Transformers Provably Learn Sparse Token Selection While Fully-Connected Nets Cannot

The transformer architecture has prevailed in various deep learning settings due to its exceptional capabilities to select and compose structural information. Motivated by these capabilities, Sanford et al. proposed the sparse token selection task, in which transformers excel while fully-connected networks (FCNs) fail in the worst case. Building upon that, we strengthen the FCN lower bound to an average-case setting and establish an algorithmic separation of transformers over FCNs. Specifically, a one-layer transformer trained with gradient descent provably learns the sparse token selection task and, surprisingly, exhibits strong out-of-distribution length generalization. We provide empirical simulations to justify our theoretical findings.

Group-wise oracle-efficient algorithms for online multi-group learning

We study the problem of online multi-group learning, a learning model in which an online learner must simultaneously achieve small prediction regret on a large collection of (possibly overlapping) subsequences corresponding to a family of groups. Groups are subsets of the context space, and in fairness applications, they may correspond to subpopulations defined by expressive functions of demographic attributes. In contrast to previous work on this learning model, we consider scenarios in which the family of groups is too large to explicitly enumerate, and hence we seek algorithms that only access groups via an optimization oracle. In this paper, we design such oracle-efficient algorithms with sublinear regret under a variety of settings, including: (i) the i.i.d. setting, (ii) the adversarial setting with smoothed context distributions, and (iii) the adversarial transductive setting.

Seasonality Patterns in 311-Reported Foodborne Illness Cases and Machine Learning-Identified Indications of Foodborne Illnesses from Yelp Reviews, New York City, 2022-2023

Restaurants are critical venues at which to investigate foodborne illness outbreaks due to shared sourcing, preparation, and distribution of foods. Formal channels to report illness after food consumption, such as 311, New York City's non-emergency municipal service platform, are underutilized. Given this, online social media platforms serve as abundant sources of user-generated content that provide critical insights into the needs of individuals and populations. We extracted restaurant reviews and metadata from Yelp to identify potential outbreaks of foodborne illness in connection with consuming food from restaurants. Because the prevalence of foodborne illnesses may increase in warmer months as higher temperatures breed more favorable conditions for bacterial growth, we aimed to identify seasonal patterns in foodborne illness reports from 311 and identify seasonal patterns of foodborne illness from Yelp reviews for New York City restaurants using a Hierarchical Sigmoid Attention Network (HSAN). We found no evidence of significant bivariate associations between any variables of interest. Given the inherent limitations of relying solely on user-generated data for public health insights, it is imperative to complement these sources with other data streams and insights from subject matter experts. Future investigations should involve conducting these analyses at more granular spatial and temporal scales to explore the presence of such differences or associations.

Transformers, parallel computation, and logarithmic depth

We show that a constant number of self-attention layers can efficiently simulate, and be simulated by, a constant number of communication rounds of Massively Parallel Computation. As a consequence, we show that logarithmic depth is sufficient for transformers to solve basic computational tasks that cannot be efficiently solved by several other neural sequence models and sub-quadratic transformer approximations. We thus establish parallelism as a key distinguishing property of transformers.

Multi-group Learning for Hierarchical Groups

The multi-group learning model formalizes the learning scenario in which a single predictor must generalize well on multiple, possibly overlapping subgroups of interest. We extend the study of multi-group learning to the natural case where the groups are hierarchically structured. We design an algorithm for this setting that outputs an interpretable and deterministic decision tree predictor with near-optimal sample complexity. We then conduct an empirical evaluation of our algorithm and find that it achieves attractive generalization properties on real datasets with hierarchical group structure.

