huashen218/convxai-cia-dataset huggingface dataset:
Prototype memory and attention mechanisms for few shot image generation
Keywords: neuroscience, deep learning

Recent discoveries indicate that the neural codes in the primary visual cortex (V1) of macaque monkeys are complex, diverse and sparse. This leads us to ponder the computational advantages and functional role of these “grandmother cells." Here, we propose that such cells can serve as prototype memory priors that bias and shape the distributed feature processing within the image generation process in the brain. These memory prototypes are learned by momentum online clustering and are utilized via a memory-based attention operation, which we define as Memory Concept Attention (MoCA). To test our proposal, we show in a few-shot image generation task, that having a prototype memory during attention can improve image synthesis quality, learn interpretable visual concept clusters, as well as improve the robustness of the model. Interestingly, we also find that our attentional memory mechanism can implicitly modify the horizontal connections by updating the transformation into the prototype embedding space for self-attention. Insofar as GANs can be seen as plausible models for reasoning about the top-down synthesis in the analysis-by-synthesis loop of the hierarchical visual cortex, our findings demonstrate a plausible computational role for these “prototype concept" neurons in visual processing in the brain.
TPU-GAN: Learning temporal coherence from dynamic point cloud sequences
Keywords: Point cloud super resolution, Temporal learning, Generative Adversarial Networks

Point cloud sequence is an important data representation that provides flexible shape and motion information. Prior work demonstrates that incorporating scene flow information into loss can make model learn temporally coherent feature spaces. However, it is prohibitively expensive to acquire point correspondence information across frames in real-world environments. In this work, we propose a super-resolution generative adversarial network (GAN) for upsampling dynamic point cloud sequences, which does not require point correspondence annotation.  Our model, Temporal Point cloud Upsampling GAN (TPU-GAN), can implicitly learn the underlying temporal coherence from point cloud sequence, which in turn guides the generator to produce temporally coherent output. In addition, we propose a learnable masking module to adapt upsampling ratio according to the point distribution. We conduct extensive experiments on point cloud sequences from two different domains: particles in the fluid dynamical system and human action scanned data. The quantitative and qualitative evaluation demonstrates the effectiveness of our method on upsampling tasks as well as learning temporal coherence from irregular point cloud sequences.
A First-Occupancy Representation for Reinforcement Learning
Keywords: successor representation, successor features, generalized policy improvement, GPI

Both animals and artificial agents benefit from state representations that support rapid transfer of learning across tasks and which enable them to efficiently traverse their environments to reach rewarding states.  The successor representation (SR), which measures the expected cumulative, discounted state occupancy under a fixed policy, enables efficient transfer to different reward structures in an otherwise constant Markovian environment and has been hypothesized to underlie aspects of biological behavior and neural activity.  However, in the real world, rewards may only be available for consumption once, may shift location, or agents may simply aim to reach goal states as rapidly as possible without the constraint of artificially imposed task horizons. In such cases, the most behaviorally-relevant representation would carry information about when the agent was likely to first reach states of interest, rather than how often it should expect to visit them over a potentially infinite time span.  To reflect such demands, we introduce the first-occupancy representation (FR), which measures the expected temporal discount to the first time a state is accessed.  We demonstrate that the FR facilitates exploration, the selection of efficient paths to desired states, allows the agent, under certain conditions, to plan provably optimal trajectories defined by a sequence of subgoals, and induces similar behavior to animals avoiding threatening stimuli.
Deep ReLU Networks Preserve Expected Length
Keywords: deep learning theory, random ReLU networks, length distortion, initialization, expressivity

Assessing the complexity of functions computed by a neural network helps us understand how the network will learn and generalize. One natural measure of complexity is how the network distorts length - if the network takes a unit-length curve as input, what is the length of the resulting curve of outputs? It has been widely believed that this length grows exponentially in network depth. We prove that in fact this is not the case: the expected length distortion does not grow with depth, and indeed shrinks slightly, for ReLU networks with standard random initialization. We also generalize this result by proving upper bounds both for higher moments of the length distortion and for the distortion of higher-dimensional volumes. These theoretical results are corroborated by our experiments.
Phenomenology of Double Descent in Finite-Width Neural Networks
Keywords: double descent, generalization, neural networks, hessian, flatness

