Learning continuous-time point processes is essential to many discrete event forecasting tasks.

This highlights the need for better approaches to handle complex, multifaceted queries in scientific research.

Computation of confidence sets is central to data science and machine learning, serving as the workhorse of A/B testing and underpinning the operation and analysis of reinforcement learning algorithms. Among all valid confidence sets for the multinomial parameter, minimum-volume confidence sets (MVCs) are optimal in that they minimize average volume, but they are defined as level sets of an exact p-value that is discontinuous and difficult to compute. Rather than attempting to characterize the geometry of MVCs directly, this paper studies a practically motivated decision problem: given two observed multinomial outcomes, can one certify whether their MVCs intersect? We present a certified, tolerance-aware algorithm for this intersection problem. The method exploits the fact that likelihood ordering induces halfspace constraints in log-odds coordinates, enabling adaptive geometric partitioning of parameter space and computable lower and upper bounds on p-values over each cell. For three categories, this yields an efficient and provably sound algorithm that either certifies intersection, certifies disjointness, or returns an indeterminate result when the decision lies within a prescribed margin. We further show how the approach extends to higher dimensions. The results demonstrate that, despite their irregular geometry, MVCs admit reliable certified decision procedures for core tasks in A/B testing.

We study when geometric simplicity of decision boundaries, used here as a notion of interpretability, can conflict with accurate approximation of axis-aligned decision trees by shallow neural networks. Decision trees induce rule-based, axis-aligned decision regions (finite unions of boxes), whereas shallow ReLU networks are typically trained as score models whose predictions are obtained by thresholding. We analyze the infinite-width, bounded-norm, single-hidden-layer ReLU class through the Radon total variation ($\mathrm{R}\mathrm{TV}$) seminorm, which controls the geometric complexity of level sets. We first show that the hard tree indicator $1_A$ has infinite $\mathrm{R}\mathrm{TV}$. Moreover, two natural split-wise continuous surrogates--piecewise-linear ramp smoothing and sigmoidal (logistic) smoothing--also have infinite $\mathrm{R}\mathrm{TV}$ in dimensions $d>1$, while Gaussian convolution yields finite $\mathrm{R}\mathrm{TV}$ but with an explicit exponential dependence on $d$. We then separate two goals that are often conflated: classification after thresholding (recovering the decision set) versus score learning (learning a calibrated score close to $1_A$). For classification, we construct a smooth barrier score $S_A$ with finite $\mathrm{R}\mathrm{TV}$ whose fixed threshold $τ=1$ exactly recovers the box. Under a mild tube-mass condition near $\partial A$, we prove an $L_1(P)$ calibration bound that decays polynomially in a sharpness parameter, along with an explicit $\mathrm{R}\mathrm{TV}$ upper bound in terms of face measures. Experiments on synthetic unions of rectangles illustrate the resulting accuracy--complexity tradeoff and how threshold selection shifts where training lands along it.

Transformer models rely heavily on the scaled dot-product attention (SDPA) operation, typically implemented as FlashAttention. Characterized by its frequent interleaving of matrix multiplications and softmax operations, FlashAttention fails to fully utilize the compute resources of modern systolic-array-based accelerators designed for consecutive and large matrix multiplications. To fully unleash the performance potential of systolic arrays for FlashAttention, we propose FSA, an enhanced systolic array architecture that runs the entire FlashAttention on the array without external vector units. Combined with SystolicAttention, an optimized kernel for FSA that achieves fine-grained and element-wise overlapping of FlashAttention operations, FSA maximizes array utilization while preserving the original floating-point operation order of FlashAttention. We implement FSA in synthesizable RTL and evaluate its performance against state-of-the-art systolic-array-based accelerators. Our results show that FSA achieves 1.77x and 4.83x higher attention FLOPs/s utilization compared to AWS Neuron-v2 and Google TPUv5e, respectively. We synthesize FSA in a 16 nm technology at 1.5 GHz, and results indicate only a 12% area overhead compared to a standard weight-stationary systolic array.

