DeepNLP/ICML-2024-Accepted-Papers huggingface dataset:
Efficient Value Iteration for s-rectangular Robust Markov Decision Processes
Authors: Navdeep Kumar, Kaixin Wang, Kfir Yehuda Levy, Shie Mannor

We focus on s-rectangular robust Markov decision processes (MDPs), which capture interconnected uncertainties across different actions within each state. This framework is more general compared to sa-rectangular robust MDPs, where uncertainties in each action are independent. However, the introduced interdependence significantly amplifies the complexity of the problem. Existing methods either have slow performance guarantees or are inapplicable to even moderately large state spaces. In this work, we derive optimal robust Bellman operators in explicit forms. This leads to robust value iteration methods with significantly faster time complexities than existing approaches, which can be used in large state spaces. Further, our findings reveal that the optimal policies demonstrate a novel threshold behavior, selectively favoring a limited set of actions based on their respective advantage functions. Additionally, our study uncovers a noteworthy connection between the robustness of a policy and the variance in its value function, highlighting that policies with lower variance exhibit greater resilience.
Minimum Norm Interpolation Meets The Local Theory of Banach Spaces
Authors: Gil Kur, Pedro Abdalla, Pierre Bizeul, Fanny Yang

Minimum-norm interpolators have recently gained attention primarily as an analyzable model to shed light on the double descent phenomenon observed for neural networks. The majority of the work has focused on analyzing interpolators in Hilbert spaces, where typically an effectively low-rank structure of the feature covariance prevents a large bias. More recently, tight vanishing bounds have also been shown for isotropic high-dimensional data for $\ell_p$-spaces with $p\in[1,2)$, leveraging sparse structure of the ground truth. However, these proofs are tailored to specific settings and hard to generalize. This paper takes a first step towards establishing a general framework that connects generalization properties of the interpolators to well-known concepts from high-dimensional geometry, specifically, from the local theory of Banach spaces. In particular, we show that under $2$-uniform convexity, the bias of the minimal norm solution is bounded by the Gaussian complexity of the class. We then prove a “reverse” Efron-Stein lower bound on the expected conditional variance of the minimal norm solution under cotype $2$. Finally, we prove that this bound is sharp for $\ell_p$-linear regression under sub-Gaussian covariates.
Prospective Side Information for Latent MDPs
Authors: Jeongyeol Kwon, Yonathan Efroni, Shie Mannor, Constantine Caramanis

In many interactive decision-making problems, there is contextual side information that remains fixed within the course of an interaction. This problem has been studied quite extensively under the assumption the context is fully observed, as well as in the opposing limit when the context is unobserved, a special type of POMDP also referred to as a Latent MDP (LMDP). In this work, we consider a class of decision problems that interpolates between the settings, namely, between the case the context is fully observed, and the case the context is unobserved. We refer to this class of decision problems as LMDPs with prospective side information. In such an environment an agent receives additional, weakly revealing, information on the latent context at the beginning of each episode. We show that, surprisingly, this problem is not captured by contemporary POMDP settings and is not solved by RL algorithms designed for partially observed environments. We then establish that any sample efficient algorithm must suffer at least $\Omega(K^{2/3})$-regret, as opposed to standard $\Omega(\sqrt{K})$ lower bounds. We design an algorithm with a matching upper bound that depends only polynomially on the problem parameters. This establishes exponential improvement in the sample complexity relative to the existing LMDP lower bound, when prospective information is not given in prior work.
On The Complexity of First-Order Methods in Stochastic Bilevel Optimization
Authors: Jeongyeol Kwon, Dohyun Kwon, Hanbaek Lyu

