ICLR 2024 Papers

We consider a binary classification problem under group fairness constraints, which can be one of Demographic Parity (DP), Equalized Opportunity (EOp), or Equalized Odds (EO). We propose an explicit characterization of Bayes optimal classifier under the fairness constraints, which turns out to be a simple modification rule of the unconstrained classifier. Namely, we introduce a novel instance-level measure of bias, which we call bias score, and the modification rule is a simple linear rule on top of the finite amount of bias scores. Based on this characterization, we develop a post-hoc approach that allows us to adapt to fairness constraints while maintaining high accuracy. In the case of DP and EOp constraints, the modification rule is thresholding a single bias score, while in the case of EO constraints we are required to fit a linear modification rule with 2 parameters. The method can also be applied for composite group-fairness criteria, such as ones involving several sensitive attributes. We achieve competitive or better performance compared to both in-processing and post-processing methods across three datasets: Adult, COMPAS, and CelebA. Unlike most post-processing methods, we do not require access to sensitive attributes during the inference time.

In many domains, autoregressive models can attain high likelihood on the task of predicting the next observation. However, this maximum-likelihood (MLE) objective does not necessarily match a downstream use-case of autoregressively generating high-quality sequences. The MLE objective weights sequences proportionally to their frequency under the data distribution, with no guidance for the model's behaviour out of distribution (OOD): leading to compounding error during autoregressive generation. In order to address this compounding error problem, we formulate sequence generation as an imitation learning (IL) problem. This allows us to minimize a variety of divergences between the distribution of sequences generated by an autoregressive model and sequences from a dataset, including divergences with weight on OOD generated sequences. The IL framework also allows us to incorporate backtracking by introducing a backspace action into the generation process. This further mitigates the compounding error problem by allowing the model to revert a sampled token if it takes the sequence OOD. Our resulting method, SequenceMatch, can be implemented without adversarial training or major architectural changes. We identify the SequenceMatch-χ2 divergence as a more suitable training objective for autoregressive models which are used for generation. We show that empirically, SequenceMatch training leads to improvements over MLE on text generation with language models and arithmetic

Developing autonomous agents that can interact with changing environments is an open challenge in machine learning. Robustness is particularly important in these settings as agents are often fit offline on expert demonstrations but deployed online where they must generalize to the closed feedback loop within the environment. In this work, we explore the application of recurrent neural networks to tasks of this nature and understand how a parameterization of their recurrent connectivity influences robustness in closed-loop settings. Specifically, we represent the recurrent connectivity as a function of rank and sparsity and show both theoretically and empirically that modulating these two variables has desirable effects on network dynamics. The proposed low-rank, sparse connectivity induces an interpretable prior on the network that proves to be most amenable for a class of models known as closed-form continuous-time neural networks (CfCs). We find that CfCs with fewer parameters can outperform their full-rank, fully-connected counterparts in the online setting under distribution shift. This yields memory-efficient and robust agents while opening a new perspective on how we can modulate network dynamics through connectivity.

Widely used language models (LMs) are typically built by scaling up a two-stage training pipeline: a pre-training stage that uses a very large, diverse dataset of text and a fine-tuning (sometimes, 'alignment') stage that uses targeted examples or other specifications of desired behaviors. While it has been hypothesized that knowledge and skills come from pre-training, and fine-tuning mostly filters this knowledge and skillset, this intuition has not been extensively tested. To aid in doing so, we introduce a novel technique for decoupling the knowledge and skills gained in these two stages, enabling a direct answer to the question, *What would happen if we combined the knowledge learned by a large model during pre-training with the knowledge learned by a small model during fine-tuning (or vice versa)?* Using an RL-based framework derived from recent developments in learning from human preferences, we introduce *emulated fine-tuning (EFT)*, a principled and practical method for sampling from a distribution that approximates (or 'emulates') the result of pre-training and fine-tuning at different scales. Our experiments with EFT show that scaling up fine-tuning tends to improve helpfulness, while scaling up pre-training tends to improve factuality. Beyond decoupling scale, we show that EFT enables test-time adjustment of competing behavioral traits like helpfulness and harmlessness without additional training. Finally, a special case of emulated fine-tuning, which we call LM *up-scaling*, avoids resource-intensive fine-tuning of large pre-trained models by ensembling them with small fine-tuned models, essentially emulating the result of fine-tuning the large pre-trained model. Up-scaling consistently improves helpfulness and factuality of instruction-following models in the Llama, Llama-2, and Falcon families, without additional hyperparameters or training. For reference implementation, see [https://github.com/eric-mitchell/emulated-fine-tuning](https://github.com/eric-mitchell/emulated-fine-tuning).

