Large language models (LLMs) with long context windows have gained significant attention. However, the KV cache, stored to avoid re-computation, becomes a bottleneck. Various dynamic sparse or TopK-based attention approximation methods have been proposed to leverage the common insight that attention is sparse. In this paper, we first show that TopK attention itself suffers from quality degradation in certain downstream tasks because attention is not always as sparse as expected. Rather than selecting the keys and values with the highest attention scores, sampling with theoretical guarantees can provide a better estimation for attention output. To make the sampling-based approximation practical in LLM generation, we propose MagicPIG, a heterogeneous system based on Locality Sensitive Hashing (LSH). MagicPIG significantly reduces the workload of attention computation while preserving high accuracy for diverse tasks. MagicPIG stores the LSH hash tables and runs the attention computation on the CPU, which allows it to serve longer contexts and larger batch sizes with high approximation accuracy. MagicPIG can improve decoding throughput by up to $5\times$ across various GPU hardware and achieve 54ms decoding latency on a single RTX 4090 for Llama-3.1-8B-Instruct model with a context of 96k tokens.

Memory Mosaics are networks of associative memories working in concert to achieve a prediction task of interest. Like transformers, memory mosaics possess compositional capabilities and in-context learning capabilities. Unlike transformers, memory mosaics achieve these capabilities in comparatively transparent way (“predictive disentanglement”). We illustrate these capabilities on a toy example and also show that memory mosaics perform as well or better than transformers on medium-scale language modeling tasks.

Recent masked diffusion models (MDMs) have shown competitive performance compared to autoregressive models (ARMs) for language modeling. While most literature has focused on performance enhancing sampling procedures, efficient sampling from MDMs has been scarcely explored. We make the observation that often a given sequence of partially masked tokens determines the values of multiple unknown tokens deterministically, meaning that a single prediction of a masked model holds additional information unused by standard sampling procedures. Based on this observation, we introduce *EB-Sampler*, a simple drop-in replacement for existing samplers, utilizing an **E**ntropy **B**ounded unmasking procedure that dynamically unmasks multiple tokens in one function evaluation with predefined approximate error tolerance. We formulate the EB-Sampler as part of a broad family of adaptive samplers for which we provide an error analysis that motivates our algorithmic choices. EB-Sampler accelerates sampling from current state of the art MDMs by roughly 2-3x on standard coding and math reasoning benchmarks without loss in performance. We also validate the same procedure works well on smaller reasoning tasks including maze navigation and sudoku, tasks ARMs often struggle with.

Mechanistic Interpretability (MI) proposes a path toward fully understanding how neural networks make their predictions. Prior work demonstrates that even when trained to perform simple arithmetic, models can implement a variety of algorithms (sometimes concurrently) depending on initialization and hyperparameters. Does this mean neuron-level interpretability techniques have limited applicability? Here, we argue that high-dimensional neural networks can learn useful low-dimensional representations of the data they were trained on, going beyond simply making good predictions: Such representations can be understood with the MI lens and provide insights that are surprisingly faithful to human-derived domain knowledge. This indicates that such approaches to interpretability can be useful for deriving a new understanding of a problem from models trained to solve it. As a case study, we extract nuclear physics concepts by studying models trained to reproduce nuclear data.

Today's best language models still struggle with "hallucinations", factually incorrect generations, which impede their ability to reliably retrieve information seen during training. The *reversal curse*, where models cannot recall information when probed in a different order than was encountered during training, exemplifies limitations in information retrieval. To better understand these limitations, we reframe the reversal curse as a *factorization curse* --- a failure of models to learn the same joint distribution under different factorizations. We more closely simulate finetuning workflows which train pretrained models on specialized knowledge by introducing *WikiReversal*, a realistic testbed based on Wikipedia knowledge graphs. Through a series of controlled experiments with increasing levels of realism, including non-reciprocal relations, we find that reliable information retrieval is an inherent failure of the next-token prediction objective used in popular large language models. Moreover, we demonstrate reliable information retrieval cannot be solved with scale, reversed tokens, or even naive bidirectional-attention training. Consequently, various approaches to finetuning on specialized data would necessarily provide mixed results on downstream tasks, unless the model has already seen the right sequence of tokens. Across five tasks of varying levels of complexity, our results uncover a promising path forward: factorization-agnostic objectives can significantly mitigate the reversal curse and hint at improved knowledge storage and planning capabilities.

We aim to understand grokking, a phenomenon where models generalize long after overfitting their training set. We present both a microscopic analysis anchored by an effective theory and a macroscopic analysis of phase diagrams describing learning performance across hyperparameters. We find that generalization originates from structured representations, whose training dynamics and dependence on training set size can be predicted by our effective theory (in a toy setting). We observe empirically the presence of four learning phases: comprehension, grokking, memorization, and confusion. We find representation learning to occur only in a "Goldilocks zone" (including comprehension and grokking) between memorization and confusion. Compared to the comprehension phase, the grokking phase stays closer to the memorization phase, leading to delayed generalization. The Goldilocks phase is reminiscent of "intelligence from starvation" in Darwinian evolution, where resource limitations drive discovery of more efficient solutions. This study not only provides intuitive explanations of the origin of grokking, but also highlights the usefulness of physics-inspired tools, e.g., effective theories and phase diagrams, for understanding deep learning.