Edoardo Cetin, Philip Ball, Stephen Roberts, Oya Celiktutan

Off-policy reinforcement learning (RL) from pixel observations is notoriously unstable. As a result, many successful algorithms must combine different domain-specific practices and auxiliary losses to learn meaningful behaviors in complex environments. In this work, we provide novel analysis demonstrating that these instabilities arise from performing temporal-difference learning with a convolutional encoder and low-magnitude rewards. We show that this new visual deadly triad causes unstable training and premature convergence to degenerate solutions, a phenomenon we name catastrophic self-overfitting. Based on our analysis, we propose A-LIX, a method providing adaptive regularization to the encoder's gradients that explicitly prevents the occurrence of catastrophic self-overfitting using a dual objective. By applying A-LIX, we significantly outperform the prior state-of-the-art on the DeepMind Control and Atari benchmarks without any data augmentation or auxiliary losses.

David Ireland, Giovanni Montana

Combinatorial Optimisation problems arise in several application domains and are often formulated in terms of graphs. Many of these problems are NP-hard, but exact solutions are not always needed. Several heuristics have been developed to provide near-optimal solutions; however, they do not typically scale well with the size of the graph. We propose a low-complexity approach for identifying a (possibly much smaller) subgraph of the original graph where the heuristics can be run in reasonable time and with a high likelihood of finding a global near-optimal solution. The core component of our approach is LeNSE, a reinforcement learning algorithm that learns how to navigate the space of possible subgraphs using an Euclidean subgraph embedding as its map. To solve CO problems, LeNSE is provided with a discriminative embedding trained using any existing heuristics using only on a small portion of the original graph. When tested on three problems (vertex cover, max-cut and influence maximisation) using real graphs with up to $10$ million edges, LeNSE identifies small subgraphs yielding solutions comparable to those found by running the heuristics on the entire graph, but at a fraction of the total run time. Code for the experiments is available in the public GitHub repo at https://github.com/davidireland3/LeNSE.

Nicola Branchini, Virginia Aglietti, Neil Dhir, Theodoros Damoulas

We study the problem of globally optimizing the causal effect on a target variable of an unknown causal graph in which interventions can be performed. This problem arises in many areas of science including biology, operations research and healthcare. We propose Causal Entropy Optimization (CEO), a framework that generalizes Causal Bayesian Optimization (CBO) to account for all sources of uncertainty, including the one arising from the causal graph structure. CEO incorporates the causal structure uncertainty both in the surrogate models for the causal effects and in the mechanism used to select interventions via an information-theoretic acquisition function. The resulting algorithm automatically trades-off structure learning and causal effect optimization, while naturally accounting for observation noise. For various synthetic and real-world structural causal models, CEO achieves faster convergence to the global optimum compared with CBO while also learning the graph. Furthermore, our joint approach to structure learning and causal optimization improves upon sequential, structure-learning-first approaches.

Sanae Lotfi, Pavel Izmailov, Gregory Benton, Micah Goldblum, Andrew Wilson

How do we compare between hypotheses that are entirely consistent with observations? The marginal likelihood (aka Bayesian evidence), which represents the probability of generating our observations from a prior, provides a distinctive approach to this foundational question, automatically encoding Occam's razor. Although it has been observed that the marginal likelihood can overfit and is sensitive to prior assumptions, its limitations for hyperparameter learning and discrete model comparison have not been thoroughly investigated. We first revisit the appealing properties of the marginal likelihood for learning constraints and hypothesis testing. We then highlight the conceptual and practical issues in using the marginal likelihood as a proxy for generalization. Namely, we show how marginal likelihood can be negatively correlated with generalization, with implications for neural architecture search, and can lead to both underfitting and overfitting in hyperparameter learning. We provide a partial remedy through a conditional marginal likelihood, which we show is more aligned with generalization, and practically valuable for large-scale hyperparameter learning, such as in deep kernel learning.

Abdullah Alchihabi, Yuhong Guo

Graph Neural Networks (GNNs) require a relatively large number of labeled nodes and a reliable/uncorrupted graph connectivity structure to obtain good performance on the semi-supervised node classification task. The performance of GNNs can degrade significantly as the number of labeled nodes decreases or the graph connectivity structure is corrupted by adversarial attacks or noise in data measurement/collection. Therefore, it is important to develop GNN models that are able to achieve good performance when there is limited supervision knowledge–a few labeled nodes and a noisy graph structure. In this paper, we propose a novel Dual GNN learning framework to address this challenging task. The proposed framework has two GNN based node prediction modules. The primary module uses the input graph structure to induce typical node embeddings and predictions with a regular GNN baseline, while the auxiliary module constructs a new graph structure through fine-grained spectral clustering and learns new node embeddings and predictions. By integrating the two modules in a dual GNN learning framework, we perform joint learning in an end-to-end fashion. This general framework can be applied on many GNN baseline models. The experimental results show that the proposed dual GNN framework can greatly outperform the GNN baseline methods and yield superior performance over many state-of-the-art methods when the labeled nodes are scarce and the graph connectivity structure is noisy.

Lukas Zierahn, Dirk van der Hoeven, Nicolò Cesa-Bianchi, Gergely Neu

We study a contextual version of online combinatorial optimisation with full and semi-bandit feedback. In this sequential decision-making problem, an online learner has to select an action from a combinatorial decision space after seeing a vector-valued context in each round. As a result of its action, the learner incurs a loss that is a bilinear function of the context vector and the vector representation of the chosen action. We consider two natural versions of the problem: semi-bandit where the losses are revealed for each component appearing in the learner’s combinatorial action, and full-bandit where only the total loss is observed. We design computationally efficient algorithms based on a new loss estimator that takes advantage of the special structure of the problem, and show regret bounds order $\sqrt{T}$ with respect to the time horizon. The bounds demonstrate polynomial scaling with the relevant problem parameters which is shown to be nearly optimal. The theoretical results are complemented by a set of experiments on simulated data.