`Double descent' delineates the generalization behaviour of models depending on the regime they belong to: under- or over-parameterized. The current theoretical understanding behind the occurrence of this phenomenon is primarily based on linear and kernel regression models --- with informal parallels to neural networks via the Neural Tangent Kernel. Therefore such analyses do not adequately capture the mechanisms behind double descent in finite-width neural networks, as well as, disregard crucial components --- such as the choice of the loss function. We address these shortcomings by leveraging influence functions in order to derive suitable expressions of the population loss and its lower bound, while imposing minimal assumptions on the form of the parametric model. Our derived bounds bear an intimate connection with the spectrum of the Hessian at the optimum, and importantly, exhibit a double descent behaviour at the interpolation threshold. Building on our analysis, we further investigate how the loss function affects double descent --- and thus uncover interesting properties of neural networks and their Hessian spectra near the interpolation threshold.
How Attentive are Graph Attention Networks?
Keywords: graph attention networks, dynamic attention, GAT, GNN

Graph Attention Networks (GATs) are one of the most popular GNN architectures and are considered as the state-of-the-art architecture for representation learning with graphs. In GAT, every node attends to its neighbors given its own representation as the query.
        However, in this paper we show that GAT computes a very limited kind of attention: the ranking of the attention scores is unconditioned on the query node. We formally define this restricted kind of attention as static attention and distinguish it from a strictly more expressive dynamic attention.
        Because GATs use a static attention mechanism, there are simple graph problems that GAT cannot express: in a controlled problem, we show that static attention hinders GAT from even fitting the training data. 
        To remove this limitation, we introduce a simple fix by modifying the order of operations and propose GATv2: a dynamic graph attention variant that is strictly more expressive than GAT. We perform an extensive evaluation and show that GATv2 outperforms GAT across 12 OGB and other benchmarks while we match their parametric costs. 
        Our code is available at https://github.com/tech-srl/how_attentive_are_gats . GATv2 is available as part of the PyTorch Geometric library, the Deep Graph Library, and the TensorFlow GNN library.
CKConv: Continuous Kernel Convolution For Sequential Data
Keywords: Convolutional Networks, Continuous kernel Convolutions, Continuous Convolutional Kernels, Implicit Neural Representations, Sequential Data.

Conventional neural architectures for sequential data present important limitations. Recurrent neural networks suffer from exploding and vanishing gradients, small effective memory horizons, and must be trained sequentially. Convolutional neural networks cannot handle sequences of unknown size and their memory horizon must be defined a priori. In this work, we show that these problems can be solved by formulating the convolutional kernels of CNNs as continuous functions. The resulting Continuous Kernel Convolution (CKConv) handles arbitrarily long sequences in a parallel manner, within a single operation, and without relying on any form of recurrence. We show that Continuous Kernel Convolutional Networks (CKCNNs) obtain state-of-the-art results in multiple datasets, e.g., permuted MNIST, and, thanks to their continuous nature, are able to handle non-uniformly sampled datasets and irregularly-sampled data natively. CKCNNs match or perform better than neural ODEs designed for these purposes in a faster and simpler manner.
Towards Empirical Sandwich Bounds on the Rate-Distortion Function
Keywords: information theory, deep generative modeling, lossy data compression

Rate-distortion (R-D) function, a key quantity in information theory, characterizes the fundamental limit of how much a data source can be compressed subject to a fidelity criterion, by any compression algorithm. As researchers push for ever-improving compression performance, establishing the R-D function of a given data source is not only of scientific interest, but also reveals the possible room for improvement in existing compression algorithms. Previous work on this problem relied on distributional assumptions on the data source (Gibson, 2017) or only applied to discrete data (Blahut, 1972; Arimoto, 1972). By contrast, this paper makes the first attempt at an algorithm for sandwiching the R-D function of a general (not necessarily discrete) source requiring only i.i.d. data samples. We estimate R-D sandwich bounds for a variety of artificial and real-world data sources, in settings far beyond the feasibility of any known method, and shed light on the optimality of neural data compression (Ballé et al., 2021; Yang et al., 2022). Our R-D upper bound on natural images indicates theoretical room for improving state-of-the-art image compression methods by at least one dB in PSNR at various bitrates. Our data and code can be found at https://github.com/mandt-lab/RD-sandwich.
Pareto Policy Adaptation
Keywords: multi-objective reinforcement learning, policy gradient, pareto optimality, policy adaptation

We present a policy gradient method for Multi-Objective Reinforcement Learning under unknown, linear preferences. By enforcing Pareto stationarity, a first-order condition for Pareto optimality, we are able to design a simple policy gradient algorithm that approximates the Pareto front and infers the unknown preferences. Our method relies on a projected gradient descent solver that identifies common ascent directions for all objectives. Leveraging the solution of that solver, we introduce Pareto Policy Adaptation (PPA), a loss function that adapts the policy to be optimal with respect to any distribution over preferences. PPA uses implicit differentiation to back-propagate the loss gradient bypassing the operations of the projected gradient descent solver. Our approach is straightforward, easy to implement and can be used with all existing policy gradient and actor-critic methods. We evaluate our method in a series of reinforcement learning tasks
Fair Normalizing Flows
Keywords: fairness, fair representation learning, adversarial fairness, trustworthy machine learning

