it does not grant alone a publication in NIPS since it's hard to imagine how this can contribute to better theoretical understanding or practical applications of SPNs. The interpretation of SPNs as mixtures of tree structured SPNs, which is reported as a novelty by the authors, was actually first derived in [Dennis and Vantura, Greedy Structure Search for Sum-Product Networks, 2015]. The paper is overall well written, clearly structured and the derivation of the results is really interesting. My main concern, as detailed above, is that in my opinion the potential impact of this paper is low, and the novelty is also somewhat limited due to the fact that the interpretation of SPN as mixture of trees was already given in [Dennis and Vantura, Greedy Structure Search for Sum-Product Networks, 2015] and that this is basically just an alternative derivation of EM.

Controlling the parameters' norm often yields good generalisation when training neural networks. Beyond simple intuitions, the relation between regularising parameters' norm and obtained estimators remains theoretically misunderstood. For one hidden ReLU layer networks with unidimensional data, this work shows the parameters' norm required to represent a function is given by the total variation of its second derivative, weighted by a \sqrt{1 x 2} factor. Notably, this weighting factor disappears when the norm of bias terms is not regularised. The presence of this additional weighting factor is of utmost significance as it is shown to enforce the uniqueness and sparsity (in the number of kinks) of the minimal norm interpolator.

If so, I am confused why this is highlighted as a virtue of adding noise, since the purely deterministic dynamics of GD also evince this behavior. Numerical experiments: These are slightly hard to interpret. First, which plots show SGD dynamics, and which are for GD? Second, I'm puzzled by how to interpret the dotted lines in each plot. In the case of RBF, how are we to make sense of the empirical n {-2} decay? Is this somehow predicted in the analysis of the GD, or is it an empirical phenomenon which is not theoretically addressed in this work.

If you missed the previous part of this blog "In to Decision Trees Part: 1", please visit it. In this blog, we will explore more about Decision Trees Algorithm and its capability. The Process of Decision trees on Numerical (Discrete/Continuous) features is slightly different than categorical features. While the Decision trees can handle categorical variables with ease. There are two types of categorical values.

Transformers are used for translation and text summarising tasks because they can analyze sequential input data, such as natural language. Transformers use the self-attention process and weights the importance of each component of the input data differently. Large-scale transformer-based language models have gained a lot of popularity recently in the disciplines of computer vision and natural language processing (NLP). They expand in size and complexity frequently, yet it costs millions of dollars, hires the greatest experts, and takes years to construct these models. Because of this, many companies have been unable to use it, and only significant IT organizations have access to this cutting-edge technology.