Huilin Qu, Congqiao Li, Sitian Qian

Jet tagging is a critical yet challenging classification task in particle physics. While deep learning has transformed jet tagging and significantly improved performance, the lack of a large-scale public dataset impedes further enhancement. In this work, we present JetClass, a new comprehensive dataset for jet tagging. The JetClass dataset consists of 100 M jets, about two orders of magnitude larger than existing public datasets. A total of 10 types of jets are simulated, including several types unexplored for tagging so far. Based on the large dataset, we propose a new Transformer-based architecture for jet tagging, called Particle Transformer (ParT). By incorporating pairwise particle interactions in the attention mechanism, ParT achieves higher tagging performance than a plain Transformer and surpasses the previous state-of-the-art, ParticleNet, by a large margin. The pre-trained ParT models, once fine-tuned, also substantially enhance the performance on two widely adopted jet tagging benchmarks. The dataset, code and models are publicly available at https://github.com/jet-universe/particle_transformer.

Srshti Putcha, Christopher Nemeth, Paul Fearnhead

Stochastic gradient MCMC (SGMCMC) offers a scalable alternative to traditional MCMC, by constructing an unbiased estimate of the gradient of the log-posterior with a small, uniformly-weighted subsample of the data. While efficient to compute, the resulting gradient estimator may exhibit a high variance and impact sampler performance. The problem of variance control has been traditionally addressed by constructing a better stochastic gradient estimator, often using control variates. We propose to use a discrete, non-uniform probability distribution to preferentially subsample data points that have a greater impact on the stochastic gradient. In addition, we present a method of adaptively adjusting the subsample size at each iteration of the algorithm, so that we increase the subsample size in areas of the sample space where the gradient is harder to estimate. We demonstrate that such an approach can maintain the same level of accuracy while substantially reducing the average subsample size that is used.

Tian Zhou, Ziqing MA, Qingsong Wen, Xue Wang, Liang Sun, rong jin

Long-term time series forecasting is challenging since prediction accuracy tends to decrease dramatically with the increasing horizon. Although Transformer-based methods have significantly improved state-of-the-art results for long-term forecasting, they are not only computationally expensive but more importantly, are unable to capture the global view of time series (e.g. overall trend). To address these problems, we propose to combine Transformer with the seasonal-trend decomposition method, in which the decomposition method captures the global profile of time series while Transformers capture more detailed structures. To further enhance the performance of Transformer for long-term prediction, we exploit the fact that most time series tend to have a sparse representation in a well-known basis such as Fourier transform, and develop a frequency enhanced Transformer. Besides being more effective, the proposed method, termed as Frequency Enhanced Decomposed Transformer (FEDformer), is more efficient than standard Transformer with a linear complexity to the sequence length. Our empirical studies with six benchmark datasets show that compared with state-of-the-art methods, Fedformer can reduce prediction error by 14.8% and 22.6% for multivariate and univariate time series, respectively. Code is publicly available at https://github.com/MAZiqing/FEDformer.

Christian Carmona, Geoff Nicholls

Bayesian statistical inference loses predictive optimality when generative models are misspecified.Working within an existing coherent loss-based generalisation of Bayesian inference, we show existing Modular/Cut-model inference is coherent, and write down a new family of Semi-Modular Inference (SMI) schemes, indexed by an influence parameter, with Bayesian inference and Cut-models as special cases. We give a meta-learning criterion and estimation procedure to choose the inference scheme. This returns Bayesian inference when there is no misspecification.The framework applies naturally to Multi-modular models. Cut-model inference allows directed information flow from well-specified modules to misspecified modules, but not vice versa. An existing alternative power posterior method gives tunable but undirected control of information flow, improving prediction in some settings. In contrast, SMI allows \emph{tunable and directed} information flow between modules.We illustrate our methods on two standard test cases from the literature and a motivating archaeological data set.

Bo Li, Qili Wang, Gim Hee Lee

Steerable CNN imposes the prior knowledge of transformation invariance or equivariance in the network architecture to enhance the the network robustness on geometry transformation of data and reduce overfitting. It has been an intuitive and widely used technique to construct a steerable filter by augmenting a filter with its transformed copies in the past decades, which is named as filter transform in this paper. Recently, the problem of steerable CNN has been studied from aspect of group representation theory, which reveals the function space structure of a steerable kernel function. However, it is not yet clear on how this theory is related to the filter transform technique. In this paper, we show that kernel constructed by filter transform can also be interpreted in the group representation theory. This interpretation help complete the puzzle of steerable CNN theory and provides a novel and simple approach to implement steerable convolution operators. Experiments are executed on multiple datasets to verify the feasibility of the proposed approach.

Shuze Liu, Shangtong Zhang

Most reinforcement learning practitioners evaluate their policies with online Monte Carlo estimators for either hyperparameter tuning or testing different algorithmic design choices, where the policy is repeatedly executed in the environment to get the average outcome. Such massive interactions with the environment are prohibitive in many scenarios. In this paper, we propose novel methods that improve the data efficiency of online Monte Carlo estimators while maintaining their unbiasedness. We first propose a tailored closed-form behavior policy that provably reduces the variance of an online Monte Carlo estimator. We then design efficient algorithms to learn this closed-form behavior policy from previously collected offline data. Theoretical analysis is provided to characterize how the behavior policy learning error affects the amount of reduced variance. Compared with previous works, our method achieves better empirical performance in a broader set of environments, with fewer requirements for offline data.

Gaurav Pandey, Yatin Nandwani, Tahira Naseem, Mayank Mishra, Guangxuan Xu, Dinesh Raghu, Sachindra Joshi, Asim Munawar, Ramón Astudillo

Distribution matching methods for language model alignment such as Generation with Distributional Control (GDC) and Distributional Policy Gradient (DPG) have not received the same level of attention in reinforcement learning from human feedback (RLHF) as contrastive methods such as Sequence Likelihood Calibration (SLiC), Direct Preference Optimization (DPO) and its variants. We identify high variance of the gradient estimate as the primary reason for the lack of success of these methods and propose a self-normalized baseline to reduce the variance. We further generalize the target distribution in DPG, GDC and DPO by using Bayes' rule to define the reward-conditioned posterior. The resulting approach, referred to as BRAIn - Bayesian Reward-conditioned Amortized Inference acts as a bridge between distribution matching methods and DPO and significantly outperforms prior art in summarization and Antropic HH tasks.

