ZETA: Leveraging Z-order Curves for Efficient Top-k Attention

Over recent years, the Transformer has become a fundamental building block for sequence modeling architectures. Yet at its core is the use of self-attention, whose memory and computational cost grow quadratically with the sequence length $N$, rendering it prohibitively expensive for long sequences. A promising approach is top-$k$ attention, which selects only the $k$ most relevant tokens and achieves performance comparable to vanilla self-attention while significantly reducing space and computational demands. However, causal masks require the current query token to only attend to past tokens, preventing the existing top-$k$ attention method from efficiently searching for the most relevant tokens in parallel, thereby limiting training efficiency. In this work, we propose ZETA, leveraging \textbf{Z}-Order Curves for \textbf{E}fficient \textbf{T}op-$k$ \textbf{A}ttention, to enable parallel querying of past tokens for entire sequences. % in both space and time complexity of $\mathcal{O}(N \log N)$. We first theoretically show that the choice of key and query dimensions involves a trade-off between the curse of dimensionality and the preservation of relative distances after projection. In light of this insight, we propose reducing the dimensionality of keys and queries in contrast to values and further leverage $Z$-order curves to map low-dimensional keys and queries into \emph{one}-dimensional space, which permits parallel sorting, thereby largely improving the efficiency for top-$k$ token selection. Experimental results demonstrate that ZETA matches the performance of standard attention on the synthetic \textsc{Multi-Query Associative Recall} task and outperforms attention and its variants on \textsc{Long Range Arena} and \textsc{WikiText-103} language modeling.

Do Robot Snakes Dream like Electric Sheep? Investigating the Effects of Architectural Inductive Biases on Hallucination

The growth in prominence of large language models (LLMs) in everyday life can be largely attributed to their generative abilities, yet some of this is also owed to the risks and costs associated with their use. On one front is their tendency to \textit{hallucinate} false or misleading information, limiting their reliability. On another is the increasing focus on the computational limitations associated with traditional self-attention based LLMs, which has brought about new alternatives, in particular recurrent models, meant to overcome them. Yet it remains uncommon to consider these two concerns simultaneously. Do changes in architecture exacerbate/alleviate existing concerns about hallucinations? Do they affect how and where they occur? Through an extensive evaluation, we study how these architecture-based inductive biases affect the propensity to hallucinate. While hallucination remains a general phenomenon not limited to specific architectures, the situations in which they occur and the ease with which specific types of hallucinations can be induced can significantly differ based on the model architecture. These findings highlight the need for better understanding both these problems in conjunction with each other, as well as consider how to design more universal techniques for handling hallucinations.

Predicting adaptively chosen observables in quantum systems

Recent advances have demonstrated that $\mathcal{O}(\log M)$ measurements suffice to predict $M$ properties of arbitrarily large quantum many-body systems. However, these remarkable findings assume that the properties to be predicted are chosen independently of the data. This assumption can be violated in practice, where scientists adaptively select properties after looking at previous predictions. This work investigates the adaptive setting for three classes of observables: local, Pauli, and bounded-Frobenius-norm observables. We prove that $\Omega(\sqrt{M})$ samples of an arbitrarily large unknown quantum state are necessary to predict expectation values of $M$ adaptively chosen local and Pauli observables. We also present computationally-efficient algorithms that achieve this information-theoretic lower bound. In contrast, for bounded-Frobenius-norm observables, we devise an algorithm requiring only $\mathcal{O}(\log M)$ samples, independent of system size. Our results highlight the potential pitfalls of adaptivity in analyzing data from quantum experiments and provide new algorithmic tools to safeguard against erroneous predictions in quantum experiments.

Context-Aware Assistant Selection for Improved Inference Acceleration with Large Language Models

Despite their widespread adoption, large language models (LLMs) remain prohibitive to use under resource constraints, with their ever growing sizes only increasing the barrier for use. One noted issue is the high latency associated with auto-regressive generation, rendering large LLMs use dependent on advanced computing infrastructure. Assisted decoding, where a smaller draft model guides a larger target model's generation, has helped alleviate this, but remains dependent on alignment between the two models. Thus if the draft model is insufficiently capable on some domain relative to the target model, performance can degrade. Alternatively, one can leverage multiple draft models to better cover the expertise of the target, but when multiple black-box draft models are available, selecting an assistant without details about its construction can be difficult. To better understand this decision making problem, we observe it as a contextual bandit, where a policy must choose a draft model based on a context. We show that even without prior knowledge of the draft models, creating an offline dataset from only outputs of independent draft/target models and training a policy over the alignment of these outputs can accelerate performance on multiple domains provided the candidates are effective. Further results show this to hold on various settings with multiple assisted decoding candidates, highlighting its flexibility and the advantageous role that such decision making can play.