We consider the problem of finding stationary points in Bilevel optimization when the lower-level problem is unconstrained and strongly convex. The problem has been extensively studied in recent years; the main technical challenge is to keep track of lower-level solutions $y^*(x)$ in response to the changes in the upper-level variables $x$. Subsequently, all existing approaches tie their analyses to a genie algorithm that knows lower-level solutions and, therefore, need not query any points far from them. We consider a dual question to such approaches: suppose we have an oracle, which we call $y^*$-aware, that returns an $O(\epsilon)$-estimate of the lower-level solution, in addition to first-order gradient estimators locally unbiased within the $\Theta(\epsilon)$-ball around $y^*(x)$. We study the complexity of finding stationary points with such an $y^*$-aware oracle: we propose a simple first-order method that converges to an $\epsilon$ stationary point using $O(\epsilon^{-6}), O(\epsilon^{-4})$ access to first-order $y^*$-aware oracles. Our upper bounds also apply to standard unbiased first-order oracles, improving the best-known complexity of first-order methods by $O(\epsilon)$ with minimal assumptions. We then provide the matching $\Omega(\epsilon^{-6})$, $\Omega(\epsilon^{-4})$ lower bounds without and with an additional smoothness assumption, respectively. Our results imply that any approach that simulates an algorithm with an $y^*$-aware oracle must suffer the same lower bounds.
TinyTrain: Resource-Aware Task-Adaptive Sparse Training of DNNs at the Data-Scarce Edge
Authors: Young D. Kwon, Rui Li, Stylianos Venieris, Jagmohan Chauhan, Nicholas Donald Lane, Cecilia Mascolo

On-device training is essential for user personalisation and privacy. With the pervasiveness of IoT devices and microcontroller units (MCUs), this task becomes more challenging due to the constrained memory and compute resources, and the limited availability of labelled user data. Nonetheless, prior works neglect the data scarcity issue, require excessively long training time ($\textit{e.g.}$ a few hours), or induce substantial accuracy loss ($\geq$10%). In this paper, we propose TinyTrain, an on-device training approach that drastically reduces training time by selectively updating parts of the model and explicitly coping with data scarcity. TinyTrain introduces a task-adaptive sparse-update method that $\textit{dynamically}$ selects the layer/channel to update based on a multi-objective criterion that jointly captures user data, the memory, and the compute capabilities of the target device, leading to high accuracy on unseen tasks with reduced computation and memory footprint. TinyTrain outperforms vanilla fine-tuning of the entire network by 3.6-5.0% in accuracy, while reducing the backward-pass memory and computation cost by up to 1,098$\times$ and 7.68$\times$, respectively. Targeting broadly used real-world edge devices, TinyTrain achieves 9.5$\times$ faster and 3.5$\times$ more energy-efficient training over status-quo approaches, and 2.23$\times$ smaller memory footprint than SOTA methods, while remaining within the 1 MB memory envelope of MCU-grade platforms.
Dynamic Spectral Clustering with Provable Approximation Guarantee
Authors: Steinar Laenen, He Sun

This paper studies clustering algorithms for dynamically evolving graphs $\{G_t\}$, in which new edges (and potential new vertices) are added into a graph, and the underlying cluster structure of the graph can gradually change. The paper proves that, under some mild condition on the cluster-structure, the clusters of the final graph $G_T$ of $n_T$ vertices at time $T$ can be well approximated by a dynamic variant of the spectral clustering algorithm. The algorithm runs in amortised update time $O(1)$ and query time $o(n_T)$. Experimental studies on both synthetic and real-world datasets further confirm the practicality of our designed algorithm.
Collective Certified Robustness against Graph Injection Attacks
Authors: Yuni Lai, Bailin Pan, Kaihuang Chen, Yancheng Yuan, Kai Zhou

We investigate certified robustness for GNNs under graph injection attacks. Existing research only provides sample-wise certificates by verifying each node independently, leading to very limited certifying performance. In this paper, we present the first collective certificate, which certifies a set of target nodes simultaneously. To achieve it, we formulate the problem as a binary integer quadratic constrained linear programming (BQCLP). We further develop a customized linearization technique that allows us to relax the BQCLP into linear programming (LP) that can be efficiently solved. Through comprehensive experiments, we demonstrate that our collective certification scheme significantly improves certification performance with minimal computational overhead. For instance, by solving the LP within 1 minute on the Citeseer dataset, we achieve a significant increase in the certified ratio from 0.0% to 81.2% when the injected node number is 5% of the graph size. Our paper marks a crucial step towards making provable defense more practical. Our source code is available at https://github.com/Yuni-Lai/CollectiveLPCert.
Position: Evolving AI Collectives Enhance Human Diversity and Enable Self-Regulation
Authors: Shiyang Lai, Yujin Potter, Junsol Kim, Richard Zhuang, Dawn Song, James Evans