Fast and accurate underwater acoustic charting is crucial for downstream tasks such as environment-aware sensor placement optimization and autonomous vehicle path planning. Conventional methods rely on computationally expensive while accurate numerical solvers, which are not scalable for large-scale or real-time applications. Although deep learning-based surrogate models can accelerate these computations, they often suffer from limitations such as fixed-resolution constraints or dependence on explicit partial differential equation formulations. These issues hinder their applicability and generalization across diverse environments. We propose Hankel-FNO, a Fourier Neural Operator (FNO)-based model for efficient and accurate acoustic charting. By incorporating sound propagation knowledge and bathymetry, our method has high accuracy while maintaining high computational speed. Results demonstrate that Hankel-FNO outperforms traditional solvers in speed and surpasses data-driven alternatives in accuracy, especially in long-range predictions. Experiments show the model's adaptability to diverse environments and sound source settings with minimal fine-tuning.

Post-training quantization (PTQ) plays a crucial role in the democratization of large language models (LLMs). However, existing low-bit quantization and sparsification techniques are difficult to balance accuracy and efficiency due to the limited hardware support. For example, W4A8 can only achieve the same peak TOPS as W8A8 whereas the GPU-supported sparse data format (2:4 semi-structure sparse) is seldomly adopted due to the loss of accuracy. To bridge this gap, in this paper, we propose the Sparse-Quantized Format (SQ-format), which is a unified data format for quantization and sparsification potentially easily supported by new hardware and existing GPUs. SQ-format makes use of the fact that sparse matrix can be accelerated in high-precision, and low-precision matrix multiplication can also be accelerated accordingly. As such, SQ-format is proposed to achieve Pareto improvement between performance and throughput. This format is particularly suitable for activations with outlier inequality status and makes their static compression possible. We show the state-of-the-art PTQ performance with SQ-format, propose the hardware required to support it, and further offer the design exploration and insights for the next-generation AI accelerators.

Spectral gradient methods, such as the recently popularized Muon optimizer, are a promising alternative to standard Euclidean gradient descent for training deep neural networks and transformers, but it is still unclear in which regimes they are expected to perform better. We propose a simple layerwise condition that predicts when a spectral update yields a larger decrease in the loss than a Euclidean gradient step. This condition compares, for each parameter block, the squared nuclear-to-Frobenius ratio of the gradient to the stable rank of the incoming activations. To understand when this condition may be satisfied, we first prove that post-activation matrices have low stable rank at Gaussian initialization in random feature regression, feedforward networks, and transformer blocks. In spiked random feature models we then show that, after a short burn-in, the Euclidean gradient's nuclear-to-Frobenius ratio grows with the data dimension while the stable rank of the activations remains bounded, so the predicted advantage of spectral updates scales with dimension. We validate these predictions in synthetic regression experiments and in NanoGPT-scale language model training, where we find that intermediate activations have low-stable-rank throughout training and the corresponding gradients maintain large nuclear-to-Frobenius ratios. Together, these results identify conditions for spectral gradient methods, such as Muon, to be effective in training deep networks and transformers.

DeepSeek-OCR demonstrates that rendered text can be reconstructed with high fidelity from a small number of vision tokens. This finding has sparked excitement about vision-based context compression for language models. But the evaluation stops at reconstruction; whether these representations help language modeling remains untested. We test two assumptions implicit in the optical-compression narrative: that vision-based compression provides unique advantages for text reconstruction from compressed representations, and that DeepSeek-OCR's reconstruction results are evidence that vision-based compression will be useful for language modeling. Comparing their vision encoder against simple alternatives--parameter-free mean pooling and a learned hierarchical encoder--we find that these simple approaches match or surpass vision for reconstruction at matched compression ratios, and outperform it for language modeling--where vision-based compression fails to beat truncation. The excitement around optical context compression outpaces the evidence. Code and checkpoints are available at https://github.com/ivnle/bad-autoencoding