How Well Can a Long Sequence Model Model Long Sequences? Comparing Architechtural Inductive Biases on Long-Context Abilities

Long sequences occur in abundance within real-world scenarios, hence properly modelling them opens numerous down-stream use-cases. Deep neural networks, however, have often struggled with these for a variety of reasons. Recent advances, both in system engineering as well as model design, have enabled the scaling up of model that are purported to support extended context length. In particular, the state-space and linear recurrent neural network families of models hypothetically can entend to infinite sequence lenth. However, is this too good to be true? We conduct an evaluation to show that while such claims may be sound theoretically, there remain large practical gaps that are empirically observed. In particular, recurrent models still suffer in the same settings as long-context LLMs with attention. We further show that different inductive biases have inconsistent extrapolation capabilities, highlighting the need to further study such paradigms and investigate why long-context models seemingly fail to behave as one might expect.

Predicting the Impact of Model Expansion through the Minima Manifold: A Loss Landscape Perspective

The optimal model for a given task is often challenging to determine, requiring training multiple models from scratch which becomes prohibitive as dataset and model sizes grow. A more efficient alternative is to reuse smaller pre-trained models by expanding them, however, this is not widely adopted as how this impacts training dynamics remains poorly understood. While prior works have introduced statistics to measure these effects, they remain flawed. To rectify this, we offer a new approach for understanding and quantifying the impact of expansion through the lens of the loss landscape, which has been shown to contain a manifold of linearly connected minima. Building on this new perspective, we propose a metric to study the impact of expansion by estimating the size of the manifold. Experimental results show a clear relationship between gains in performance and manifold size, enabling the comparison of candidate models and presenting a first step towards expanding models more reliably based on geometric properties of the loss landscape.

Towards Practical Tool Usage for Continually Learning LLMs

Large language models (LLMs) show an innate skill for solving language based tasks. But insights have suggested an inability to adjust for information or task-solving skills becoming outdated, as their knowledge, stored directly within their parameters, remains static in time. Tool use helps by offloading work to systems that the LLM can access through an interface, but LLMs that use them still must adapt to nonstationary environments for prolonged use, as new tools can emerge and existing tools can change. Nevertheless, tools require less specialized knowledge, therefore we hypothesize they are better suited for continual learning (CL) as they rely less on parametric memory for solving tasks and instead focus on learning when to apply pre-defined tools. To verify this, we develop a synthetic benchmark and follow this by aggregating existing NLP tasks to form a more realistic testing scenario. While we demonstrate scaling model size is not a solution, regardless of tool usage, continual learning techniques can enable tool LLMs to both adapt faster while forgetting less, highlighting their potential as continual learners.

EpiK-Eval: Evaluation for Language Models as Epistemic Models

In the age of artificial intelligence, the role of large language models (LLMs) is becoming increasingly central. Despite their growing prevalence, their capacity to consolidate knowledge from different training documents - a crucial ability in numerous applications - remains unexplored. This paper presents the first study examining the capability of LLMs to effectively combine such information within their parameter space. We introduce EpiK-Eval, a novel question-answering benchmark tailored to evaluate LLMs' proficiency in formulating a coherent and consistent knowledge representation from segmented narratives. Evaluations across various LLMs reveal significant weaknesses in this domain. We contend that these shortcomings stem from the intrinsic nature of prevailing training objectives. Consequently, we advocate for refining the approach towards knowledge consolidation, as it harbors the potential to dramatically improve their overall effectiveness and performance. The findings from this study offer insights for developing more robust and reliable LLMs. Our code and benchmark are available at https://github.com/chandar-lab/EpiK-Eval

Online Algorithms with Uncertainty-Quantified Predictions

Online algorithms with predictions have become a trending topic in the field of beyond worst-case analysis of algorithms. These algorithms incorporate predictions about the future to obtain performance guarantees that are of high quality when the predictions are good, while still maintaining bounded worst-case guarantees when predictions are arbitrarily poor. In general, the algorithm is assumed to be unaware of the prediction's quality. However, recent developments in the machine learning literature have studied techniques for providing uncertainty quantification on machine-learned predictions, which describes how certain a model is about its quality. This paper examines the question of how to optimally utilize uncertainty-quantified predictions in the design of online algorithms. In particular, we consider predictions augmented with uncertainty quantification describing the likelihood of the ground truth falling in a certain range, designing online algorithms with these probabilistic predictions for two classic online problems: ski rental and online search. In each case, we demonstrate that non-trivial modifications to algorithm design are needed to fully leverage the probabilistic predictions. Moreover, we consider how to utilize more general forms of uncertainty quantification, proposing a framework based on online learning that learns to exploit uncertainty quantification to make optimal decisions in multi-instance settings.

Promoting Exploration in Memory-Augmented Adam using Critical Momenta

Adaptive gradient-based optimizers, particularly Adam, have left their mark in training large-scale deep learning models. The strength of such optimizers is that they exhibit fast convergence while being more robust to hyperparameter choice. However, they often generalize worse than non-adaptive methods. Recent studies have tied this performance gap to flat minima selection: adaptive methods tend to find solutions in sharper basins of the loss landscape, which in turn hurts generalization. To overcome this issue, we propose a new memory-augmented version of Adam that promotes exploration towards flatter minima by using a buffer of critical momentum terms during training. Intuitively, the use of the buffer makes the optimizer overshoot outside the basin of attraction if it is not wide enough. We empirically show that our method improves the performance of several variants of Adam on standard supervised language modelling and image classification tasks.