ICML 2024 Papers

Since its debut in 2016, ResNet has become arguably the most favorable architecture in deep neural network (DNN) design. It effectively addresses the gradient vanishing/exploding issue in DNN training, allowing engineers to fully unleash DNN's potential in tackling challenging problems in various domains. Despite its practical success, an essential theoretical question remains largely open: how well/best can ResNet approximate functions? In this paper, we answer this question for several important function classes, including polynomials and smooth functions. In particular, we show that ResNet with constant width can approximate Lipschitz continuous function with a Lipschitz constant $\mu$ using $\mathcal{O}(c(d)(\varepsilon/\mu)^{-d/2})$ tunable weights, where $c(d)$ is a constant depending on the input dimension $d$ and $\epsilon>0$ is the target approximation error. Further, we extend such a result to Lebesgue-integrable functions with the upper bound characterized by the modulus of continuity. These results indicate a factor of $d$ reduction in the number of tunable weights compared with the classical results for ReLU networks. Our results are also order-optimal in $\varepsilon$, thus achieving optimal approximation rate, as they match a generalized lower bound derived in this paper. This work adds to the theoretical justifications for ResNet's stellar practical performance.

This work considers a repeated principal-agent bandit game, where the principal can only interact with her environment through the agent. The principal and the agent have misaligned objectives and the choice of action is only left to the agent. However, the principal can influence the agent's decisions by offering incentives which add up to his rewards. The principal aims to iteratively learn an incentive policy to maximize her own total utility. This framework extends usual bandit problems and is motivated by several practical applications, such as healthcare or ecological taxation, where traditionally used mechanism design theories often overlook the learning aspect of the problem. We present nearly optimal (with respect to a horizon $T$) learning algorithms for the principal's regret in both multi-armed and linear contextual settings. Finally, we support our theoretical guarantees through numerical experiments.

We demonstrate a substantial gap between the privacy guarantees of the Adaptive Batch Linear Queries (ABLQ) mechanism under different types of batch sampling: (i) Shuffling, and (ii) Poisson subsampling; the typical analysis of Differentially Private Stochastic Gradient Descent (DP-SGD) follows by interpreting it as a post-processing of ABLQ. While shuffling-based DP-SGD is more commonly used in practical implementations, it has not been amenable to easy privacy analysis, either analytically or even numerically. On the other hand, Poisson subsampling-based DP-SGD is challenging to scalably implement, but has a well-understood privacy analysis, with multiple open-source numerically tight privacy accountants available. This has led to a common practice of using shuffling-based DP-SGD in practice, but using the privacy analysis for the corresponding Poisson subsampling version. Our result shows that there can be a substantial gap between the privacy analysis when using the two types of batch sampling, and thus advises caution in reporting privacy parameters for DP-SGD.

Autonomous agents trained using deep reinforcement learning (RL) often lack the ability to successfully generalise to new environments, even when these environments share characteristics with the ones they have encountered during training. In this work, we investigate how the sampling of individual environment instances, or levels, affects the zero-shot generalisation (ZSG) ability of RL agents. We discover that, for deep actor-critic architectures sharing their base layers, prioritising levels according to their value loss minimises the mutual information between the agent's internal representation and the set of training levels in the generated training data. This provides a novel theoretical justification for the regularisation achieved by certain adaptive sampling strategies. We then turn our attention to unsupervised environment design (UED) methods, which assume control over level generation. We find that existing UED methods can significantly shift the training distribution, which translates to low ZSG performance. To prevent both overfitting and distributional shift, we introduce *data-regularised environment design* (DRED). DRED generates levels using a generative model trained to approximate the ground truth distribution of an initial set of level parameters. Through its grounding, DRED achieves significant improvements in ZSG over adaptive level sampling strategies and UED methods.

