Daily Papers

Traveling wave solutions to Kawahara equation (KE), transmission line (TL), and Korteweg-de Vries (KdV) equation are found by using an elliptic function method which is more general than the tanh-method. The method works by assuming that a polynomial ansatz satisfies a Weierstrass equation, and has two advantages: first, it reduces the number of terms in the ansatz by an order of two, and second, it uses Weierstrass functions which satisfy an elliptic equation for the dependent variable instead of the hyperbolic tangent functions which only satisfy the Riccati equation with constant coefficients. When the polynomial ansatz in the traveling wave variable is of first order, the equation reduces to the KdV equation with only a cubic dispersion term, while for the KE which includes a fifth order dispersion term the polynomial ansatz must necessary be of quadratic type. By solving the elliptic equation with coefficients that depend on the boundary conditions, velocity of the traveling waves, nonlinear strength, and dispersion coefficients, in the case of KdV equation we find the well-known solitary waves (solitons) for zero boundary conditions, as well as wave-trains of cnoidal waves for nonzero boundary conditions. Both solutions are either compressive (bright) or rarefactive (dark), and either propagate to the left or right with arbitrary velocity.

Face parsing aims to predict pixel-wise labels for facial components of a target face in an image. Existing approaches usually crop the target face from the input image with respect to a bounding box calculated during pre-processing, and thus can only parse inner facial Regions of Interest~(RoIs). Peripheral regions like hair are ignored and nearby faces that are partially included in the bounding box can cause distractions. Moreover, these methods are only trained and evaluated on near-frontal portrait images and thus their performance for in-the-wild cases has been unexplored. To address these issues, this paper makes three contributions. First, we introduce iBugMask dataset for face parsing in the wild, which consists of 21,866 training images and 1,000 testing images. The training images are obtained by augmenting an existing dataset with large face poses. The testing images are manually annotated with 11 facial regions and there are large variations in sizes, poses, expressions and background. Second, we propose RoI Tanh-polar transform that warps the whole image to a Tanh-polar representation with a fixed ratio between the face area and the context, guided by the target bounding box. The new representation contains all information in the original image, and allows for rotation equivariance in the convolutional neural networks~(CNNs). Third, we propose a hybrid residual representation learning block, coined HybridBlock, that contains convolutional layers in both the Tanh-polar space and the Tanh-Cartesian space, allowing for receptive fields of different shapes in CNNs. Through extensive experiments, we show that the proposed method improves the state-of-the-art for face parsing in the wild and does not require facial landmarks for alignment.

Pre-Layer Normalization (Pre-LN) is the de facto choice for large language models (LLMs) and is crucial for stable pretraining and effective transfer learning. However, Pre-LN is inefficient due to repeated statistical calculations and suffers from the curse of depth. As layers grow, the magnitude and variance of the hidden state escalate, destabilizing training. Efficiency-oriented normalization-free methods such as Dynamic Tanh (DyT) improve speed but remain fragile at depth. To jointly address stability and efficiency, we propose Bounded Hyperbolic Tanh (BHyT), a drop-in replacement for Pre-LN. BHyT couples a tanh nonlinearity with explicit, data-driven input bounding to keep activations within a non-saturating range. It prevents depth-wise growth in activation magnitude and variance and comes with a theoretical stability guarantee. For efficiency, BHyT computes exact statistics once per block and replaces a second normalization with a lightweight variance approximation, enhancing efficiency. Empirically, BHyT demonstrates improved stability and efficiency during pretraining, achieving an average of 15.8% faster training and an average of 4.2% higher token generation throughput compared to RMSNorm., while matching or surpassing its inference performance and robustness across language understanding and reasoning benchmarks. Our code is available at: https://anonymous.4open.science/r/BHyT

Layer-sequential unit-variance (LSUV) initialization - a simple method for weight initialization for deep net learning - is proposed. The method consists of the two steps. First, pre-initialize weights of each convolution or inner-product layer with orthonormal matrices. Second, proceed from the first to the final layer, normalizing the variance of the output of each layer to be equal to one. Experiment with different activation functions (maxout, ReLU-family, tanh) show that the proposed initialization leads to learning of very deep nets that (i) produces networks with test accuracy better or equal to standard methods and (ii) is at least as fast as the complex schemes proposed specifically for very deep nets such as FitNets (Romero et al. (2015)) and Highway (Srivastava et al. (2015)). Performance is evaluated on GoogLeNet, CaffeNet, FitNets and Residual nets and the state-of-the-art, or very close to it, is achieved on the MNIST, CIFAR-10/100 and ImageNet datasets.

Recently, there have been numerous attempts to enhance the sample efficiency of off-policy reinforcement learning (RL) agents when interacting with the environment, including architecture improvements and new algorithms. Despite these advances, they overlook the potential of directly constraining the initial representations of the input data, which can intuitively alleviate the distribution shift issue and stabilize training. In this paper, we introduce the Tanh function into the initial layer to fulfill such a constraint. We theoretically unpack the convergence property of the temporal difference learning with the Tanh function under linear function approximation. Motivated by theoretical insights, we present our Constrained Initial Representations framework, tagged CIR, which is made up of three components: (i) the Tanh activation along with normalization methods to stabilize representations; (ii) the skip connection module to provide a linear pathway from the shallow layer to the deep layer; (iii) the convex Q-learning that allows a more flexible value estimate and mitigates potential conservatism. Empirical results show that CIR exhibits strong performance on numerous continuous control tasks, even being competitive or surpassing existing strong baseline methods.

Domain generalization is critical for real-world applications of machine learning to microscopy images, including histopathology and fluorescence imaging. Artifacts in these modalities arise through a complex combination of factors relating to tissue collection and laboratory processing, as well as factors intrinsic to patient samples. In fluorescence imaging, these artifacts stem from variations across experimental batches. The complexity and subtlety of these artifacts make the enumeration of data domains intractable. Therefore, augmentation-based methods of domain generalization that require domain identifiers and manual fine-tuning are inadequate in this setting. To overcome this challenge, we introduce ContriMix, a domain generalization technique that learns to generate synthetic images by disentangling and permuting the biological content ("content") and technical variations ("attributes") in microscopy images. ContriMix does not rely on domain identifiers or handcrafted augmentations and makes no assumptions about the input characteristics of images. We assess the performance of ContriMix on two pathology datasets dealing with patch classification and Whole Slide Image label prediction tasks respectively (Camelyon17-WILDS and RCC subtyping), and one fluorescence microscopy dataset (RxRx1-WILDS). Without any access to domain identifiers at train or test time, ContriMix performs similar or better than current state-of-the-art methods in all these datasets, motivating its usage for microscopy image analysis in real-world settings where domain information is hard to come by. The code for ContriMix can be found at https://gitlab.com/huutan86/contrimix