Mechanistic interpretability aims to attribute high-level model behaviors to specific, interpretable learned features. It is hypothesized that these features manifest as directions or low-dimensional subspaces within activation space. Accordingly, recent studies have explored the identification and manipulation of such subspaces to reverse-engineer computations, employing methods such as activation patching. In this work, we demonstrate that naïve approaches to subspace interventions can give rise to interpretability illusions. Specifically, even if patching along a subspace has the intended end-to-end causal effect on model behavior, this effect may be achieved by activating \emph{a dormant parallel pathway} using a component that is \textit{causally disconnected} from the model output. We demonstrate this in a mathematical example, realize the example empirically in two different settings (the Indirect Object Identification (IOI) task and factual recall), and argue that activating dormant pathways ought to be prevalent in practice. In the context of factual recall, we further show that the illusion is related to rank-1 fact editing, providing a mechanistic explanation for previous work observing an inconsistency between fact editing performance and fact localisation. However, this does not imply that activation patching of subspaces is intrinsically unfit for interpretability. To contextualize our findings, we also show what a success case looks like in a task (IOI) where prior manual circuit analysis allows an understanding of the location of the ground truth feature. We explore the additional evidence needed to argue that a patched subspace is faithful.

Prompt-tuning has demonstrated impressive performance in continual learning by querying relevant prompts for each input instance, which can avoid the introduction of task identifier. Its forgetting is therefore reduced as this instance-wise query mechanism enables us to select and update only relevant prompts. In this paper, we further integrate prompt-tuning with gradient projection approach. Our observation is: prompt-tuning releases the necessity of task identifier for gradient projection method; and gradient projection provides theoretical guarantees against forgetting for prompt-tuning. This inspires a new prompt gradient projection approach (PGP) for continual learning. In PGP, we deduce that reaching the orthogonal condition for prompt gradient can effectively prevent forgetting via the self-attention mechanism in vision-transformer. The condition equations are then realized by conducting Singular Value Decomposition (SVD) on an element-wise sum space between input space and prompt space. We validate our method on diverse datasets and experiments demonstrate the efficiency of reducing forgetting both in class incremental, online class incremental, and task incremental settings. The code is available at https://github.com/JingyangQiao/prompt-gradient-projection.

Krylov subspace, which is generated by multiplying a given vector by the matrix of a linear transformation and its successive powers, has been extensively studied in classical optimization literature to design algorithms that converge quickly for large linear inverse problems. For example, the conjugate gradient method (CG), one of the most popular Krylov subspace methods, is based on the idea of minimizing the residual error in the Krylov subspace. However, with the recent advancement of high-performance diffusion solvers for inverse problems, it is not clear how classical wisdom can be synergistically combined with modern diffusion models. In this study, we propose a novel and efficient diffusion sampling strategy that synergistically combines the diffusion sampling and Krylov subspace methods. Specifically, we prove that if the tangent space at a denoised sample by Tweedie's formula forms a Krylov subspace, then the CG initialized with the denoised data ensures the data consistency update to remain in the tangent space. This negates the need to compute the manifold-constrained gradient (MCG), leading to a more efficient diffusion sampling method. Our method is applicable regardless of the parametrization and setting (i.e., VE, VP). Notably, we achieve state-of-the-art reconstruction quality on challenging real-world medical inverse imaging problems, including multi-coil MRI reconstruction and 3D CT reconstruction. Moreover, our proposed method achieves more than 80 times faster inference time than the previous state-of-the-art method. Code is available at https://github.com/HJ-harry/DDS

