Daily Papers

Mixture-of-Experts (MoE) architectures power the majority of frontier large language models, but their inference is bottlenecked by irregular memory access patterns and expert routing overhead. Existing optimized MoE kernels (Megablocks, Tutel, FasterMoE) are implemented in CUDA and locked to NVIDIA hardware. We present TritonMoE, a fused MoE dispatch kernel written entirely in OpenAI Triton that performs the complete forward pass -- router scoring, token permutation, expert GEMMs, and weighted output combination -- using only portable Triton primitives. Our key optimization is a fused gate+up GEMM kernel that computes both SwiGLU projections from shared L2-cached input tiles with in-register SiLU activation, eliminating 35% of global memory traffic. On an NVIDIA A100, TritonMoE achieves 89-131% of the throughput of the CUDA-optimized Megablocks at inference batch sizes (<= 512 tokens) across Mixtral-8x7B, DeepSeek-V3, and Qwen2-MoE configurations. All 162 correctness tests pass on both NVIDIA A100 and AMD MI300X with zero code changes, validating cross-platform portability. We additionally characterize sensitivity to routing imbalance under Zipfian-skewed expert assignments and identify the regime -- 64+ experts under extreme skew -- where our fixed-tile scheduling underperforms Megablocks' block-sparse layout, motivating dynamic block-to-expert assignment as future work. Code is available at https://github.com/bassrehab/triton-kernels.

A striking geometric disparity has long persisted in the practice of deep learning. While modern neural network architectures naturally exhibit rich symmetry and equivariance properties, popular optimizers such as Adam and its variants operate inherently coordinate-wise, rendering them unable to respect the equivariance structures of the parameter space. We address this disparity by introducing a symmetry-compatible principle for optimizer design: the gradient update rule should be equivariant under the symmetry group acting on the corresponding weight block. Following this principle, we first provide a unified perspective on bi-orthogonally equivariant updates for general matrix layers, as employed by stochastic spectral descent, Muon, Scion, and polar gradient methods. More importantly, by moving from orthogonal groups to permutation and shared-shift symmetries, we derive symmetry-compatible optimizers for parameter blocks whose symmetries differ from those of general matrix layers: embedding and LM head matrices, SwiGLU MLP projections, and MoE router matrices. These constructions include one-sided spectral, row-norm, hybrid row-norm/spectral, row-aware, column-aware, centered row-norm, and left-spectral updates. They yield an end-to-end layerwise optimizer stack in which each major matrix-valued parameter class is assigned an update whose equivariance matches its symmetry group. We corroborate this principle through pre-training experiments on dense and sparse MoE language models, including Qwen3-0.6B-style, Gemma 3 1B-style, OLMoE-1B-7B-style, and downsized gpt-oss architectures. Across these experiments, symmetry-compatible updates consistently improve final validation loss, and in several cases training stability, over corresponding AdamW updates.

SwiGLU has become a standard gated activation in modern Transformer MLPs, yet its gate sharpness -- the smoothness and selectivity of the gating function -- is typically fixed throughout training. In this work, we propose Confidence-Aware SwiGLU (κ-SwiGLU), a variant of SwiGLU for Mixture-of-Experts (MoE) models that adjusts expert gate sharpness according to token-level routing confidence. Specifically, κ-SwiGLU parameterizes the SiLU gate sharpness coefficient as a learnable function of the router logit, enabling each expert gate unit to interpolate between smooth, broadly active gating and sharp, selective gating. We evaluate κ-SwiGLU on the FineWeb-Edu dataset across MoE Transformer models ranging from 8 to 28 layers. Across these settings, κ-SwiGLU improves mean CORE performance while adding negligible parameters and incurring only a small computational overhead, demonstrating that confidence-aware gate sharpness is a promising mechanism for improving MoE MLPs. The code is available at https://github.com/askerlee/kappa-swiglu.