A common approach to explaining NLP models is to use importance measures that express which tokens are important for a prediction. Unfortunately, such explanations are often wrong despite being persuasive. Therefore, it is essential to measure their faithfulness. One such metric is if tokens are truly important, then masking them should result in worse model performance. However, token masking introduces out-of-distribution issues, and existing solutions that address this are computationally expensive and employ proxy models. Furthermore, other metrics are very limited in scope. This work proposes an inherently faithfulness measurable model that addresses these challenges. This is achieved using a novel fine-tuning method that incorporates masking, such that masking tokens become in-distribution by design. This differs from existing approaches, which are completely model-agnostic but are inapplicable in practice. We demonstrate the generality of our approach by applying it to 16 different datasets and validate it using statistical in-distribution tests. The faithfulness is then measured with 9 different importance measures. Because masking is in-distribution, importance measures that themselves use masking become consistently more faithful. Additionally, because the model makes faithfulness cheap to measure, we can optimize explanations towards maximal faithfulness; thus, our model becomes indirectly inherently explainable.

Static sparse training aims to train sparse models from scratch, achieving remarkable results in recent years. A key design choice is given by the sparse initialization, which determines the trainable sub-network through a binary mask. Existing methods mainly select such mask based on a predefined dense initialization. Such an approach may not efficiently leverage the mask's potential impact on the optimization. An alternative direction, inspired by research into dynamical isometry, is to introduce orthogonality in the sparse subnetwork, which helps in stabilizing the gradient signal. In this work, we propose Exact Orthogonal Initialization (EOI), a novel sparse orthogonal initialization scheme based on composing random Givens rotations. Contrary to other existing approaches, our method provides exact (not approximated) orthogonality and enables the creation of layers with arbitrary densities. We demonstrate the superior effectiveness and efficiency of EOI through experiments, consistently outperforming common sparse initialization techniques. Our method enables training highly sparse 1000-layer MLP and CNN networks without residual connections or normalization techniques, emphasizing the crucial role of weight initialization in static sparse training alongside sparse mask selection.

Discovering new drug molecules is a pivotal yet challenging process due to the near-infinitely large chemical space and notorious demands on time and resources. Numerous generative models have recently been introduced to accelerate the drug discovery process, but their progression to experimental validation remains limited, largely due to a lack of consideration for synthetic accessibility in practical settings. In this work, we introduce a novel framework that is capable of generating new chemical structures while ensuring synthetic accessibility. Specifically, we introduce a postfix notation of synthetic pathways to represent molecules in chemical space. Then, we design a transformer-based model to translate molecular graphs into postfix notations of synthesis. We highlight the model's ability to: (a) perform bottom-up synthesis planning more accurately, (b) generate structurally similar, synthesizable analogs for unsynthesizable molecules proposed by generative models with their properties preserved, and (c) explore the local synthesizable chemical space around hit molecules.

We propose a new procedure named PASOA, for Bayesian experimental design, that performs sequential design optimization by simultaneously providing accurate estimates of successive posterior distributions for parameter inference. The sequential design process is carried out via a contrastive estimation principle, using stochastic optimization and Sequential Monte Carlo (SMC) samplers to maximise the Expected Information Gain (EIG). As larger information gains are obtained for larger distances between successive posterior distributions, this EIG objective may worsen classical SMC performance. To handle this issue, tempering is proposed to have both a large information gain and an accurate SMC sampling, that we show is crucial for performance. This novel combination of stochastic optimization and tempered SMC allows to jointly handle design optimization and parameter inference. We provide a proof that the obtained optimal design estimators benefit from some consistency property. Numerical experiments confirm the potential of the approach, which outperforms other recent existing procedures.

Feedback Alignment (FA) methods are biologically inspired local learning rules for training neural networks with reduced communication between layers. While FA has potential applications in distributed and privacy-aware ML, limitations in multi-class classification and lack of theoretical understanding of the alignment mechanism have constrained its impact. This study introduces a unified framework elucidating the operational principles behind alignment in FA. Our key contributions include: (1) a novel conservation law linking changes in synaptic weights to implicit regularization that maintains alignment with the gradient, with support from experiments, (2) sufficient conditions for convergence based on the concept of alignment dominance, and (3) empirical analysis showing better alignment can enhance FA performance on complex multi-class tasks. Overall, these theoretical and practical advancements improve interpretability of bio-plausible learning rules and provide groundwork for developing enhanced FA algorithms.

We introduce a new framework for studying meta-learning methods using PAC-Bayesian theory. Its main advantage over previous work is that it allows for more flexibility in how the transfer of knowledge between tasks is realized. For previous approaches, this could only happen indirectly, by means of learning prior distributions over models. In contrast, the new generalization bounds that we prove express the process of meta-learning much more directly as learning the learning algorithm that should be used for future tasks. The flexibility of our framework makes it suitable to analyze a wide range of meta-learning mechanisms and even design new mechanisms. Other than our theoretical contributions we also show empirically that our framework improves the prediction quality in practical meta-learning mechanisms.