State-space models (SSMs) have recently emerged as a framework for learning long-range sequence tasks. An example is the structured state-space sequence (S4) layer, which uses the diagonal-plus-low-rank structure of the HiPPO initialization framework. However, the complicated structure of the S4 layer poses challenges; and, in an effort to address these challenges, models such as S4D and S5 have considered a purely diagonal structure. This choice simplifies the implementation, improves computational efficiency, and allows channel communication. However, diagonalizing the HiPPO framework is itself an ill-posed problem. In this paper, we propose a general solution for this and related ill-posed diagonalization problems in machine learning. We introduce a generic, backward-stable ``perturb-then-diagonalize'' (PTD) methodology, which is based on the pseudospectral theory of non-normal operators, and which may be interpreted as the approximate diagonalization of the non-normal matrices defining SSMs. Based on this, we introduce the S4-PTD and S5-PTD models. Through theoretical analysis of the transfer functions of different initialization schemes, we demonstrate that the S4-PTD/S5-PTD initialization strongly converges to the HiPPO framework, while the S4D/S5 initialization only achieves weak convergences. As a result, our new models show resilience to Fourier-mode noise-perturbed inputs, a crucial property not achieved by the S4D/S5 models. In addition to improved robustness, our S5-PTD model averages 87.6% accuracy on the Long-Range Arena benchmark, demonstrating that the PTD methodology helps to improve the accuracy of deep learning models.

Federated Learning (FL) is an important privacy-preserving learning paradigm that plays an important role in the Intelligent Internet of Things. Training a global model in FL, however, is vulnerable to the noise in the heterogeneous data across the clients. In this paper, we introduce **FedTrans**, a novel client-transparent client utility estimation method designed to guide client selection for noisy scenarios, mitigating performance degradation problems. To estimate the client utility, we propose a Bayesian framework that models client utility and its relationships with the weight parameters and the performance of local models. We then introduce a variational inference algorithm to effectively infer client utility, given only a small amount of auxiliary data. Our evaluation demonstrates that leveraging FedTrans as a guide for client selection can lead to a better accuracy performance (up to 7.8\%), ensuring robustness in noisy scenarios.

Physics-Informed Neural Networks (PINNs) have emerged as a promising deep learning framework for approximating numerical solutions to partial differential equations (PDEs). However, conventional PINNs, relying on multilayer perceptrons (MLP), neglect the crucial temporal dependencies inherent in practical physics systems and thus fail to propagate the initial condition constraints globally and accurately capture the true solutions under various scenarios. In this paper, we introduce a novel Transformer-based framework, termed PINNsFormer, designed to address this limitation. PINNsFormer can accurately approximate PDE solutions by utilizing multi-head attention mechanisms to capture temporal dependencies. PINNsFormer transforms point-wise inputs into pseudo sequences and replaces point-wise PINNs loss with a sequential loss. Additionally, it incorporates a novel activation function, \texttt{Wavelet}, which anticipates Fourier decomposition through deep neural networks. Empirical results demonstrate that PINNsFormer achieves superior generalization ability and accuracy across various scenarios, including PINNs failure modes and high-dimensional PDEs. Moreover, PINNsFormer offers flexibility in integrating existing learning schemes for PINNs, further enhancing its performance.

As LLMs become commonplace, machine-generated text has the potential to flood the internet with spam, social media bots, and valueless content. _Watermarking_ is a simple and effective strategy for mitigating such harms by enabling the detection and documentation of LLM-generated text. Yet a crucial question remains: How reliable is watermarking in realistic settings in the wild? There, watermarked text may be modified to suit a user's needs, or entirely rewritten to avoid detection. We study the robustness of watermarked text after it is re-written by humans, paraphrased by a non-watermarked LLM, or mixed into a longer hand-written document. We find that watermarks remain detectable even after human and machine paraphrasing. While these attacks dilute the strength of the watermark, paraphrases are statistically likely to leak n-grams or even longer fragments of the original text, resulting in high-confidence detections when enough tokens are observed. For example, after strong human paraphrasing the watermark is detectable after observing 800 tokens on average, when setting a $1\mathrm{e}{-5}$ false positive rate. We also consider a range of new detection schemes that are sensitive to short spans of watermarked text embedded inside a large document, and we compare the robustness of watermarking to other kinds of detectors.