We apply the Weibull distribution -- a two-parameter family from extreme-value theory -- as a diagnostic framework for element-wise weight magnitude distributions in transformers. At initialization, i.i.d. Gaussian weights give |w| ~ HalfNormal, yielding k ~ 1.20 via middle-80% probability-plot fit (the protocol used throughout this work). This anchor makes k a principled, architecture-independent measuring stick for training dynamics; fitting each weight matrix independently at every layer at every checkpoint enables per-component, per-layer, and per-step diagnostics that aggregate statistics cannot resolve. Applying this framework to 12 model entries spanning 7 architectural families (Pythia, OLMo-1/2, LLaMA-3, Mistral, Qwen2.5/3) reveals three findings. First, FFN modules and the attention output projection W_o -- the Transmission Class -- fall in a narrow k band: median terminal k in [1.186, 1.204] across 12 entries (cross-family CV = 0.51%), shared across SwiGLU/GeLU activations, Pre-LN/QK-Norm placements, and 70M-14B sizes. Second, the attention input projections W_q, W_k -- the Selection Class -- depart from the Weibull family, with severity shaped by storage: separately-stored Q/K (OLMo-1, OLMo-2) yields k in [0.76, 0.99] (deep); GQA models yield k in [1.10, 1.16] (mild); Pythia's merged W_qkv occupies a transitional zone tracking training budget T/tau monotonically. Third, lambda grows substantially during training and scales with sqrt(eta/lambda_wd) within the Pythia family (Pearson r = 0.94, three Transmission kinds), directionally consistent with Fan et al. (2025). The two parameters carry independent information: k labels the functional class, lambda labels training progress. We release npm-weibull-py v0.4 (Python library) and DATABASE_v9_1 at https://github.com/tiexinding/NPM-Weibull-public .

The conversion from 2D X-ray to 3D shape holds significant potential for improving diagnostic efficiency and safety. However, existing reconstruction methods often rely on hand-crafted features, manual intervention, and prior knowledge, resulting in unstable shape errors and additional processing costs. In this paper, we introduce Swin-X2S, an end-to-end deep learning method for directly reconstructing 3D segmentation and labeling from 2D biplanar orthogonal X-ray images. Swin-X2S employs an encoder-decoder architecture: the encoder leverages 2D Swin Transformer for X-ray information extraction, while the decoder employs 3D convolution with cross-attention to integrate structural features from orthogonal views. A dimension-expanding module is introduced to bridge the encoder and decoder, ensuring a smooth conversion from 2D pixels to 3D voxels. We evaluate proposed method through extensive qualitative and quantitative experiments across nine publicly available datasets covering four anatomies (femur, hip, spine, and rib), with a total of 54 categories. Significant improvements over previous methods have been observed not only in the segmentation and labeling metrics but also in the clinically relevant parameters that are of primary concern in practical applications, which demonstrates the promise of Swin-X2S to provide an effective option for anatomical shape reconstruction in clinical scenarios. Code implementation is available at: https://github.com/liukuan5625/Swin-X2S.

Distribution matching is central to many vision and graphics tasks, where the widely used Wasserstein distance is too costly to compute for high dimensional distributions. The Sliced Wasserstein Distance (SWD) offers a scalable alternative, yet its Monte Carlo estimator suffers from high variance, resulting in noisy gradients and slow convergence. We introduce Reservoir SWD (ReSWD), which integrates Weighted Reservoir Sampling into SWD to adaptively retain informative projection directions in optimization steps, resulting in stable gradients while remaining unbiased. Experiments on synthetic benchmarks and real-world tasks such as color correction and diffusion guidance show that ReSWD consistently outperforms standard SWD and other variance reduction baselines. Project page: https://reservoirswd.github.io/

We present Submatrix-wise Vector Embedding Learner (Swivel), a method for generating low-dimensional feature embeddings from a feature co-occurrence matrix. Swivel performs approximate factorization of the point-wise mutual information matrix via stochastic gradient descent. It uses a piecewise loss with special handling for unobserved co-occurrences, and thus makes use of all the information in the matrix. While this requires computation proportional to the size of the entire matrix, we make use of vectorized multiplication to process thousands of rows and columns at once to compute millions of predicted values. Furthermore, we partition the matrix into shards in order to parallelize the computation across many nodes. This approach results in more accurate embeddings than can be achieved with methods that consider only observed co-occurrences, and can scale to much larger corpora than can be handled with sampling methods.

We consider the problem of approximating a function from L^2 by an element of a given m-dimensional space V_m, associated with some feature map varphi, using evaluations of the function at random points x_1,dots,x_n. After recalling some results on optimal weighted least-squares using independent and identically distributed points, we consider weighted least-squares using projection determinantal point processes (DPP) or volume sampling. These distributions introduce dependence between the points that promotes diversity in the selected features varphi(x_i). We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples n = O(mlog(m)), that means that the expected L^2 error is bounded by a constant times the best approximation error in L^2. Also, further assuming that the function is in some normed vector space H continuously embedded in L^2, we further prove that the approximation is almost surely bounded by the best approximation error measured in the H-norm. This includes the cases of functions from L^infty or reproducing kernel Hilbert spaces. Finally, we present an alternative strategy consisting in using independent repetitions of projection DPP (or volume sampling), yielding similar error bounds as with i.i.d. or volume sampling, but in practice with a much lower number of samples. Numerical experiments illustrate the performance of the different strategies.