Fair representation learning is an attractive approach that promises fairness of downstream predictors by encoding sensitive data. Unfortunately, recent work has shown that strong adversarial predictors can still exhibit unfairness by recovering sensitive attributes from these representations. In this work, we present Fair Normalizing Flows (FNF), a new approach offering more rigorous fairness guarantees for learned representations. Specifically, we consider a practical setting where we can estimate the probability density for sensitive groups. The key idea is to model the encoder as a normalizing flow trained to minimize the statistical distance between the latent representations of different groups. The main advantage of FNF is that its exact likelihood computation allows us to obtain guarantees on the maximum unfairness of any potentially adversarial downstream predictor. We experimentally demonstrate the effectiveness of FNF in enforcing various group fairness notions, as well as other attractive properties such as interpretability and transfer learning, on a variety of challenging real-world datasets.
The Convex Geometry of Backpropagation: Neural Network Gradient Flows Converge to Extreme Points of the Dual Convex Program
Keywords: Two-layer ReLU networks, convex optimization, convex duality, gradient flow

We study non-convex subgradient flows for training two-layer ReLU neural networks from a convex geometry and duality perspective. We characterize the implicit bias of unregularized non-convex gradient flow as convex regularization of an equivalent convex model. We then show that the limit points of non-convex subgradient flows can be identified via primal-dual correspondence in this convex optimization problem.  Moreover, we derive a sufficient condition on the dual variables which ensures that the stationary points of the non-convex objective are the KKT points of the convex objective, thus proving convergence of non-convex gradient flows to the global optimum. For a class of regular training data distributions such as orthogonal separable data, we show that this sufficient condition holds. Therefore, non-convex gradient flows in fact converge to optimal solutions of a convex optimization problem. We present numerical results verifying the predictions of our theory for non-convex subgradient descent.
Adaptive Wavelet Transformer Network for 3D Shape Representation Learning

We present a novel method for 3D shape representation learning using multi-scale wavelet decomposition. Previous works often decompose 3D shapes into complementary components in spatial domain at a single scale. In this work, we study to decompose 3D shapes into sub-bands components in frequency domain at multiple scales, resulting in a hierarchical decomposition tree in a principled manner rooted in multi-resolution wavelet analysis. Specifically, we propose Adaptive Wavelet Transformer Network (AWT-Net) that firstly generates approximation or detail wavelet coefficients per point, classifying each point into high or low sub-bands components, using lifting scheme at multiple scales recursively and hierarchically. Then, AWT-Net exploits Transformer to enhance the original shape features by querying and fusing features from different but integrated sub-bands. The wavelet coefficients can be learned without direct supervision on coefficients, and AWT-Net is fully differentiable and can be learned in an end-to-end fashion. Extensive experiments demonstrate that AWT-Net achieves competitive performance on 3D shape classification and segmentation benchmarks.
On the Convergence of mSGD and AdaGrad for Stochastic Optimization
Keywords: stochastic gradient descent, adaptive gradient algorithm, asymptotic convergence

As one of the most fundamental stochastic optimization algorithms, stochastic gradient descent (SGD) has been intensively developed and extensively applied in machine learning in the past decade. There have been some modified SGD-type algorithms, which outperform the SGD in many competitions and applications in terms of convergence rate and accuracy, such as momentum-based SGD (mSGD) and adaptive gradient algorithm (AdaGrad). Despite these empirical successes, the theoretical properties of these algorithms have not been well established due to technical difficulties. With this motivation, we focus on convergence analysis of mSGD and AdaGrad for any smooth (possibly non-convex) loss functions in stochastic optimization. First, we prove that the iterates of mSGD are asymptotically convergent to a connected set of stationary points with probability one, which is more general than existing works on subsequence convergence or convergence of time averages. Moreover, we prove that the loss function of mSGD decays at a certain rate faster than that of SGD. In addition, we prove the iterates of AdaGrad are asymptotically convergent to a connected set of stationary points with probability one. Also, this result extends the results from the literature on subsequence convergence and the convergence of time averages. Despite the generality of the above convergence results, we have relaxed some assumptions of gradient noises, convexity of loss functions, as well as boundedness of iterates.
Likelihood Training of Schrödinger Bridge using Forward-Backward SDEs Theory
Keywords: Schrödinger Bridge, score-based generative model, optimal transport, forward-backward stochastic differential equations, stochastic optimal control