Haotian Ye, James Zou, Linjun Zhang

The existence of spurious correlations such as image backgrounds in the training environment can make empirical risk minimization (ERM) perform badly in the test environment. To address this problem, Kirichenko et al. (2022) empirically found that the core features that are related to the outcome can still be learned well even with the presence of spurious correlations. This opens a promising strategy to first train a feature learner rather than a classifier, and then perform linear probing (last layer retraining) in the test environment. However, a theoretical understanding of when and why this approach works is lacking. In this paper, we find that core features are only learned well when their associated non-realizable noise is smaller than that of spurious features, which is not necessarily true in practice. We provide both theories and experiments to support this finding and to illustrate the importance of non-realizable noise. Moreover, we propose an algorithm called Freeze then Train (FTT), that first freezes certain salient features and then trains the rest of the features using ERM. We theoretically show that FTT preserves features that are more beneficial to test time probing. Across two commonly used spurious correlation datasets, FTT outperforms ERM, IRM, JTT and CVaR-DRO, with substantial improvement in accuracy (by 4.5) when the feature noise is large. FTT also performs better on general distribution shift benchmarks.

Yuhang He, Andrew Markham

We propose synperiodic filter banks, a novel multi-scale learnable filter bank construction strategy that all filters are synchronized by their rotating periodicity. By synchronizing in a certain periodicity, we naturally get filters whose temporal length are reduced if they carry higher frequency response, and vice versa. Such filters internally maintain a better time-frequency resolution trade-off. By further alternating the periodicity, we can easily obtain a group of synperiodic filter bank (we call synperiodic filter banks), where filters of same frequency response in different groups differ in temporal length. Convolving these filter banks with sound raw waveform achieves multi-scale perception in time domain. Moreover, applying the same filter banks to recursively process the 2x-downsampled waveform enables multi-scale perception in the frequency domain. Benefiting from the multi-scale perception in both time and frequency domains, our proposed synperiodic filter banks learn multi-scale time-frequency representation in a data-driven way. Experiments on both sound source direction of arrival (DoA) and physical location detection task show the superiority of synperiodic filter banks.

Akhil Kedia, Mohd Abbas Zaidi, Sushil Khyalia, JungHo Jung, Harshith Goka, Haejun Lee

In spite of their huge success, transformer models remain difficult to scale in depth. In this work, we develop a unified signal propagation theory and provide formulae that govern the moments of the forward and backward signal through the transformer model. Our framework can be used to understand and mitigate vanishing/exploding gradients, rank collapse, and instability associated with high attention scores. We also propose DeepScaleLM, an initialization and scaling scheme that conserves unit output/gradient moments throughout the model, enabling the training of very deep models with 1000 layers. We find that transformer models could be much deeper - our deep models with fewer parameters outperform shallow models in Language Modeling, Speech Translation, and Image Classification, across encoder-only, decoder-only and encoder-decoder variants, for both Pre-LN and Post-LN transformers, for multiple datasets and model sizes. These improvements also translate into improved performance on downstream Question Answering tasks and improved robustness for Image Classification.

Kamesh Munagala, Govind S. Sankar

In this paper, we consider classic randomized low diameter decomposition procedures for planar graphs that obtain connected clusters that are cohesive in that close by pairs of nodes are assigned to the same cluster with high probability. We consider the additional aspect of *individual fairness* -- pairs of nodes at comparable distances should be separated with comparable probability. We show that classic decomposition procedures do not satisfy this property. We present novel algorithms that achieve various trade-offs between this property and additional desiderata of connectivity of the clusters and optimality in number of clusters. We show that our individual fairness bounds may be difficult to improve by tying the improvement to resolving a major open question in metric embeddings. We finally show the efficacy of our algorithms on real planar networks modeling Congressional redistricting.

Ting Cai, Kirthevasan Kandasamy

We study actively labeling streaming data, where an active learner is faced with a stream of data points and must carefully choose which of these points to label via an expensive experiment. Such problems frequently arise in applications such as healthcare and astronomy. We first study a setting when the data’s inputs belong to one of K discrete distributions and formalize this problem via a loss that captures the labeling cost and the prediction error. When the labeling cost is B, our algorithm, which chooses to label a point if the uncertainty is larger than a time and cost dependent threshold, achieves a worst-case upper bound of $\tilde{O}(B^{\frac{1}{3}}{K}^{\frac{1}{3}}{T}^{\frac{2}{3}})$ on the loss after T rounds. We also provide a more nuanced upper bound which demonstrates that the algorithm can adapt to the arrival pattern, and achieves better performance when the arrival pattern is more favorable. We complement both upper bounds with matching lower bounds. We next study this problem when the inputs belong to a continuous domain and the output of the experiment is a smooth function with bounded RKHS norm. After T rounds in d dimensions, we show that the loss is bounded by $\tilde{O}(B^{\frac{1}{d+3}}{T}^{\frac{d+2}{d+3}})$ in an RKHS with a squared exponential kernel and by $\tilde{O}(B^{\frac{1}{2d+3}}{T}^{\frac{2d+2}{2d+3}})$ in an RKHS with a Matérn kernel. Our empirical evaluation demonstrates that our method outperforms other baselines in several synthetic experiments and two real experiments in medicine and astronomy.