In this paper, we propose a novel approach to Bayesian experimental design for non-exchangeable data that formulates it as risk-sensitive policy optimization. We develop the Inside-Out SMC$^2$ algorithm, a nested sequential Monte Carlo technique to infer optimal designs, and embed it into a particle Markov chain Monte Carlo framework to perform gradient-based policy amortization. Our approach is distinct from other amortized experimental design techniques, as it does not rely on contrastive estimators. Numerical validation on a set of dynamical systems showcases the efficacy of our method in comparison to other state-of-the-art strategies.

Human motion taxonomies serve as high-level hierarchical abstractions that classify how humans move and interact with their environment. They have proven useful to analyse grasps, manipulation skills, and whole-body support poses. Despite substantial efforts devoted to design their hierarchy and underlying categories, their use remains limited. This may be attributed to the lack of computational models that fill the gap between the discrete hierarchical structure of the taxonomy and the high-dimensional heterogeneous data associated to its categories. To overcome this problem, we propose to model taxonomy data via hyperbolic embeddings that capture the associated hierarchical structure. We achieve this by formulating a novel Gaussian process hyperbolic latent variable model that incorporates the taxonomy structure through graph-based priors on the latent space and distance-preserving back constraints. We validate our model on three different human motion taxonomies to learn hyperbolic embeddings that faithfully preserve the original graph structure. We show that our model properly encodes unseen data from existing or new taxonomy categories, and outperforms its Euclidean and VAE-based counterparts. Finally, through proof-of-concept experiments, we show that our model may be used to generate realistic trajectories between the learned embeddings.

Effective brain representation learning is a key step toward the understanding of cognitive processes and diagnosis of neurological diseases/disorders. Existing studies have focused on either (1) voxel-level activity, where only a single weight relating the voxel activity to the task (i.e., aggregation of voxel activity over a time window) is considered, missing their temporal dynamics, or (2) functional connectivity of the brain in the level of region of interests, missing voxel-level activities. We bridge this gap and design BrainMixer, an unsupervised learning framework that effectively utilizes both functional connectivity and associated time series of voxels to learn voxel-level representation in an unsupervised manner. BrainMixer employs two simple yet effective MLP-based encoders to simultaneously learn the dynamics of voxel-level signals and their functional correlations. To encode voxel activity, BrainMixer fuses information across both time and voxel dimensions via a dynamic attention mechanism. To learn the structure of the functional connectivity, BrainMixer presents a temporal graph patching and encodes each patch by combining its nodes' features via a new adaptive temporal pooling. Our experiments show that BrainMixer attains outstanding performance and outperforms 14 baselines in different downstream tasks and setups.

Causal discovery aims to uncover cause-and-effect relationships encoded in causal graphs by leveraging observational, interventional data, or their combination. The majority of existing causal discovery methods are developed assuming infinite interventional data. We focus on interventional data efficiency and formalize causal discovery from the perspective of online learning, inspired by pure exploration in bandit problems. A graph separating system, consisting of interventions that cut every edge of the graph at least once, is sufficient for learning causal graphs when infinite interventional data is available, even in the worst case. We propose a track-and-stop causal discovery algorithm that adaptively selects interventions from the graph separating system via allocation matching and learns the causal graph based on sampling history. Given any desired confidence value, the algorithm determines a termination condition and runs until it is met. We analyze the algorithm to establish a problem-dependent upper bound on the expected number of required interventional samples. Our proposed algorithm outperforms existing methods in simulations across various randomly generated causal graphs. It achieves higher accuracy, measured by the structural hamming distance (SHD) between the learned causal graph and the ground truth, with significantly fewer samples.

