Message Passing Graph Neural Networks are known to suffer from two problems that are sometimes believed to be diametrically opposed: over-squashing and over-smoothing. The former results from topological bottlenecks that hamper the information flow from distant nodes and are mitigated by spectral gap maximization, primarily, by means of edge additions. However, such additions often promote over-smoothing that renders nodes of different classes less distinguishable. Inspired by the Braess phenomenon, we argue that deleting edges can address over-squashing and over-smoothing simultaneously. This insight explains how edge deletions can improve generalization, thus connecting spectral gap optimization to a seemingly disconnected objective of reducing computational resources by pruning graphs for lottery tickets. To this end, we propose a computationally effective spectral gap optimization framework to add or delete edges and demonstrate its effectiveness on the long range graph benchmark and on larger heterophilous datasets.

Transformer-based large language models (LLMs) typically have a limited context window, resulting in significant performance degradation when processing text beyond the length of the context window. Extensive studies have been proposed to extend the context window and achieve length extrapolation of LLMs, but there is still a lack of in-depth interpretation of these approaches. In this study, we explore the positional information within and beyond the context window for deciphering the underlying mechanism of LLMs. By using a mean-based decomposition method, we disentangle positional vectors from hidden states of LLMs and analyze their formation and effect on attention. Furthermore, when texts exceed the context window, we analyze the change of positional vectors in two settings, i.e., direct extrapolation and context window extension. Based on our findings, we design two training-free context window extension methods, positional vector replacement and attention window extension. Experimental results show that our methods can effectively extend the context window length.

The sampling problem under local differential privacy has recently been studied with potential applications to generative models, but a fundamental analysis of its privacy-utility trade-off (PUT) remains incomplete. In this work, we define the fundamental PUT of private sampling in the minimax sense, using the $f$-divergence between original and sampling distributions as the utility measure. We characterize the exact PUT for both finite and continuous data spaces under some mild conditions on the data distributions, and propose sampling mechanisms that are universally optimal for all $f$-divergences. Our numerical experiments demonstrate the superiority of our mechanisms over baselines, in terms of theoretical utilities for finite data space and of empirical utilities for continuous data space.

Invariance to a broad array of image corruptions, such as warping, noise, or color shifts, is an important aspect of building robust models in computer vision. Recently, several new data augmentations have been proposed that significantly improve performance on ImageNet-C, a benchmark of such corruptions. However, there is still a lack of basic understanding on the relationship between data augmentations and test-time corruptions. To this end, we develop a feature space for image transforms, and then use a new measure in this space between augmentations and corruptions called the Minimal Sample Distance to demonstrate there is a strong correlation between similarity and performance. We then investigate recent data augmentations and observe a significant degradation in corruption robustness when the test-time corruptions are sampled to be perceptually dissimilar from ImageNet-C in this feature space. Our results suggest that test error can be improved by training on perceptually similar augmentations, and data augmentations may not generalize well beyond the existing benchmark. We hope our results and tools will allow for more robust progress towards improving robustness to image corruptions.

In this paper, we introduce Cosine Autoencoder (CosAE), a novel, generic Autoencoder that seamlessly leverages the classic Fourier series with a feed-forward neural network. CosAE represents an input image as a series of 2D Cosine time series, each defined by a tuple of learnable frequency and Fourier coefficients. This method stands in contrast to a conventional Autoencoder that often sacrifices detail in their reduced-resolution bottleneck latent spaces.

The expressive power of transformers over inputs of unbounded size can be studied through their ability to recognize classes of formal languages. In this paper, we establish exact characterizations of transformers with hard attention (in which all attention is focused on exactly one position) and attention masking (in which each position only attends to positions on one side). With strict masking (each position cannot attend to itself) and without position embeddings, these transformers are expressively equivalent to linear temporal logic (LTL), which defines exactly the star-free languages. A key technique is the use of Boolean RASP as a convenient intermediate language between transformers and LTL. We then take numerous results known for LTL and apply them to transformers, showing how position embeddings, strict masking, and depth all increase expressive power.

Importantly, this matches the optimal bound $G\|w_\star\|\sqrt{T}$ available with such knowledge (up to logarithmic factors), unless either $\|w_\star\|$ or $G$ is so large that even $G\|w_\star\|\sqrt{T}$ is roughly linear in $T$. Thus, at a high level it matches the optimal bound in all cases in which one can achieve sublinear regret.

Finetuning foundation models for specific tasks is an emerging paradigm in modern machine learning. The efficacy of task-specific finetuning largely depends on the selection of appropriate training data. We present TSDS (Task-Specific Data Selection), a framework to select data for task-specific model finetuning, guided by a small but representative set of examples from the target task. To do so, we formulate data selection for task-specific finetuning as an optimization problem with a distribution alignment loss based on optimal transport to capture the discrepancy between the selected data and the target distribution. In addition, we add a regularizer to encourage the diversity of the selected data and incorporate kernel density estimation into the regularizer to reduce the negative effects of near-duplicates among the candidate data.We connect our optimization problem to nearest neighbor search and design efficient algorithms to compute the optimal solution based on approximate nearest neighbor search techniques.We evaluate our method on data selection for both continued pretraining and instruction tuning of language models.We show that instruction tuning using data selected by our method with a 1\% selection ratio often outperforms using the full dataset and beats the baseline selection methods by 1.5 points in F1 score on average.

Automated scientific discovery promises to accelerate progress across scientific domains, but evaluating an agent's capacity for end-to-end scientific reasoning is challenging as running real-world experiments is often prohibitively expensive or infeasible. In this work we introduce DiscoveryWorld, a virtual environment that enables benchmarking an agent's ability to perform complete cycles of novel scientific discovery in an inexpensive, simulated, multi-modal, long-horizon, and fictional setting.DiscoveryWorld consists of 24 scientific tasks across three levels of difficulty, each with parametric variations that provide new discoveries for agents to make across runs. Tasks require an agent to form hypotheses, design and run experiments, analyze results, and act on conclusions. Task difficulties are normed to range from straightforward to challenging for human scientists with advanced degrees. DiscoveryWorld further provides three automatic metrics for evaluating performance, including: (1) binary task completion, (2) fine-grained report cards detailing procedural scoring of task-relevant actions, and (3) the accuracy of discovered explanatory knowledge.While simulated environments such as DiscoveryWorld are low-fidelity compared to the real world, we find that strong baseline agents struggle on most DiscoveryWorld tasks, highlighting the utility of using simulated environments as proxy tasks for near-term development of scientific discovery competency in agents.

We study learning-based approaches to semantic route planning, which concerns producing routes in response to rich queries that specify various criteria and preferences. Semantic routing is already widely found in industry applications, especially navigational services like Google Maps; however, existing implementations only support limited route criteria and narrow query sets as they rely on repurposing classical route optimization algorithms. We argue for a learning-based approach to semantic routing as a more scalable and general alternative. To foster interest in this important application of graph learning, we are releasing a large-scale publicly-licensed benchmark for semantic routing consisting of real-world multi-objective navigation problems---expressed via natural language queries---on the richly annotated road networks of US cities. In addition to being intractable with existing approaches to semantic routing, our benchmark poses a significant scaling challenge for graph learning methods. As a proof-of-concept, we show that---at scale---even a standard transformer network is a powerful semantic routing system and achieves non-trivial performance on our benchmark. In the process, we demonstrate a simple solution to the challenge of scaling up graph learning: an autoregressive approach that decomposes semantic routing into smaller ``next-edge'' prediction problems.