Zhiyong Yang, Qianqian Xu, Zitai Wang, Sicong Li, Boyu Han, Shilong Bao, Xiaochun Cao, Qingming Huang

This paper explores test-agnostic long-tail recognition, a challenging long-tail task where the test label distributions are unknown and arbitrarily imbalanced. We argue that the variation in these distributions can be broken down hierarchically into global and local levels. The global ones reflect a broad range of diversity, while the local ones typically arise from milder changes, often focused On a particular neighbor. Traditional methods predominantly use a Mixture-of-Expert (MoE) approach, targeting a few fixed test label distributions that exhibit substantial global variations. However, the local variations are left unconsidered. To address this issue, we propose a new MoE strategy, $\mathsf{DirMixE}$, which assigns experts to different Dirichlet meta-distributions of the label distribution, each targeting a specific aspect of local variations. Additionally, the diversity among these Dirichlet meta-distributions inherently captures global variations. This dual-level approach also leads to a more stable objective function, allowing us to sample different test distributions better to quantify the mean and variance of performance outcomes. Theoretically, we show that our proposed objective benefits from enhanced generalization by virtue of the variance-based regularization. Comprehensive experiments across multiple benchmarks confirm the effectiveness of $\mathsf{DirMixE}$.

Yi-Fan Zhang, Min-Ling Zhang

Despite great advances in algorithms for multi-label learning, research on the theoretical analysis of generalization is still in the early stage. Some recent theoretical results has investigated the generalization performance of multi-label learning under several evaluation metrics, however, how to reduce the dependency on the number of labels, explicitly introduce label correlations, and quantitatively analyze the impact of various inductive biases in the generalization analysis of multi-label learning is still a crucial and open problem. In an attempt to make up for the gap in the generalization theory of multi-label learning, we develop several novel vector-contraction inequalities, which exploit the Lipschitz continuity of loss functions, and derive generalization bounds with a weaker dependency on the number of labels than the state of the art in the case of decoupling the relationship among different components, which serves as theoretical guarantees for the generalization of multi-label learning. In addition, we derive the generalization bound for Macro-Averaged AUC and analyze its relationship with class-imbalance. The mild bounds without strong assumptions explain the good generalization ability of multi-label learning with first-order label correlations and high-order label correlations induced by norm regularizers.

Hadi Mohaghegh Dolatabadi, Sarah Erfani, Christopher Leckie

Normalizing flows attempt to model an arbitrary probability distribution through a set of invertible mappings. These transformations are required to achieve a tractable Jacobian determinant that can be used in high-dimensional scenarios. The first normalizing flow designs used coupling layer mappings built upon affine transformations. The significant advantage of such models is their easy-to-compute inverse. Nevertheless, making use of affine transformations may limit the expressiveness of such models. Recently, invertible piecewise polynomial functions as a replacement for affine transformations have attracted attention. However, these methods require solving a polynomial equation to calculate their inverse. In this paper, we explore using linear rational splines as a replacement for affine transformations used in coupling layers. Besides having a straightforward inverse, inference and generation have similar cost and architecture in this method. Moreover, simulation results demonstrate the competitiveness of this approach’s performance compared to existing methods.

My Phan, Kianté Brantley, Stephanie Milani, Soroush Mehri, Gokul Swamy, Geoff Gordon

We present a general framework for transfer learning that is flexible enough to capture transfer in supervised, reinforcement, and imitation learning. Our framework enables new insights into the fundamental question of *when* we can successfully transfer learned information across problems. We model the learner as interacting with a sequence of problem instances, or *environments*, each of which is generated from a common structural causal model (SCM) by choosing the SCM's parameters from restricted sets. We derive a procedure that can propagate restrictions on SCM parameters through the SCM's graph structure to other parameters that we are trying to learn. The propagated restrictions then enable more efficient learning (i.e., transfer). By analyzing the procedure, we are able to challenge widely-held beliefs about transfer learning. First, we show that having *sparse* changes across environments is neither necessary nor sufficient for transfer. Second, we show an example where the common heuristic of *freezing* a layer in a network causes poor transfer performance. We then use our procedure to select a more refined set of parameters to freeze, leading to successful transfer learning.

Romain Cosentino, Behnaam Aazhang

We propose a novel approach to filter bank learning for time-series by considering spectral decompositions of signals defined as a Group Transform. This framework allows us to generalize classical time-frequency transformations such as the Wavelet Transform, and to efficiently learn the representation of signals. While the creation of the wavelet transform filter-bank relies on affine transformations of a mother filter, our approach allows for non-linear transformations. The transformations induced by such maps enable us to span a larger class of signal representations, from wavelet to chirplet-like filters. We propose a parameterization of such a non-linear map such that its sampling can be optimized for a specific task and signal. The Learnable Group Transform can be cast into a Deep Neural Network. The experiments on diverse time-series datasets demonstrate the expressivity of this framework, which competes with state-of-the-art performances.

Hongchang Gao, Bin Gu, My T. Thai

Bilevel optimization has been applied to a wide variety of machine learning models and numerous stochastic bilevel optimization algorithms have been developed in recent years. However, most existing algorithms restrict their focus on the single-machine setting so that they are incapable of handling the distributed data. To address this issue, under the setting where all participants compose a network and perform peer-to-peer communication in this network, we developed two novel decentralized stochastic bilevel optimization algorithms based on the gradient tracking communication mechanism and two different gradient estimators. Additionally, we established their convergence rates for nonconvex-strongly-convex problems with novel theoretical analysis strategies. To our knowledge, this is the first work achieving these theoretical results. Finally, we applied our algorithms to practical machine learning models, and the experimental results confirmed the efficacy of our algorithms.

Pei Liu, Luping Ji

Uncertainty estimation (UE), as an effective means of quantifying predictive uncertainty, is crucial for safe and reliable decision-making, especially in high-risk scenarios. Existing UE schemes usually assume that there are completely-labeled samples to support fully-supervised learning. In practice, however, many UE tasks often have no sufficiently-labeled data to use, such as the Multiple Instance Learning (MIL) with only weak instance annotations. To bridge this gap, this paper, for the first time, addresses the weakly-supervised issue of *Multi-Instance UE* (MIUE) and proposes a new baseline scheme, *Multi-Instance Residual Evidential Learning* (MIREL). Particularly, at the fine-grained instance UE with only weak supervision, we derive a multi-instance residual operator through the Fundamental Theorem of Symmetric Functions. On this operator derivation, we further propose MIREL to jointly model the high-order predictive distribution at bag and instance levels for MIUE. Extensive experiments empirically demonstrate that our MIREL not only could often make existing MIL networks perform better in MIUE, but also could surpass representative UE methods by large margins, especially in instance-level UE tasks. Our source code is available at https://github.com/liupei101/MIREL.