Large language model behavior is shaped by the language of those with whom they interact. This capacity and their increasing prevalence online portend that they will intentionally or unintentionally "program" one another and form emergent AI subjectivities, relationships, and collectives. Here, we call upon the research community to investigate these "societies" of interacting artificial intelligences to increase their rewards and reduce their risks for human society and the health of online environments. We use a small "community" of models and their evolving outputs to illustrate how such emergent, decentralized AI collectives can spontaneously expand the bounds of human diversity and reduce the risk of toxic, anti-social behavior online. Finally, we discuss opportunities for AI cross-moderation and address ethical issues and design challenges associated with creating and maintaining free-formed AI collectives.
Invariant Risk Minimization Is A Total Variation Model
Authors: Zhao-Rong Lai, Weiwen Wang

Invariant risk minimization (IRM) is an arising approach to generalize invariant features to different environments in machine learning. While most related works focus on new IRM settings or new application scenarios, the mathematical essence of IRM remains to be properly explained. We verify that IRM is essentially a total variation based on $L^2$ norm (TV-$\ell_2$) of the learning risk with respect to the classifier variable. Moreover, we propose a novel IRM framework based on the TV-$\ell_1$ model. It not only expands the classes of functions that can be used as the learning risk and the feature extractor, but also has robust performance in denoising and invariant feature preservation based on the coarea formula. We also illustrate some requirements for IRM-TV-$\ell_1$ to achieve out-of-distribution generalization. Experimental results show that the proposed framework achieves competitive performance in several benchmark machine learning scenarios.
Privately Learning Smooth Distributions on the Hypercube by Projections
Authors: Clément Lalanne, Sébastien Gadat

Fueled by the ever-increasing need for statistics that guarantee the privacy of their training sets, this article studies the centrally-private estimation of Sobolev-smooth densities of probability over the hypercube in dimension d. The contributions of this article are two-fold : Firstly, it generalizes the one-dimensional results of (Lalanne et al., 2023) to non-integer levels of smoothness and to a high-dimensional setting, which is important for two reasons : it is more suited for modern learning tasks, and it allows understanding the relations between privacy, dimensionality and smoothness, which is a central question with differential privacy. Secondly, this article presents a private strategy of estimation that is data-driven (usually referred to as adaptive in Statistics) in order to privately choose an estimator that achieves a good bias-variance trade-off among a finite family of private projection estimators without prior knowledge of the ground-truth smoothness β. This is achieved by adapting the Lepskii method for private selection, by adding a new penalization term that makes the estimation privacy-aware.
A Neural-Preconditioned Poisson Solver for Mixed Dirichlet and Neumann Boundary Conditions
Authors: Kai Weixian Lan, Elias Gueidon, Ayano Kaneda, Julian Panetta, Joseph Teran

We introduce a neural-preconditioned iterative solver for Poisson equations with mixed boundary conditions. Typical Poisson discretizations yield large, ill-conditioned linear systems. Iterative solvers can be effective for these problems, but only when equipped with powerful preconditioners. Unfortunately, effective preconditioners like multigrid require costly setup phases that must be re-executed every time domain shapes or boundary conditions change, forming a severe bottleneck for problems with evolving boundaries. In contrast, we present a neural preconditioner trained to efficiently approximate the inverse of the discrete Laplacian in the presence of such changes. Our approach generalizes to domain shapes, boundary conditions, and grid sizes outside the training set. The key to our preconditioner’s success is a novel, lightweight neural network architecture featuring spatially varying convolution kernels and supporting fast inference. We demonstrate that our solver outperforms state-of-the-art methods like algebraic multigrid as well as recently proposed neural preconditioners on challenging test cases arising from incompressible fluid simulations.
Sub-token ViT Embedding via Stochastic Resonance Transformers
Authors: Dong Lao, Yangchao Wu, Tian Yu Liu, Alex Wong, Stefano Soatto