Polynomial time auditing of statistical subgroup fairness for Gaussian data

We study the problem of auditing classifiers with the notion of statistical subgroup fairness. Kearns et al. (2018) has shown that the problem of auditing combinatorial subgroups fairness is as hard as agnostic learning. Essentially all work on remedying statistical measures of discrimination against subgroups assumes access to an oracle for this problem, despite the fact that no efficient algorithms are known for it. If we assume the data distribution is Gaussian, or even merely log-concave, then a recent line of work has discovered efficient agnostic learning algorithms for halfspaces. Unfortunately, the boosting-style reductions given by Kearns et al. required the agnostic learning algorithm to succeed on reweighted distributions that may not be log-concave, even if the original data distribution was. In this work, we give positive and negative results on auditing for the Gaussian distribution: On the positive side, we an alternative approach to leverage these advances in agnostic learning and thereby obtain the first polynomial-time approximation scheme (PTAS) for auditing nontrivial combinatorial subgroup fairness: we show how to audit statistical notions of fairness over homogeneous halfspace subgroups when the features are Gaussian. On the negative side, we find that under cryptographic assumptions, no polynomial-time algorithm can guarantee any nontrivial auditing, even under Gaussian feature distributions, for general halfspace subgroups.

Efficient Estimation of the Central Mean Subspace via Smoothed Gradient Outer Products

We consider the problem of sufficient dimension reduction (SDR) for multi-index models. The estimators of the central mean subspace in prior works either have slow (non-parametric) convergence rates, or rely on stringent distributional conditions (e.g., the covariate distribution $P_{\mathbf{X}}$ being elliptical symmetric). In this paper, we show that a fast parametric convergence rate of form $C_d \cdot n^{-1/2}$ is achievable via estimating the \emph{expected smoothed gradient outer product}, for a general class of distribution $P_{\mathbf{X}}$ admitting Gaussian or heavier distributions. When the link function is a polynomial with a degree of at most $r$ and $P_{\mathbf{X}}$ is the standard Gaussian, we show that the prefactor depends on the ambient dimension $d$ as $C_d \propto d^r$.

On the sample complexity of estimation in logistic regression

The logistic regression model is one of the most popular data generation model in noisy binary classification problems. In this work, we study the sample complexity of estimating the parameters of the logistic regression model up to a given $\ell_2$ error, in terms of the dimension and the inverse temperature, with standard normal covariates. The inverse temperature controls the signal-to-noise ratio of the data generation process. While both generalization bounds and asymptotic performance of the maximum-likelihood estimator for logistic regression are well-studied, the non-asymptotic sample complexity that shows the dependence on error and the inverse temperature for parameter estimation is absent from previous analyses. We show that the sample complexity curve has two change-points (or critical points) in terms of the inverse temperature, clearly separating the low, moderate, and high temperature regimes.

Representational Strengths and Limitations of Transformers

Attention layers, as commonly used in transformers, form the backbone of modern deep learning, yet there is no mathematical description of their benefits and deficiencies as compared with other architectures. In this work we establish both positive and negative results on the representation power of attention layers, with a focus on intrinsic complexity parameters such as width, depth, and embedding dimension. On the positive side, we present a sparse averaging task, where recurrent networks and feedforward networks all have complexity scaling polynomially in the input size, whereas transformers scale merely logarithmically in the input size; furthermore, we use the same construction to show the necessity and role of a large embedding dimension in a transformer. On the negative side, we present a triple detection task, where attention layers in turn have complexity scaling linearly in the input size; as this scenario seems rare in practice, we also present natural variants that can be efficiently solved by attention layers. The proof techniques emphasize the value of communication complexity in the analysis of transformers and related models, and the role of sparse averaging as a prototypical attention task, which even finds use in the analysis of triple detection.

Group conditional validity via multi-group learning

We consider the problem of distribution-free conformal prediction and the criterion of group conditional validity. This criterion is motivated by many practical scenarios including hidden stratification and group fairness. Existing methods achieve such guarantees under either restrictive grouping structure or distributional assumptions, or they are overly-conservative under heteroskedastic noise. We propose a simple reduction to the problem of achieving validity guarantees for individual populations by leveraging algorithms for a problem called multi-group learning. This allows us to port theoretical guarantees from multi-group learning to obtain obtain sample complexity guarantees for conformal prediction. We also provide a new algorithm for multi-group learning for groups with hierarchical structure. Using this algorithm in our reduction leads to improved sample complexity guarantees with a simpler predictor structure.