Low precision (LP) datatypes such as MXFP4 can accelerate matrix multiplications (GEMMs) and reduce training costs. However, directly using MXFP4 instead of BF16 during training significantly degrades model quality. In this work, we present the first near-lossless training recipe that uses MXFP4 GEMMs, which are $2\times$ faster than FP8 on supported hardware. Our key insight is to compute unbiased gradient estimates with stochastic rounding (SR), resulting in more accurate model updates. However, directly applying SR to MXFP4 can result in high variance from block-level outliers, harming convergence. To overcome this, we use the random Hadamard tranform to theoretically bound the variance of SR. We train GPT models up to 6.7B parameters and find that our method induces minimal degradation over mixed-precision BF16 training. Our recipe computes $>1/2$ the training FLOPs in MXFP4, enabling an estimated speedup of $>1.3\times$ over FP8 and $>1.7\times$ over BF16 during backpropagation.

Hyperbolic space has proven to be well-suited for capturing hierarchical relations in data, such as trees and directed acyclic graphs. Prior work introduced the concept of entailment cones, which uses partial orders defined by nested cones in the Poincar\'e ball to model hierarchies. Here, we introduce the ``shadow cones" framework, a physics-inspired entailment cone construction. Specifically, we model partial orders as subset relations between shadows formed by a light source and opaque objects in hyperbolic space. The shadow cones framework generalizes entailment cones to a broad class of formulations and hyperbolic space models beyond the Poincar\'e ball. This results in clear advantages over existing constructions: for example, shadow cones possess better optimization properties over constructions limited to the Poincar\'e ball. Our experiments on datasets of various sizes and hierarchical structures show that shadow cones consistently and significantly outperform existing entailment cone constructions. These results indicate that shadow cones are an effective way to model partial orders in hyperbolic space, offering physically intuitive and novel insights about the nature of such structures.

Post-training quantization (PTQ) reduces the memory footprint of LLMs by quantizing their weights to low-precision. In this work, we introduce QuIP#, a weight-only PTQ method that achieves state-of-the-art results in extreme compression regimes ($\le$ 4 bits per weight) using three novel techniques. First, QuIP# improves QuIP’s (Chee et al., 2023) incoherence processing by using the randomized Hadamard transform, which is faster and has better theoretical properties. Second, QuIP# uses vector quantization to take advantage of the ball-shaped sub-Gaussian distribution that incoherent weights possess: specifically, we introduce a set of hardware-efficient codebooks based on the highly symmetric $E_8$ lattice, which achieves the optimal 8-dimension unit ball packing. Third, QuIP# uses fine-tuning to improve fidelity to the original model. Our experiments show that QuIP# outperforms existing PTQ methods, enables new behaviors in PTQ scaling, and supports fast inference. Our code can be found at https://github.com/Cornell-RelaxML/quip-sharp.

Post-training quantization (PTQ) reduces the memory footprint of LLMs by quantizing weights to low-precision datatypes. Since LLM inference is usually memory-bound, PTQ methods can improve inference throughput. Recent state-of-the-art PTQ approaches use vector quantization (VQ) to quantize multiple weights at once, which improves information utilization through better shaping. However, VQ requires a codebook with size exponential in the dimension. This limits current VQ-based PTQ works to low VQ dimensions ($\le 8$) that in turn limit quantization quality. Here, we introduce QTIP, which instead uses trellis coded quantization (TCQ) to achieve ultra-high-dimensional quantization. TCQ uses a stateful decoder that separates the codebook size from the bitrate and effective dimension. QTIP introduces a spectrum of lookup-only to computed lookup-free trellis codes designed for a hardware-efficient "bitshift" trellis structure; these codes achieve state-of-the-art results in both quantization quality and inference speed.

Attention networks such as transformers have achieved state-of-the-art performance in many domains. These networks rely heavily on the dot product attention operator, which computes the similarity between two points by taking their inner product. However, the inner product does not explicitly model the complex structural properties of real world datasets, such as hierarchies between data points. To remedy this, we introduce cone attention, a drop-in replacement for dot product attention based on hyperbolic entailment cones. Cone attention associates two points by the depth of their lowest common ancestor in a hierarchy defined by hyperbolic cones, which intuitively measures the divergence of two points and gives a $\textit{hierarchy aware}$ similarity score. We test cone attention on a wide variety of models and tasks and show that it improves task-level performance over dot product attention and other baselines, and is able to match dot-product attention with significantly fewer parameters. Our results suggest that cone attention is an effective way to capture hierarchical relationships when calculating attention.

Obtaining annotations for large training sets is expensive, especially in settings where domain knowledge is required, such as behavior analysis. Weak supervision has been studied to reduce annotation costs by using weak labels from task-specific labeling functions (LFs) to augment ground truth labels. However, domain experts still need to hand-craft different LFs for different tasks, limiting scalability. To reduce expert effort, we present AutoSWAP: a framework for automatically synthesizing data-efficient task-level LFs. The key to our approach is to efficiently represent expert knowledge in a reusable domain-specific language and more general domain-level LFs, with which we use state-of-the-art program synthesis techniques and a small labeled dataset to generate task-level LFs. Additionally, we propose a novel structural diversity cost that allows for efficient synthesis of diverse sets of LFs, further improving AutoSWAP's performance. We evaluate AutoSWAP in three behavior analysis domains and demonstrate that AutoSWAP outperforms existing approaches using only afraction of the data. Our results suggest that AutoSWAP is an effective way to automatically generate LFs that can significantly reduce expert effort for behavior analysis.

We study the problem of controllable generation of long-term sequential behaviors, where the goal is to calibrate to multiple behavior styles simultaneously. In contrast to the well-studied areas of controllable generation of images, text, and speech, there are two questions that pose significant challenges when generating long-term behaviors: how should we specify the factors of variation to control, and how can we ensure that the generated behavior faithfully demonstrates combinatorially many styles? We leverage programmatic labeling functions to specify controllable styles, and derive a formal notion of style-consistency as a learning objective, which can then be solved using conventional policy learning approaches. We evaluate our framework using demonstrations from professional basketball players and agents in the MuJoCo physics environment, and show that existing approaches that do not explicitly enforce style-consistency fail to generate diverse behaviors whereas our learned policies can be calibrated for up to $4^5 (1024)$ distinct style combinations.