Quantization plays a crucial role in accelerating the inference of large-scale models, and rotational matrices have been shown to effectively improve quantization performance by smoothing outliers. However, end-to-end fine-tuning of rotational optimization algorithms incurs high computational costs and is prone to overfitting. To address this challenge, we propose an efficient distribution-aware rotational calibration method, DartQuant, which reduces the complexity of rotational optimization by constraining the distribution of the activations after rotation. This approach also effectively reduces reliance on task-specific losses, thereby mitigating the risk of overfitting. Additionally, we introduce the QR-Orth optimization scheme, which replaces expensive alternating optimization with a more efficient solution. In a variety of model quantization experiments, DartQuant demonstrates superior performance. Compared to existing methods, it achieves 47 acceleration and 10 memory savings for rotational optimization on a 70B model. Furthermore, it is the first to successfully complete rotational calibration for a 70B model on a single 3090 GPU, making quantization of large language models feasible in resource-constrained environments.

While Large language models (LLMs) are driving the rapid advancement of artificial intelligence, effectively and reliably training these large models remains one of the field's most significant challenges. To address this challenge, we propose POET, a novel reParameterized training algorithm that uses Orthogonal Equivalence Transformation to optimize neurons. Specifically, POET reparameterizes each neuron with two learnable orthogonal matrices and a fixed random weight matrix. Because of its provable preservation of spectral properties of weight matrices, POET can stably optimize the objective function with improved generalization. We further develop efficient approximations that make POET flexible and scalable for training large-scale neural networks.

We propose Metric Automata Theory, an elegant generalisation of classic Automata Theory to continuous dynamical systems, that constitutes a unifying theory of all kinds of Recurrent Neural Networks (RNNs), including widely-adopted architectures such as xLSTM and State Space Models (SSMs). The theory allows one to analyse RNNs both in the finite and unbounded precision settings seamlessly, while utilising fundamental results of Automata Theory. It also provides a novel notion of robustness that guarantees numerical stability and contributes to stability of learning. We employ the theory to prove a comprehensive set of expressivity results for widely-adopted RNNs, with a focus on robustness and finite-precision. Notably, we contrast the capabilities of xLSTM and SSMs for robustly modelling all star-free regular languages--xLSTM can do so, while SSMs cannot robustly recognize the FLIP-FLOP language.

Contemporary large models often exhibit behaviors suggesting the presence of low-level primitives that compose into modules with richer functionality, but these fundamental building blocks remain poorly understood. We investigate this compositional structure in linear layers by asking: can we identify/synthesize linear transformations from a minimal set of geometric primitives? Using Clifford algebra, we show that linear layers can be expressed as compositions of bivectors--geometric objects encoding oriented planes--and introduce a differentiable algorithm that decomposes them into products of rotors. This construction uses only O log2 d parameters, versus O(d2) required by dense matrices. Applied to the key, query, and value projections in LLM attention layers, rotor-based layers match the performance of strong baselines such as block-Hadamard and low-rank approximations. Our findings provide an algebraic perspective on how these geometric primitives can compose into higher-level functions within deep models.

We propose a novel diffusion-based framework for automatic colorization of Animestyle facial sketches, which preserves the structural fidelity of the input sketch while effectively transferring stylistic attributes from a reference image. Our approach builds upon recent continuous-time diffusion models, but departs from traditional methods that rely on predefined noise schedules, which often fail to maintain perceptual consistency across the generative trajectory. To address this, we introduce SSIMBaD (Sigma Scaling with SSIM-Guided Balanced Diffusion), a sigma-space transformation that ensures linear alignment of perceptual degradation, as measured by structural similarity. This perceptual scaling enforces uniform visual difficulty across timesteps, enabling more balanced and faithful reconstructions.

Reconstructing dynamic 3D scenes from monocular videos remains a fundamental challenge in 3D vision. While 3DGaussian Splatting (3DGS) achieves real-time rendering in static settings, extending it to dynamic scenes is challenging due to the difficulty of learning structured and temporally consistent motion representations.

Mixture-of-Experts (MoE) models have become popular in machine learning, boosting performance by partitioning tasks across multiple experts. However, the need for several experts often results in high computational costs, limiting their application on resource-constrained devices with stringent real-time requirements, such as cochlear implants (CIs). We introduce the Omni-Expert (OE) - a simple and efficient solution that leverages feature transformations to achieve the'divideand-conquer' functionality of a full MoE ensemble in a single expert model. We demonstrate the effectiveness of the OE using phoneme-specific time-frequency masking for speech dereverberation in a CI. Empirical results show that the OE delivers statistically significant improvements in objective intelligibility measures of CI vocoded speech at different levels of reverberation across various speech datasets at a much reduced computational cost relative to a counterpart MoE.

The constant πhas fascinated scholars throughout the centuries, inspiring numerous formulas for its evaluation, such as infinite sums and continued fractions. Despite their individual significance, many of the underlying connections among formulas remain unknown, missing unifying theories that could unveil deeper understanding. The absence of a unifying theory reflects a broader challenge across math and science: knowledge is typically accumulated through isolated discoveries, while deeper connections often remain hidden. In this work, we present an automated framework for the unification of mathematical formulas. Our system combines large language models (LLMs) for systematic formula harvesting, an LLM-code feedback loop for validation, and a novel symbolic algorithm for clustering and eventual unification. We demonstrate this methodology on the hallmark case of π, an ideal testing ground for symbolic unification. Applying this approach to 455,050 arXiv papers, we validate 385 distinct formulas for π and prove relations between 360 (94%) of them, of which 166 (43%) can be derived from a single mathematical object--linking canonical formulas by Euler, Gauss, Brouncker, and newer ones from algorithmic discoveries by the Ramanujan Machine. Our method generalizes to other constants, including e, ζ(3), and Catalan's constant, demonstrating the potential of AI-assisted mathematics to uncover hidden structures and unify knowledge across domains.

Self-supervised learning (SSL) has emerged as a powerful paradigm for learning representations without labeled data. Most SSL approaches rely on strong, well-established, handcrafted data augmentations to generate diverse views for representation learning. However, designing such augmentations requires domainspecific knowledge and implicitly imposes representational invariances on the model, which can limit generalization. In this work, we propose an unsupervised representation learning method that replaces augmentations by generating views using orthonormal bases and overcomplete frames. We show that embeddings learned from orthonormal and overcomplete spaces reside on distinct manifolds, shaped by the geometric biases introduced by representing samples in different spaces. By jointly leveraging the complementary geometry of these distinct manifolds, our approach achieves superior performance without artificially increasing data diversity through strong augmentations. We demonstrate the effectiveness of our method on nine datasets across five temporal sequence tasks, where signalspecific characteristics make data augmentations particularly challenging. Without relying on augmentation-induced diversity, our method achieves performance gains of up to 15-20% over existing self-supervised approaches.

In this work, we explore the trade-offs of explicit structural priors, particularly group-equivariance. We address this through theoretical analysis and a comprehensive empirical study focusing on point clouds. To enable controlled and fair comparisons, we introduce Rapidash, a unified group convolutional architecture that allows for different variants of equivariant and non-equivariant models. Our results suggest that more constrained equivariant models outperform less constrained alternatives when aligned with the geometry of the task, and increasing representation capacity does not fully eliminate performance gaps. We see improved performance of models with equivariance and symmetry-breaking through tasks like segmentation, regression, and generation across diverse datasets. Explicit symmetry breaking via geometric reference frames consistently improves performance, while breaking equivariance through geometric input features can be helpful when aligned with task geometry. Our results provide task-specific performance trends that offer a more nuanced way for model selection.