Reyna Abhyankar, Zijian He, Vikranth Srivatsa, Hao Zhang, Yiying Zhang

Large language models are increasingly integrated with external environments, tools, and agents like ChatGPT plugins to extend their capability beyond language-centric tasks. However, today's LLM inference systems are designed for standalone LLMs. They treat each external interaction as the end of LLM generation and form a new request when the interaction finishes, causing unnecessary recomputation of already computed contexts, which accounts for 37-40% of total model forwarding time. This paper presents **InferCept, the first LLM inference framework targeting augmented LLMs** and supporting the efficient interception of LLM generation. InferCept minimizes the GPU resource waste caused by LLM interceptions and dedicates saved memory for serving more requests.InferCept improves the overall serving throughput by **1.6x-2x** and completes 2x more requests per second compared to the state-of-the-art LLM inference systems.

Pan Xu

In this paper, we consider a model called *Online Capacitated Coverage Maximization*, characterized by two features: (1) the dynamic arrival of online agents following a known identical and independent distribution, and (2) each offline agent is associated with a specific coverage valuation over the groundset of online agents. Additionally, both offline and online agents are assigned integer capacities, reflecting finite budgets and operational constraints. We introduce and analyze two matching policies. The first, a non-adaptive policy, utilizes offline statistics derived from solving a benchmark linear program. The second is an enhanced version equipped with real-time boostings and attenuations. We conduct a comprehensive competitive analysis and characterize the competitive ratio for both policies as functions of two crucial parameters: a lower bound on the matching capacity among offline agents and an upper bound on the number of online agents covering any specific feature for offline agents.

Louis Grenioux, Maxence Noble, Marylou Gabrié, Alain Oliviero Durmus

Building upon score-based learning, new interest in stochastic localization techniques has recently emerged. In these models, one seeks to noise a sample from the data distribution through a stochastic process, called observation process, and progressively learns a denoiser associated to this dynamics. Apart from specific applications, the use of stochastic localization for the problem of sampling from an unnormalized target density has not been explored extensively. This work contributes to fill this gap. We consider a general stochastic localization framework and introduce an explicit class of observation processes, associated with flexible denoising schedules. We provide a complete methodology, *Stochastic Localization via Iterative Posterior Sampling* (**SLIPS**), to obtain approximate samples of these dynamics, and as a by-product, samples from the target distribution. Our scheme is based on a Markov chain Monte Carlo estimation of the denoiser and comes with detailed practical guidelines. We illustrate the benefits and applicability of **SLIPS** on several benchmarks of multi-modal distributions, including Gaussian mixtures in increasing dimensions, Bayesian logistic regression and a high-dimensional field system from statistical-mechanics.

Nicolas Christianson, Junxuan Shen, Adam Wierman

We examine the problem of designing learning-augmented algorithms for metrical task systems (MTS) that exploit machine-learned advice while maintaining rigorous, worst-case guarantees on performance. We propose an algorithm, DART, that achieves this dual objective, providing cost within a multiplicative factor $(1+ϵ)$ of the machine-learned advice (i.e., consistency) while ensuring cost within a multiplicative factor $2^{O(1/ϵ)}$ of a baseline robust algorithm (i.e., robustness) for any $ϵ>0$. We show that this exponential tradeoff between consistency and robustness is unavoidable in general, but that in important subclasses of MTS, such as when the metric space has bounded diameter and in the $k$-server problem, our algorithm achieves improved, polynomial tradeoffs between consistency and robustness.

Cyril Bachelard, Apostolos Chalkis, Vissarion Fisikopoulos, Elias Tsigaridas

We propose novel randomized geometric tools to detect low-volatility anomalies in stock markets; a principal problem in financial economics. Our modeling of the (detection) problem results in sampling and estimating the (relative) volume of geodesically non-convex and non-connected spherical patches that arise by intersecting a non-standard simplex with a sphere. To sample, we introduce two novel Markov Chain Monte Carlo (MCMC) algorithms that exploit the geometry of the problem and employ state-of-the-art continuous geometric random walks (such as Billiard walk and Hit-and-Run) adapted on spherical patches. To our knowledge, this is the first geometric formulation and MCMC-based analysis of the volatility puzzle in stock markets. We have implemented our algorithms in C++ (along with an R interface) and we illustrate the power of our approach by performing extensive experiments on real data. Our analyses provide accurate detection and new insights into the distribution of portfolios’ performance characteristics. Moreover, we use our tools to show that classical methods for low-volatility anomaly detection in finance form bad proxies that could lead to misleading or inaccurate results.

Tenglong Liu, Yang Li, Yixing Lan, Hao Gao, Wei Pan, Xin Xu

In offline reinforcement learning, the challenge of out-of-distribution (OOD) is pronounced. To address this, existing methods often constrain the learned policy through policy regularization. However, these methods often suffer from the issue of unnecessary conservativeness, hampering policy improvement. This occurs due to the indiscriminate use of all actions from the behavior policy that generates the offline dataset as constraints. The problem becomes particularly noticeable when the quality of the dataset is suboptimal. Thus, we propose Adaptive Advantage-guided Policy Regularization (A2PR), obtaining high-advantage actions from an augmented behavior policy combined with VAE to guide the learned policy. A2PR can select high-advantage actions that differ from those present in the dataset, while still effectively maintaining conservatism from OOD actions. This is achieved by harnessing the VAE capacity to generate samples matching the distribution of the data points. We theoretically prove that the improvement of the behavior policy is guaranteed. Besides, it effectively mitigates value overestimation with a bounded performance gap. Empirically, we conduct a series of experiments on the D4RL benchmark, where A2PR demonstrates state-of-the-art performance. Furthermore, experimental results on additional suboptimal mixed datasets reveal that A2PR exhibits superior performance. Code is available at https://github.com/ltlhuuu/A2PR.