Vision Transformer (ViT) architectures represent images as collections of high-dimensional vectorized tokens, each corresponding to a rectangular non-overlapping patch. This representation trades spatial granularity for embedding dimensionality, and results in semantically rich but spatially coarsely quantized feature maps. In order to retrieve spatial details beneficial to fine-grained inference tasks we propose a training-free method inspired by "stochastic resonance." Specifically, we perform sub-token spatial transformations to the input data, and aggregate the resulting ViT features after applying the inverse transformation. The resulting "Stochastic Resonance Transformer" (SRT) retains the rich semantic information of the original representation, but grounds it on a finer-scale spatial domain, partly mitigating the coarse effect of spatial tokenization. SRT is applicable across any layer of any ViT architecture, consistently boosting performance on several tasks including segmentation, classification, depth estimation, and others by up to 14.9% without the need for any fine-tuning. Code: https://github.com/donglao/srt.
Single-Model Attribution of Generative Models Through Final-Layer Inversion
Authors: Mike Laszkiewicz, Jonas Ricker, Johannes Lederer, Asja Fischer

Recent breakthroughs in generative modeling have sparked interest in practical single-model attribution. Such methods predict whether a sample was generated by a specific generator or not, for instance, to prove intellectual property theft. However, previous works are either limited to the closed-world setting or require undesirable changes to the generative model. We address these shortcomings by, first, viewing single-model attribution through the lens of anomaly detection. Arising from this change of perspective, we propose FLIPAD, a new approach for single-model attribution in the open-world setting based on final-layer inversion and anomaly detection. We show that the utilized final-layer inversion can be reduced to a convex lasso optimization problem, making our approach theoretically sound and computationally efficient. The theoretical findings are accompanied by an experimental study demonstrating the effectiveness of our approach and its flexibility to various domains.
Towards Understanding Inductive Bias in Transformers: A View From Infinity
Authors: Itay Lavie, Guy Gur-Ari, Zohar Ringel

We study inductive bias in Transformers in the infinitely over-parameterized Gaussian process limit and argue transformers tend to be biased towards more permutation symmetric functions in sequence space. We show that the representation theory of the symmetric group can be used to give quantitative analytical predictions when the dataset is symmetric to permutations between tokens. We present a simplified transformer block and solve the model at the limit, including accurate predictions for the learning curves and network outputs. We show that in common setups, one can derive tight bounds in the form of a scaling law for the learnability as a function of the context length. Finally, we argue WikiText dataset, does indeed possess a degree of permutation symmetry.
Modeling Caption Diversity in Contrastive Vision-Language Pretraining
Authors: Samuel Lavoie, Polina Kirichenko, Mark Ibrahim, Mido Assran, Andrew Gordon Wilson, Aaron Courville, Nicolas Ballas

There are a thousand ways to caption an image. Contrastive Language Pretraining (CLIP) on the other hand, works by mapping an image and its caption to a single vector – limiting how well CLIP-like models can represent the diverse ways to describe an image. In this work, we introduce Llip, Latent Language Image Pretraining, which models the diversity of captions that could match an image. Llip’s vision encoder outputs a set of visual features that are mixed into a final representation by conditioning on information derived from the text. We show that Llip outperforms non-contextualized baselines like CLIP and SigLIP on a variety of tasks even with large-scale encoders. Llip improves zero-shot classification by an average of 2.9% zero-shot classification benchmarks with a ViT-G/14 encoder. Specifically, Llip attains a zero-shot top-1 accuracy of 83.5% on ImageNet outperforming a similarly sized CLIP by 1.4%. We also demonstrate improvement on zero-shot retrieval on MS-COCO by 6.0%. We provide a comprehensive analysis of the components introduced by the method and demonstrate that Llip leads to richer visual representations.
Offline Inverse RL: New Solution Concepts and Provably Efficient Algorithms
Authors: Filippo Lazzati, Mirco Mutti, Alberto Maria Metelli