Mixup is a highly successful technique to improve generalization by augmenting training data with combinations of random pairs. Selective mixup is a family of methods that apply mixup to specific pairs e.g. combining examples across classes or domains. Despite remarkable performance on benchmarks with distribution shifts, these methods are still poorly understood. We find that an overlooked aspect of selective mixup explains some of its success in a completely new light. The non-random selection of pairs affects the training distribution and improves generalization by means completely unrelated to the mixing. For example in binary classification, mixup across classes implicitly resamples the data to uniform class distribution - a classical solution to label shift. We verify empirically that this resampling explains some of the improvements reported in prior work. Theoretically, the effect relies on a ``regression toward the mean'', an accidental property we find in several datasets. Outcomes. We now better understand why selective mixup works. This lets us predict a yet-unknown failure mode and conditions where the method is detrimental. We also use the equivalence with resampling to design better variants that combine mixing and resampling effects.

The growing significance of RNA engineering in diverse biological applications has spurred interest in developing AI methods for structure-based RNA design. While diffusion models have excelled in protein design, adapting them for RNA presents new challenges due to RNA's conformational flexibility and the computational cost of fine-tuning large structure prediction models. To this end, we propose RNAFlow, a flow matching model for protein-conditioned RNA sequence-structure design. Its denoising network integrates an RNA inverse folding model and a pre-trained RosettaFold2NA network for generation of RNA sequences and structures. The integration of inverse folding in the structure denoising process allows us to simplify training by fixing the structure prediction network. We further enhance the inverse folding model by conditioning it on inferred conformational ensembles to model dynamic RNA conformations. Evaluation on protein-conditioned RNA structure and sequence generation tasks demonstrates RNAFlow's advantage over existing RNA design methods.

Cardinality sketches are popular data structures that enhance the efficiency of working with large data sets. The sketches are randomized representations of sets that are only of logarithmic size but can support set merges and approximate cardinality (i.e., distinct count) queries. When queries are not adaptive, that is, they do not depend on preceding query responses, the design provides strong guarantees of correctly answering a number of queries exponential in the sketch size $k$. In this work, we investigate the performance of cardinality sketches in adaptive settings and unveil inherent vulnerabilities. We design an attack against the ``standard'' estimators that constructs an adversarial input by post-processing responses to a set of simple non-adaptive queries of size linear in the sketch size $k$. Empirically, our attack used only $4k$ queries with the widely used HyperLogLog (HLL++) Flajolet et al., 2007; Heule et al., 2013) sketch. The simple attack technique suggests it can be effective with post-processed natural workloads. Finally and importantly, we demonstrate that the vulnerability is inherent as any estimator applied to known sketch structures can be attacked using a number of queries that is quadratic in $k$, matching a generic upper bound.

In this paper, we present Partially Stochastic Infinitely Deep Bayesian Neural Networks, a novel family of architectures that integrates partial stochasticity into the framework of infinitely deep neural networks. Our new class of architectures is designed to improve the computational efficiency of existing architectures at training and inference time. To do this, we leverage the advantages of partial stochasticity in the infinite-depth limit which include the benefits of full stochasticity e.g. robustness, uncertainty quantification, and memory efficiency, whilst improving their limitations around computational complexity. We present a variety of architectural configurations, offering flexibility in network design including different methods for weight partition. We also provide mathematical guarantees on the expressivity of our models by establishing that our network family qualifies as Universal Conditional Distribution Approximators. Lastly, empirical evaluations across multiple tasks show that our proposed architectures achieve better downstream task performance and uncertainty quantification than their counterparts while being significantly more efficient. The code can be found at https://github.com/Sergio20f/part_stoch_inf_deep

In differentially private (DP) machine learning, the privacy guarantees of DP mechanisms are often reported and compared on the basis of a single $(\varepsilon, \delta)$-pair. This practice overlooks that DP guarantees can vary substantially even between mechanisms sharing a given $(\varepsilon, \delta)$, and potentially introduces privacy vulnerabilities which can remain undetected. This motivates the need for robust, rigorous methods for comparing DP guarantees in such cases. Here, we introduce the $\Delta$-divergence between mechanisms which quantifies the worst-case excess privacy vulnerability of choosing one mechanism over another in terms of $(\varepsilon, \delta)$, $f$-DP and in terms of a newly presented Bayesian interpretation. Moreover, as a generalisation of the Blackwell theorem, it is endowed with strong decision-theoretic foundations. Through application examples, we show that our techniques can facilitate informed decision-making and reveal gaps in the current understanding of privacy risks, as current practices in DP-SGD often result in choosing mechanisms with high excess privacy vulnerabilities.