Schrödinger Bridge (SB) is an entropy-regularized optimal transport problem that has received increasing attention in deep generative modeling for its mathematical flexibility compared to the Scored-based Generative Model (SGM). However, it remains unclear whether the optimization principle of SB relates to the modern training of deep generative models, which often rely on constructing log-likelihood objectives.This raises questions on the suitability of SB models as a principled alternative for generative applications. In this work, we present a novel computational framework for likelihood training of SB models grounded on Forward-Backward Stochastic Differential Equations Theory – a mathematical methodology appeared in stochastic optimal control that transforms the optimality condition of SB into a set of SDEs. Crucially, these SDEs can be used to construct the likelihood objectives for SB that, surprisingly, generalizes the ones for SGM as special cases. This leads to a new optimization principle that inherits the same SB optimality yet without losing applications of modern generative training techniques, and we show that the resulting training algorithm achieves comparable results on generating realistic images on MNIST, CelebA, and CIFAR10. Our code is available at https://github.com/ghliu/SB-FBSDE.
Imitation Learning from Observations under Transition Model Disparity
Keywords: Imitation Learning, Deep Reinforcement Learning

Learning to perform tasks by leveraging a dataset of expert observations, also known as imitation learning from observations (ILO), is an important paradigm for learning skills without access to the expert reward function or the expert actions. We consider ILO in the setting where the expert and the learner agents operate in different environments, with the source of the discrepancy being the transition dynamics model. Recent methods for scalable ILO utilize adversarial learning to match the state-transition distributions of the expert and the learner, an approach that becomes challenging when the dynamics are dissimilar. In this work, we propose an algorithm that trains an intermediary policy in the learner environment and uses it as a surrogate expert for the learner. The intermediary policy is learned such that the state transitions generated by it are close to the state transitions in the expert dataset. To derive a practical and scalable algorithm, we employ concepts from prior work on estimating the support of a probability distribution. Experiments using MuJoCo locomotion tasks highlight that our method compares favorably to the baselines for ILO with transition dynamics mismatch.
MCMC Should Mix: Learning Energy-Based Model with Neural Transport Latent Space MCMC
Keywords: Generative models, energy-based models, MCMC

Learning energy-based model (EBM) requires MCMC sampling of the learned model as an inner loop of the learning algorithm. However, MCMC sampling of EBMs in high-dimensional data space is generally not mixing, because the energy function, which is usually parametrized by deep network, is highly multi-modal in the data space. This is a serious handicap for both theory and practice of EBMs. In this paper, we propose to learn EBM with a flow-based model (or in general latent variable model) serving as a backbone, so that the EBM is a correction or an exponential tilting of the flow-based model. We show that the model has a particularly simple form in the space of the latent variables of the generative model, and MCMC sampling of the EBM in the latent space mixes well and traverses modes in the data space. This enables proper sampling and learning of EBMs.
Autonomous Learning of Object-Centric Abstractions for High-Level Planning
Keywords: reinforcement learning, planning, multitask, transfer, objects

We propose a method for autonomously learning an object-centric representation of a continuous and high-dimensional environment that is suitable for planning. Such representations can immediately be transferred between tasks that share the same types of objects, resulting in agents that require fewer samples to learn a model of a new task. We first demonstrate our approach on a 2D crafting domain consisting of numerous objects where the agent learns a compact, lifted representation that generalises across objects. We then apply it to a series of Minecraft tasks to learn object-centric representations and object types - directly from pixel data - that can be leveraged to solve new tasks quickly. The resulting learned representations enable the use of a task-level planner, resulting in an agent capable of transferring learned representations to form complex, long-term plans.
A fast and accurate splitting method for optimal transport: analysis and implementation
Keywords: Optimal transport, Operator splitting, Douglas-Rachford, ADMM, GPUs

We develop a fast and reliable method for solving large-scale optimal transport (OT) problems at an unprecedented combination of speed and accuracy. Built on the celebrated Douglas-Rachford splitting technique, our method tackles the original OT problem directly instead of solving an approximate regularized problem, as many state-of-the-art techniques do. This allows us to provide sparse transport plans and avoid numerical issues of methods that use entropic regularization. The algorithm has the same cost per iteration as the popular Sinkhorn method, and each iteration can be executed efficiently, in parallel. The proposed method enjoys an iteration complexity $O(1/\epsilon)$ compared to the best-known $O(1/\epsilon^2)$ of the Sinkhorn method. In addition, we establish a linear convergence rate for our formulation of the OT problem. We detail an efficient GPU implementation of the proposed method that maintains a primal-dual stopping criterion at no extra cost. Substantial experiments demonstrate the effectiveness of our method, both in terms of computation times and robustness.