Logan Murphy, Kaiyu Yang, Jialiang Sun, Zhaoyu Li, Anima Anandkumar, Xujie Si

Autoformalization involves automatically translating informal math into formal theorems and proofs that are machine-verifiable. Euclidean geometry provides an interesting and controllable domain for studying autoformalization. In this paper, we introduce a neuro-symbolic framework for autoformalizing Euclidean geometry, which combines domain knowledge, SMT solvers, and large language models (LLMs). One challenge in Euclidean geometry is that informal proofs rely on diagrams, leaving gaps in texts that are hard to formalize. To address this issue, we use theorem provers to fill in such diagrammatic information automatically, so that the LLM only needs to autoformalize the explicit textual steps, making it easier for the model. We also provide automatic semantic evaluation for autoformalized theorem statements. We construct LeanEuclid, an autoformalization benchmark consisting of problems from Euclid's Elements and the UniGeo dataset formalized in the Lean proof assistant. Experiments with GPT-4 and GPT-4V show the capability and limitations of state-of-the-art LLMs on autoformalizing geometry problems. The data and code are available at https://github.com/loganrjmurphy/LeanEuclid.

Hila Manor, Tomer Michaeli

Editing signals using large pre-trained models, in a zero-shot manner, has recently seen rapid advancements in the image domain. However, this wave has yet to reach the audio domain. In this paper, we explore two zero-shot editing techniques for audio signals, which use DDPM inversion with pre-trained diffusion models. The first, which we coin *ZEro-shot Text-based Audio (ZETA)* editing, is adopted from the image domain. The second, named *ZEro-shot UnSupervized (ZEUS)* editing, is a novel approach for discovering semantically meaningful editing directions without supervision. When applied to music signals, this method exposes a range of musically interesting modifications, from controlling the participation of specific instruments to improvisations on the melody. Samples and code can be found on our [examples page](https://hilamanor.github.io/AudioEditing/).

Michael Matthews, Michael Beukman, Benjamin Ellis, Mikayel Samvelyan, Matthew T Jackson, Samuel Coward, Jakob Foerster

Benchmarks play a crucial role in the development and analysis of reinforcement learning (RL) algorithms. We identify that existing benchmarks used for research into open-ended learning fall into one of two categories. Either they are too slow for meaningful research to be performed without enormous computational resources, like Crafter, NetHack and Minecraft, or they are not complex enough to pose a significant challenge, like Minigrid and Procgen. To remedy this, we first present Craftax-Classic: a ground-up rewrite of Crafter in JAX that runs up to 250x faster than the Python-native original. A run of PPO using 1 billion environment interactions finishes in under an hour using only a single GPU and averages 90% of the optimal reward. To provide a more compelling challenge we present the main Craftax benchmark, a significant extension of the Crafter mechanics with elements inspired from NetHack. Solving Craftax requires deep exploration, long term planning and memory, as well as continual adaptation to novel situations as more of the world is discovered. We show that existing methods including global and episodic exploration, as well as unsupervised environment design fail to make material progress on the benchmark. We therefore believe that Craftax can for the first time allow researchers to experiment in a complex, open-ended environment with limited computational resources.

Sara Ahmadian, Maryam Negahbani

Correlation clustering is a ubiquitous paradigm in unsupervised machine learning where addressing unfairness is a major challenge. Motivated by this, we study fair correlation clustering where the data points may belong to different protected groups and the goal is to ensure fair representation of all groups across clusters. Our paper significantly generalizes and improves on the quality guarantees of previous work of Ahmadian et al. as follows. * We allow the user to specify an arbitrary upper bound on the representation of each group in a cluster. * Our algorithm allows individuals to have multiple protected features and ensure fairness simultaneously across them all. * We prove guarantees for clustering quality and fairness in this general setting. Furthermore, this improves on the results for the special cases studied in previous work. Our experiments on real-world data demonstrate that our clustering quality compared to the optimal solution is much better than what our theoretical result suggests.

Puhua Niu, Shili Wu, Mingzhou Fan, Xiaoning Qian

Generative Flow Networks (GFlowNets) have been shown effective to generate combinatorial objects with desired properties. We here propose a new GFlowNet training framework, with policy-dependent rewards, that bridges keeping flow balance of GFlowNets to optimizing the expected accumulated reward in traditional Reinforcement-Learning (RL). This enables the derivation of new policy-based GFlowNet training methods, in contrast to existing ones resembling value-based RL. It is known that the design of backward policies in GFlowNet training affects efficiency. We further develop a coupled training strategy that jointly solves GFlowNet forward policy training and backward policy design. Performance analysis is provided with a theoretical guarantee of our policy-based GFlowNet training. Experiments on both simulated and real-world datasets verify that our policy-based strategies provide advanced RL perspectives for robust gradient estimation to improve GFlowNet performance. Our code is available at: [github.com/niupuhua1234/GFN-PG](https://github.com/niupuhua1234/GFN-PG).

Pablo Villalobos, Anson Ho, Jaime Sevilla, Tamay Besiroglu, Lennart Heim, Marius Hobbhahn

We investigate the potential constraints on LLM scaling posed by the availability of public human-generated text data. We forecast the growing demand for training data based on current trends and estimate the total stock of public human text data. Our findings indicate that if current LLM development trends continue, models will be trained on datasets roughly equal in size to the available stock of public human text data between 2026 and 2032, or slightly earlier if models are overtrained. We explore how progress in language modeling can continue when human-generated text datasets cannot be scaled any further. We argue that synthetic data generation, transfer learning from data-rich domains, and data efficiency improvements might support further progress.

