Maximizing the log-likelihood is a crucial aspect of learning latent variable models, and variational inference (VI) stands as the commonly adopted method. However, VI can encounter challenges in achieving a high log-likelihood when dealing with complicated posterior distributions. In response to this limitation, we introduce a novel variational importance sampling (VIS) approach that directly estimates and maximizes the log-likelihood. VIS leverages the optimal proposal distribution, achieved by minimizing the forward $\chi^2$ divergence, to enhance log-likelihood estimation. We apply VIS to various popular latent variable models, including mixture models, variational auto-encoders, and partially observable generalized linear models. Results demonstrate that our approach consistently outperforms state-of-the-art baselines, both in terms of log-likelihood and model parameter estimation.
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Geometric deep learning extends deep learning to incorporate information about the geometry and topology data, especially in complex domains like graphs. Despite the popularity of message passing in this field, it has limitations such as the need for graph rewiring, ambiguity in interpreting data, and over-smoothing. In this paper, we take a different approach, focusing on leveraging geometric information from simplicial complexes embedded in $\mathbb{R}^n$ using node coordinates. We use differential k-forms in \mathbb{R}^n to create representations of simplices, offering interpretability and geometric consistency without message passing. This approach also enables us to apply differential geometry tools and achieve universal approximation. Our method is efficient, versatile, and applicable to various input complexes, including graphs, simplicial complexes, and cell complexes. It outperforms existing message passing neural networks in harnessing information from geometrical graphs with node features serving as coordinates.
Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions $\mathbb{R}^3$, position and orientations $\mathbb{R}^3 {\times} S^2$, and the group $SE(3)$ itself. Among these, $\mathbb{R}^3 {\times} S^2$ is an optimal choice due to the ability to represent directional information, which $\mathbb{R}^3$ methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full $SE(3)$ group. We support this claim with state-of-the-art results -- in accuracy and speed -- on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.
The rise of cloud computing has spurred a trend of transferring data storage and computational tasks to the cloud. To protect confidential information such as customer data and business details, it is essential to encrypt this sensitive data before cloud storage. Implementing encryption can prevent unauthorized access, data breaches, and the resultant financial loss, reputation damage, and legal issues. Moreover, to facilitate the execution of data mining algorithms on the cloud-stored data, the encryption needs to be compatible with domain computation. The $k$-nearest neighbor ($k$-NN) computation for a specific query vector is widely used in fields like location-based services. Sanyashi et al. (ICISS 2023) proposed an encryption scheme to facilitate privacy-preserving $k$-NN computation on the cloud by utilizing Asymmetric Scalar-Product-Preserving Encryption (ASPE). In this work, we identify a significant vulnerability in the aforementioned encryption scheme of Sanyashi et al. Specifically, we give an efficient algorithm and also empirically demonstrate that their encryption scheme is vulnerable to the ciphertext-only attack (COA).
Distillation is the task of replacing a complicated machine learning model with a simpler model that approximates the original [BCNM06,HVD15]. Despite many practical applications, basic questions about the extent to which models can be distilled, and the runtime and amount of data needed to distill, remain largely open. To study these questions, we initiate a general theory of distillation, defining PAC-distillation in an analogous way to PAC-learning [Val84]. As applications of this theory: (1) we propose new algorithms to extract the knowledge stored in the trained weights of neural networks -- we show how to efficiently distill neural networks into succinct, explicit decision tree representations when possible by using the ``linear representation hypothesis''; and (2) we prove that distillation can be much cheaper than learning from scratch, and make progress on characterizing its complexity.
We consider a distributed setup for reinforcement learning, where each agent has a copy of the same Markov Decision Process but transitions are sampled from the corresponding Markov chain independently by each agent. We show that in this setting, we can achieve a linear speedup for TD($\lambda$), a family of popular methods for policy evaluation, in the sense that $N$ agents can evaluate a policy $N$ times faster provided the target accuracy is small enough. Notably, this speedup is achieved by ``one shot averaging,'' a procedure where the agents run TD($\lambda$) with Markov sampling independently and only average their results after the final step. This significantly reduces the amount of communication required to achieve a linear speedup relative to previous work.