Real-world classifiers can benefit from the option of abstaining from predicting on samples where they have low confidence. Such abstention is particularly useful on samples which are close to the learned decision boundary, or which are outliers with respect to the training sample. These settings have been the subject of extensive but disjoint study in the selective classification (SC) and out-of-distribution (OOD) detection literature. Recent work on selective classification with OOD detection (SCOD) has argued for the unified study of these problems; however, the formal underpinnings of this problem are still nascent, and existing techniques are heuristic in nature. In this paper, we propose new plugin estimators for SCOD that are theoretically grounded, effective, and generalise existing approaches from the SC and OOD detection literature. In the course of our analysis, we formally explicate how naïve use of existing SC and OOD detection baselines may be inadequate for SCOD. We empirically demonstrate that our approaches yields competitive SC and OOD detection trade-offs compared to common baselines.

Learned lossless data compression has garnered significant attention recently due to its superior compression ratios compared to traditional compressors. However, the computational efficiency of these models jeopardizes their practicality. This paper proposes a novel system for improving the compression ratio while maintaining computational efficiency for learned lossless data compression. Our approach incorporates two essential innovations. First, we propose the Finite-State AutoRegressive (FSAR) entropy coder, an efficient autoregressive Markov model based entropy coder that utilizes a lookup table to expedite autoregressive entropy coding. Next, we present a Straight-Through Hardmax Quantization (STHQ) scheme to enhance the optimization of discrete latent space. Our experiments show that the proposed lossless compression method could improve the compression ratio by up to 6\% compared to the baseline, with negligible extra computational time. Our work provides valuable insights into enhancing the computational efficiency of learned lossless data compression, which can have practical applications in various fields. Code is available at https://github.com/alipay/Finite_State_Autoregressive_Entropy_Coding.

In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we study the landscape of BO through the lens of penalty methods, in which the upper- and lower-level objectives are combined in a weighted sum with penalty parameter $\sigma > 0$. In particular, we establish a strong connection between the penalty function and the hyper-objective by explicitly characterizing the conditions under which the values and derivatives of the two must be $O(\sigma)$-close. A by-product of our analysis is the explicit formula for the gradient of hyper-objective when the lower-level problem has multiple solutions under minimal conditions, which could be of independent interest. Next, viewing the penalty formulation as $O(\sigma)$-approximation of the original BO, we propose first-order algorithms that find an $\epsilon$-stationary solution by optimizing the penalty formulation with $\sigma = O(\epsilon)$. When the perturbed lower-level problem uniformly satisfies the {\it small-error} proximal error-bound (EB) condition, we propose a first-order algorithm that converges to an $\epsilon$-stationary point of the penalty function using in total $O(\epsilon^{-7})$ accesses to first-order stochastic gradient oracles. Under an additional assumption on stochastic oracles, we show that the algorithm can be implemented in a fully {\it single-loop} manner, {\it i.e.,} with $O(1)$ samples per iteration, and achieves the improved oracle-complexity of $O(\epsilon^{-5})$.

Federated learning (FL) inevitably confronts the challenge of system heterogeneity in practical scenarios. To enhance the capabilities of most model-homogeneous FL methods in handling system heterogeneity, we propose a training scheme that can extend their capabilities to cope with this challenge. In this paper, we commence our study with a detailed exploration of homogeneous and heterogeneous FL settings and discover three key observations: (1) a positive correlation between client performance and layer similarities, (2) higher similarities in the shallow layers in contrast to the deep layers, and (3) the smoother gradients distributions indicate the higher layer similarities. Building upon these observations, we propose InCo Aggregation that leverages internal cross-layer gradients, a mixture of gradients from shallow and deep layers within a server model, to augment the similarity in the deep layers without requiring additional communication between clients. Furthermore, our methods can be tailored to accommodate model-homogeneous FL methods such as FedAvg, FedProx, FedNova, Scaffold, and MOON, to expand their capabilities to handle the system heterogeneity. Copious experimental results validate the effectiveness of InCo Aggregation, spotlighting internal cross-layer gradients as a promising avenue to enhance the performance in heterogeneous FL.