Paarth Neekhara, Shehzeen Hussain, Rafael Valle, Boris Ginsburg, Rishabh Ranjan, Shlomo Dubnov, Farinaz Koushanfar, Julian McAuley

We propose SelfVC, a training strategy to iteratively improve a voice conversion model with self-synthesized examples. Previous efforts on voice conversion focus on factorizing speech into explicitly disentangled representations that separately encode speaker characteristics and linguistic content. However, disentangling speech representations to capture such attributes using task-specific loss terms can lead to information loss. In this work, instead of explicitly disentangling attributes with loss terms, we present a framework to train a controllable voice conversion model on entangled speech representations derived from self-supervised learning (SSL) and speaker verification models. First, we develop techniques to derive prosodic information from the audio signal and SSL representations to train predictive submodules in the synthesis model. Next, we propose a training strategy to iteratively improve the synthesis model for voice conversion, by creating a challenging training objective using self-synthesized examples. We demonstrate that incorporating such self-synthesized examples during training improves the speaker similarity of generated speech as compared to a baseline voice conversion model trained solely on heuristically perturbed inputs. Our framework is trained without any text and achieves state-of-the-art results in zero-shot voice conversion on metrics evaluating naturalness, speaker similarity, and intelligibility of synthesized audio.

Zhaoyue Chen, Yifan Sun

The Frank-Wolfe algorithm is a popular method in structurally constrained machine learning applications, due to its fast per-iteration complexity. However, one major limitation of the method is a slow rate of convergence that is difficult to accelerate due to erratic, zig-zagging step directions, even asymptotically close to the solution. We view this as an artifact of discretization; that is to say, the Frank-Wolfe flow, which is its trajectory at asymptotically small step sizes, does not zig-zag, and reducing discretization error will go hand-in-hand in producing a more stabilized method, with better convergence properties. We propose two improvements: a multistep Frank-Wolfe method that directly applies optimized higher-order discretization schemes; and an LMO-averaging scheme with reduced discretization error, and whose local convergence rate over general convex sets accelerates from a rate of $O(1/k)$ to up to $O(1/k^{3/2})$.

Zaiyan Xu, Kishan Panaganti, Dileep Kalathil

We consider the problem of learning a control policy that is robust against the parameter mismatches between the training environment and testing environment. We formulate this as a distributionally robust reinforcement learning (DR-RL) problem where the objective is to learn the policy which maximizes the value function against the worst possible stochastic model of the environment in an uncertainty set. We focus on the tabular episodic learning setting where the algorithm has access to a generative model of the nominal (training) environment around which the uncertainty set is defined. We propose the Robust Phased Value Learning (RPVL) algorithm to solve this problem for the uncertainty sets specified by four different divergences: total variation, chi-square, Kullback-Leibler, and Wasserstein. We show that our algorithm achieves $\tilde{\mathcal{O}}(|\mathcal{S}||\mathcal{A}|H^5)$ sample complexity, which is uniformly better than the existing results by a factor of $|\mathcal{S}|$, where $|\mathcal{S}|$ is number of states, $|\mathcal{A}|$ is the number of actions, and $H$ is the horizon length. We also provide the first-ever sample complexity result for the Wasserstein uncertainty set. Finally, we demonstrate the performance of our algorithm using simulation experiments.

Jaehyeong Jo, Sung Ju Hwang

Learning the distribution of data on Riemannian manifolds is crucial for modeling data from non-Euclidean space, which is required by many applications in diverse scientific fields. Yet, existing generative models on manifolds suffer from expensive divergence computation or rely on approximations of heat kernel. These limitations restrict their applicability to simple geometries and hinder scalability to high dimensions. In this work, we introduce the Riemannian Diffusion Mixture, a principled framework for building a generative diffusion process on manifolds. Instead of following the denoising approach of previous diffusion models, we construct a diffusion process using a mixture of bridge processes derived on general manifolds without requiring heat kernel estimations. We develop a geometric understanding of the mixture process, deriving the drift as a weighted mean of tangent directions to the data points that guides the process toward the data distribution. We further propose a scalable training objective for learning the mixture process that readily applies to general manifolds. Our method achieves superior performance on diverse manifolds with dramatically reduced number of in-training simulation steps for general manifolds.

Elliot Creager, David Madras, Toniann Pitassi, Richard Zemel

In many applications areas—lending, education, and online recommenders, for example—fairness and equity concerns emerge when a machine learning system interacts with a dynamically changing environment to produce both immediate and long-term effects for individuals and demographic groups. We discuss causal directed acyclic graphs (DAGs) as a unifying framework for the recent literature on fairness in such dynamical systems. We show that this formulation affords several new directions of inquiry to the modeler, where sound causal assumptions can be expressed and manipulated. We emphasize the importance of computing interventional quantities in the dynamical fairness setting, and show how causal assumptions enable simulation (when environment dynamics are known) and estimation by adjustment (when dynamics are unknown) of intervention on short- and long-term outcomes, at both the group and individual levels.

Pranjal Awasthi, Corinna Cortes, Christopher Mohri

We study a problem of batch distribution drift motivated by several applications, which consists of determining an accurate predictor for a target time segment, for which a moderate amount of labeled samples are at one’s disposal, while leveraging past segments for which substantially more labeled samples are available. We give new algorithms for this problem guided by a new theoretical analysis and generalization bounds derived for this scenario. We further extend our results to the case where few or no labeled data is available for the period of interest. Finally, we report the results of extensive experiments demonstrating the benefits of our drifting algorithm, including comparisons with natural baselines. A by-product of our study is a principled solution to the problem of multiple-source adaptation with labeled source data and a moderate amount of target labeled data, which we briefly discuss and compare with.

Nikhil Sardana, Jacob Portes, Alexandre (Sasha) Doubov, Jonathan Frankle

Large language model (LLM) scaling laws are empirical formulas that estimate changes in model quality as a result of increasing parameter count and training data. However, these formulas, including the popular Deepmind Chinchilla scaling laws, neglect to include the cost of inference. We modify the Chinchilla scaling laws to calculate the optimal LLM parameter count and pre-training data size to train and deploy a model of a given quality and inference demand. We conduct our analysis both in terms of a compute budget and real-world costs and find that LLM researchers expecting reasonably large inference demand ($\sim$1B requests) should train models smaller and longer than Chinchilla-optimal. Furthermore, we train 47 models of varying sizes and parameter counts to validate our formula and find that model quality continues to improve as we scale tokens per parameter to extreme ranges (up to 10,000). Finally, we ablate the procedure used to fit the Chinchilla scaling law coefficients and find that developing scaling laws only from data collected at typical token/parameter ratios overestimates the impact of additional tokens at these extreme ranges.