Humans learn social skills through both imitation and social interaction. This social learning process is largely understudied by existing research on building language agents. Motivated by this gap, we propose an interactive learning method, SOTOPIA-$\pi$, improving the social intelligence of language agents. This method leverages behavior cloning and self-reinforcement training on filtered social interaction data according to large language model (LLM) ratings. We show that our training method allows a 7B LLM to reach the social goal completion ability of an expert model (GPT-4-based agent), while improving the safety of language agents and maintaining general QA ability on the MMLU benchmark. We also find that this training paradigm uncovers some difficulties in LLM-based evaluation of social intelligence: LLM-based evaluators overestimate the abilities of the language agents trained specifically for social interaction.
JAX is widely used in machine learning and scientific computing, the latter of which often relies on existing high-performance code that we would ideally like to incorporate into JAX. Reimplementing the existing code in JAX is often impractical and the existing interface in JAX for binding custom code requires deep knowledge of JAX and its C++ backend. The goal of JAXbind is to drastically reduce the effort required to bind custom functions implemented in other programming languages to JAX. Specifically, JAXbind provides an easy-to-use Python interface for defining custom so-called JAX primitives that support arbitrary JAX transformations.
Constructing small-sized coresets for various clustering problems in different metric spaces has attracted significant attention for the past decade. A central problem in the coreset literature is to understand what is the best possible coreset size for $(k,z)$-clustering in Euclidean space. While there has been significant progress in the problem, there is still a gap between the state-of-the-art upper and lower bounds. For instance, the best known upper bound for $k$-means ($z=2$) is $\min \{O(k^{3/2} \varepsilon^{-2}),O(k \varepsilon^{-4})\}$ [1,2], while the best known lower bound is $\Omega(k\varepsilon^{-2})$ [1]. In this paper, we make significant progress on both upper and lower bounds. For a large range of parameters (i.e., $\varepsilon, k$), we have a complete understanding of the optimal coreset size. In particular, we obtain the following results: (1) We present a new coreset lower bound $\Omega(k \varepsilon^{-z-2})$ for Euclidean $(k,z)$-clustering when $\varepsilon \geq \Omega(k^{-1/(z+2)})$. In view of the prior upper bound $\tilde{O}_z(k \varepsilon^{-z-2})$ [1], the bound is optimal. The new lower bound also implies improved lower bounds for $(k,z)$-clustering in doubling metrics. (2) For the upper bound, we provide efficient coreset construction algorithms for $(k,z)$-clustering with improved or optimal coreset sizes in several metric spaces. In particular, we provide an $\tilde{O}_z(k^{\frac{2z+2}{z+2}} \varepsilon^{-2})$-sized coreset, with a unfied analysis, for $(k,z)$-clustering for all $z\geq 1$ in Euclidean space. [1] Cohen-Addad, Larsen, Saulpic, Schwiegelshohn. STOC'22. [2] Cohen-Addad, Larsen, Saulpic, Schwiegelshohn, Sheikh-Omar, NeurIPS'22.
This paper introduces AL$\ell_0$CORE, a new form of probabilistic non-negative tensor decomposition. AL$\ell_0$CORE is a Tucker decomposition where the number of non-zero elements (i.e., the $\ell_0$-norm) of the core tensor is constrained to a preset value $Q$ much smaller than the size of the core. While the user dictates the total budget $Q$, the locations and values of the non-zero elements are latent variables and allocated across the core tensor during inference. AL$\ell_0$CORE -- i.e., $allo$cated $\ell_0$-$co$nstrained $core$-- thus enjoys both the computational tractability of CP decomposition and the qualitatively appealing latent structure of Tucker. In a suite of real-data experiments, we demonstrate that AL$\ell_0$CORE typically requires only tiny fractions (e.g.,~1%) of the full core to achieve the same results as full Tucker decomposition at only a correspondingly tiny fraction of the cost.
Click-through rate (CTR) prediction plays a critical role in recommender systems and online advertising. The data used in these applications are multi-field categorical data, where each feature belongs to one field. Field information is proved to be important and there are several works considering fields in their models. In this paper, we proposed a novel approach to model the field information effectively and efficiently. The proposed approach is a direct improvement of FwFM, and is named as Field-matrixed Factorization Machines (FmFM, or $FM^2$). We also proposed a new explanation of FM and FwFM within the FmFM framework, and compared it with the FFM. Besides pruning the cross terms, our model supports field-specific variable dimensions of embedding vectors, which acts as soft pruning. We also proposed an efficient way to minimize the dimension while keeping the model performance. The FmFM model can also be optimized further by caching the intermediate vectors, and it only takes thousands of floating-point operations (FLOPs) to make a prediction. Our experiment results show that it can out-perform the FFM, which is more complex. The FmFM model's performance is also comparable to DNN models which require much more FLOPs in runtime.
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