Many recent efforts augment language models with retrieval, by adding retrieved data to the input context. For this approach to succeed, the retrieved data must be added at both training and test time. Moreover, as input length grows linearly with the size of retrieved data, cost in computation and memory grows quadratically for modern Transformers. To avoid these complications, we simply fine-tune the model on retrieved data at test time, using its standard training setup. We build a large-scale distributed index based on text embeddings of the Pile dataset. For each test input, our system retrieves its neighbors and fine-tunes the model on their text. Surprisingly, retrieving and training on as few as 20 neighbors, each for only one gradient iteration, drastically improves performance across more than 20 language modeling tasks in the Pile. For example, test-time training with nearest neighbors significantly narrows the performance gap between a small GPT-2 and a GPT-Neo model more than 10 times larger. Sufficient index quality and size, however, are necessary. Our work establishes a first baseline of test-time training for language modeling.

Real-life applications of deep neural networks are hindered by their unsteady predictions when faced with noisy inputs and adversarial attacks. The certified radius in this context is a crucial indicator of the robustness of models. However how to design an efficient classifier with an associated certified radius? Randomized smoothing provides a promising framework by relying on noise injection into the inputs to obtain a smoothed and robust classifier. In this paper, we first show that the variance introduced by the Monte-Carlo sampling in the randomized smoothing procedure estimate closely interacts with two other important properties of the classifier, \textit{i.e.} its Lipschitz constant and margin. More precisely, our work emphasizes the dual impact of the Lipschitz constant of the base classifier, on both the smoothed classifier and the empirical variance. To increase the certified robust radius, we introduce a different way to convert logits to probability vectors for the base classifier to leverage the variance-margin trade-off. We leverage the use of Bernstein's concentration inequality along with enhanced Lipschitz bounds for randomized smoothing. Experimental results show a significant improvement in certified accuracy compared to current state-of-the-art methods. Our novel certification procedure allows us to use pre-trained models with randomized smoothing, effectively improving the current certification radius in a zero-shot manner.

Randomized Smoothing (RS) has been proven a promising method for endowing an arbitrary image classifier with certified robustness. However, the substantial uncertainty inherent in the high-dimensional isotropic Gaussian noise imposes the curse of dimensionality on RS. Specifically, the upper bound of ${\ell_2}$ certified robustness radius provided by RS exhibits a diminishing trend with the expansion of the input dimension $d$, proportionally decreasing at a rate of $1/\sqrt{d}$. This paper explores the feasibility of providing ${\ell_2}$ certified robustness for high-dimensional input through the utilization of dual smoothing in the lower-dimensional space. The proposed Dual Randomized Smoothing (DRS) down-samples the input image into two sub-images and smooths the two sub-images in lower dimensions. Theoretically, we prove that DRS guarantees a tight ${\ell_2}$ certified robustness radius for the original input and reveal that DRS attains a superior upper bound on the ${\ell_2}$ robustness radius, which decreases proportionally at a rate of $(1/\sqrt m + 1/\sqrt n )$ with $m+n=d$. Extensive experiments demonstrate the generalizability and effectiveness of DRS, which exhibits a notable capability to integrate with established methodologies, yielding substantial improvements in both accuracy and ${\ell_2}$ certified robustness baselines of RS on the CIFAR-10 and ImageNet datasets. Code is available at https://github.com/xiasong0501/DRS.

Diffusion models, as a kind of powerful generative model, have given impressive results on image super-resolution (SR) tasks. However, due to the randomness introduced in the reverse process of diffusion models, the performances of diffusion-based SR models are fluctuating at every time of sampling, especially for samplers with few resampled steps. This inherent randomness of diffusion models results in ineffectiveness and instability, making it challenging for users to guarantee the quality of SR results. However, our work takes this randomness as an opportunity: fully analyzing and leveraging it leads to the construction of an effective plug-and-play sampling method that owns the potential to benefit a series of diffusion-based SR methods. More in detail, we propose to steadily sample high-quality SR images from pre-trained diffusion-based SR models by solving diffusion ordinary differential equations (diffusion ODEs) with optimal boundary conditions (BCs) and analyze the characteristics between the choices of BCs and their corresponding SR results. Our analysis shows the route to obtain an approximately optimal BC via an efficient exploration in the whole space. The quality of SR results sampled by the proposed method with fewer steps outperforms the quality of results sampled by current methods with randomness from the same pre-trained diffusion-based SR model, which means that our sampling method ''boosts'' current diffusion-based SR models without any additional training.