Wenlin Chen, James Wilson, Stephen Tyree, Kilian Weinberger, Yixin Chen

As deep nets are increasingly used in applications suited for mobile devices, a fundamental dilemma becomes apparent: the trend in deep learning is to grow models to absorb ever-increasing data set sizes; however mobile devices are designed with very little memory and cannot store such large models. We present a novel network architecture, HashedNets, that exploits inherent redundancy in neural networks to achieve drastic reductions in model sizes. HashedNets uses a low-cost hash function to randomly group connection weights into hash buckets, and all connections within the same hash bucket share a single parameter value. These parameters are tuned to adjust to the HashedNets weight sharing architecture with standard backprop during training. Our hashing procedure introduces no additional memory overhead, and we demonstrate on several benchmark data sets that HashedNets shrink the storage requirements of neural networks substantially while mostly preserving generalization performance.

Francesco Croce, Matthias Hein

The evaluation of robustness against adversarial manipulation of neural networks-based classifiers is mainly tested with empirical attacks as methods for the exact computation, even when available, do not scale to large networks. We propose in this paper a new white-box adversarial attack wrt the $l_p$-norms for $p\in \{1,2,\infty \}$ aiming at finding the minimal perturbation necessary to change the class of a given input. It has an intuitive geometric meaning, yields quickly high quality results, minimizes the size of the perturbation (so that it returns the robust accuracy at every threshold with a single run). It performs better or similar to state-of-the-art attacks which are partially specialized to one $l_p$-norm, and is robust to the phenomenon of gradient obfuscation.

Tam Nguyen, Tan Nguyen, Dung Le, Duy Khuong Nguyen, Viet-Anh Tran, Richard Baraniuk, Nhat Ho, Stanley Osher

Multi-head attention is a driving force behind state-of-the-art transformers, which achieve remarkable performance across a variety of natural language processing (NLP) and computer vision tasks. It has been observed that for many applications, those attention heads learn redundant embedding, and most of them can be removed without degrading the performance of the model. Inspired by this observation, we propose Transformer with a Mixture of Gaussian Keys (Transformer-MGK), a novel transformer architecture that replaces redundant heads in transformers with a mixture of keys at each head. These mixtures of keys follow a Gaussian mixture model and allow each attention head to focus on different parts of the input sequence efficiently. Compared to its conventional transformer counterpart, Transformer-MGK accelerates training and inference, has fewer parameters, and requires fewer FLOPs to compute while achieving comparable or better accuracy across tasks. Transformer-MGK can also be easily extended to use with linear attention. We empirically demonstrate the advantage of Transformer-MGK in a range of practical applications, including language modeling and tasks that involve very long sequences. On the Wikitext-103 and Long Range Arena benchmark, Transformer-MGKs with 4 heads attain comparable or better performance to the baseline transformers with 8 heads.

Dragana Bajovic, Dusan Jakovetic, Soummya Kar

Recent works have shown that high probability metrics with stochastic gradient descent (SGD) exhibit informativeness and in some cases advantage over the commonly adopted mean-square error-based ones. In this work we provide a formal framework for the study of general high probability bounds with SGD, based on the theory of large deviations. The framework allows for a generic (not-necessarily bounded) gradient noise satisfying mild technical assumptions, allowing for the dependence of the noise distribution on the current iterate. Under the preceding assumptions, we find an upper large deviations bound for SGD with strongly convex functions. The corresponding rate function captures analytical dependence on the noise distribution and other problem parameters. This is in contrast with conventional mean-square error analysis that captures only the noise dependence through the variance and does not capture the effect of higher order moments nor interplay between the noise geometry and the shape of the cost function. We also derive exact large deviation rates for the case when the objective function is quadratic and show that the obtained function matches the one from the general upper bound hence showing the tightness of the general upper bound. Numerical examples illustrate and corroborate theoretical findings.

Michael Poli, Stefano Massaroli, Stefano Ermon, Bryan Wilder, Eric Horvitz

We present a methodology for formulating simplifying abstractions in machine learning systems by identifying and harnessing the utility structure of decisions. Machine learning tasks commonly involve high-dimensional output spaces (e.g., predictions for every pixel in an image or node in a graph), even though a coarser output would often suffice for downstream decision-making (e.g., regions of an image instead of pixels). Developers often hand-engineer abstractions of the output space, but numerous abstractions are possible and it is unclear how the choice of output space for a model impacts its usefulness in downstream decision-making. We propose a method that configures the output space automatically in order to minimize the loss of decision-relevant information. Taking a geometric perspective, we formulate a step of the algorithm as a projection of the probability simplex, termed fold, that minimizes the total loss of decision-related information in the H-entropy sense. Crucially, learning in the abstracted outcome space requires significantly less data, leading to a net improvement in decision quality. We demonstrate the method in two domains: data acquisition for deep neural network training and a closed-loop wildfire management task.

Alex Boyd, Yuxin Chang, Stephan Mandt, Padhraic Smyth

Continuous-time event sequences, i.e., sequences consisting of continuous time stamps and associated event types (“marks”), are an important type of sequential data with many applications, e.g., in clinical medicine or user behavior modeling. Since these data are typically modeled in an autoregressive manner (e.g., using neural Hawkes processes or their classical counterparts), it is natural to ask questions about future scenarios such as “what kind of event will occur next” or “will an event of type $A$ occur before one of type $B$.” Addressing such queries with direct methods such as naive simulation can be highly inefficient from a computational perspective. This paper introduces a new typology of query types and a framework for addressing them using importance sampling. Example queries include predicting the $n^{\mathrm{th}}$ event type in a sequence and the hitting time distribution of one or more event types. We also leverage these findings further to be applicable for estimating general “$A$ before $B$” type of queries. We prove theoretically that our estimation method is effectively always better than naive simulation and demonstrate empirically based on three real-world datasets that our approach can produce orders of magnitude improvements in sampling efficiency compared to naive methods.