Inverse reinforcement learning (IRL) aims to recover the reward function of an expert agent from demonstrations of behavior. It is well-known that the IRL problem is fundamentally ill-posed, i.e., many reward functions can explain the demonstrations. For this reason, IRL has been recently reframed in terms of estimating the feasible reward set (Metelli et al., 2021), thus, postponing the selection of a single reward. However, so far, the available formulations and algorithmic solutions have been proposed and analyzed mainly for the online setting, where the learner can interact with the environment and query the expert at will. This is clearly unrealistic in most practical applications, where the availability of an offline dataset is a much more common scenario. In this paper, we introduce a novel notion of feasible reward set capturing the opportunities and limitations of the offline setting and we analyze the complexity of its estimation. This requires the introduction an original learning framework that copes with the intrinsic difficulty of the setting, for which data coverage is not under control. Then, we propose two computationally and statistically efficient algorithms, IRLO and PIRLO, for addressing the problem. In particular, the latter adopts a specific form of pessimism to enforce the novel, desirable property of inclusion monotonicity of the delivered feasible set. With this work, we aim to provide a panorama of the challenges of the offline IRL problem and how they can be fruitfully addressed.
Generalized Sobolev Transport for Probability Measures on a Graph
Authors: Tam Le, Truyen Nguyen, Kenji Fukumizu

We study the optimal transport (OT) problem for measures supported on a graph metric space. Recently, Le et al. (2022) leverage the graph structure and propose a variant of OT, namely Sobolev transport (ST), which yields a closed-form expression for a fast computation. However, ST is essentially coupled with the $L^p$ geometric structure within its definition which makes it nontrivial to utilize ST for other prior structures. In contrast, the classic OT has the flexibility to adapt to various geometric structures by modifying the underlying cost function. An important instance is the Orlicz-Wasserstein (OW) which moves beyond the $L^p$ structure by leveraging the Orlicz geometric structure. Comparing to the usage of standard $p$-order Wasserstein, OW remarkably helps to advance certain machine learning approaches. Nevertheless, OW brings up a new challenge on its computation due to its two-level optimization formulation. In this work, we leverage a specific class of convex functions for Orlicz structure to propose the generalized Sobolev transport (GST). GST encompasses the ST as its special case, and can be utilized for prior structures beyond the $L^p$ geometry. In connection with the OW, we show that one only needs to simply solve a univariate optimization problem to compute the GST, unlike the complex two-level optimization problem in OW. We empirically illustrate that GST is several-order faster than the OW. Moreover, we provide preliminary evidences on the advantages of GST for document classification and for several tasks in topological data analysis.
Robust Inverse Graphics via Probabilistic Inference
Authors: Tuan Anh Le, Pavel Sountsov, Matthew Douglas Hoffman, Ben Lee, Brian Patton, Rif A. Saurous

How do we infer a 3D scene from a single image in the presence of corruptions like rain, snow or fog? Straightforward domain randomization relies on knowing the family of corruptions ahead of time. Here, we propose a Bayesian approach—dubbed robust inverse graphics (RIG)—that relies on a strong scene prior and an uninformative uniform corruption prior, making it applicable to a wide range of corruptions. Given a single image, RIG performs posterior inference jointly over the scene and the corruption. We demonstrate this idea by training a neural radiance field (NeRF) scene prior and using a secondary NeRF to represent the corruptions over which we place an uninformative prior. RIG, trained only on clean data, outperforms depth estimators and alternative NeRF approaches that perform point estimation instead of full inference. The results hold for a number of scene prior architectures based on normalizing flows and diffusion models. For the latter, we develop reconstruction-guidance with auxiliary latents (ReGAL)—a diffusion conditioning algorithm that is applicable in the presence of auxiliary latent variables such as the corruption. RIG demonstrates how scene priors can be used beyond generation tasks.