pwc-archive/papers-with-abstracts huggingface dataset:
Spiking GS: Towards High-Accuracy and Low-Cost Surface Reconstruction via Spiking Neuron-based Gaussian Splatting
Authors: Weixing Zhang, Zongrui Li, De Ma, Huajin Tang, Xudong Jiang, Qian Zheng, Gang Pan
Date: 2024-10-09 00:00:00
Tasks: Surface Reconstruction

3D Gaussian Splatting is capable of reconstructing 3D scenes in minutes. Despite recent advances in improving surface reconstruction accuracy, the reconstructed results still exhibit bias and suffer from inefficiency in storage and training. This paper provides a different observation on the cause of the inefficiency and the reconstruction bias, which is attributed to the integration of the low-opacity parts (LOPs) of the generated Gaussians. We show that LOPs consist of Gaussians with overall low-opacity (LOGs) and the low-opacity tails (LOTs) of Gaussians. We propose Spiking GS to reduce such two types of LOPs by integrating spiking neurons into the Gaussian Splatting pipeline. Specifically, we introduce global and local full-precision integrate-and-fire spiking neurons to the opacity and representation function of flattened 3D Gaussians, respectively. Furthermore, we enhance the density control strategy with spiking neurons' thresholds and a new criterion on the scale of Gaussians. Our method can represent more accurate reconstructed surfaces at a lower cost. The supplementary material and code are available at https://github.com/zju-bmi-lab/SpikingGS.
Efficient Dictionary Learning with Switch Sparse Autoencoders
Authors: Anish Mudide, Joshua Engels, Eric J. Michaud, Max Tegmark, Christian Schroeder de Witt
Date: 2024-10-10 00:00:00
Tasks: Dictionary Learning, Mixture-of-Experts

Sparse autoencoders (SAEs) are a recent technique for decomposing neural network activations into human-interpretable features. However, in order for SAEs to identify all features represented in frontier models, it will be necessary to scale them up to very high width, posing a computational challenge. In this work, we introduce Switch Sparse Autoencoders, a novel SAE architecture aimed at reducing the compute cost of training SAEs. Inspired by sparse mixture of experts models, Switch SAEs route activation vectors between smaller "expert" SAEs, enabling SAEs to efficiently scale to many more features. We present experiments comparing Switch SAEs with other SAE architectures, and find that Switch SAEs deliver a substantial Pareto improvement in the reconstruction vs. sparsity frontier for a given fixed training compute budget. We also study the geometry of features across experts, analyze features duplicated across experts, and verify that Switch SAE features are as interpretable as features found by other SAE architectures.
Adam Exploits $\ell_\infty$-geometry of Loss Landscape via Coordinate-wise Adaptivity
Authors: Shuo Xie, Mohamad Amin Mohamadi, Zhiyuan Li
Date: 2024-10-10 00:00:00

Adam outperforms SGD when training language models. Yet this advantage is not well-understood theoretically -- previous convergence analysis for Adam and SGD mainly focuses on the number of steps $T$ and is already minimax-optimal in non-convex cases, which are both $\widetilde{O}(T^{-1/4})$. In this work, we argue that the exploitation of nice $\ell_\infty$-geometry is the key advantage of Adam over SGD. More specifically, we give a new convergence analysis for Adam under novel assumptions that loss is smooth under $\ell_\infty$-geometry rather than the more common $\ell_2$-geometry, which yields a much better empirical smoothness constant for GPT-2 and ResNet models. Our experiments confirm that Adam performs much worse when the favorable $\ell_\infty$-geometry is changed while SGD provably remains unaffected. We also extend the convergence analysis to blockwise Adam under novel blockwise smoothness assumptions.
Features are fate: a theory of transfer learning in high-dimensional regression
Authors: Javan Tahir, Surya Ganguli, Grant M. Rotskoff
Date: 2024-10-10 00:00:00
Tasks: Transfer Learning

With the emergence of large-scale pre-trained neural networks, methods to adapt such "foundation" models to data-limited downstream tasks have become a necessity. Fine-tuning, preference optimization, and transfer learning have all been successfully employed for these purposes when the target task closely resembles the source task, but a precise theoretical understanding of "task similarity" is still lacking. While conventional wisdom suggests that simple measures of similarity between source and target distributions, such as $\phi$-divergences or integral probability metrics, can directly predict the success of transfer, we prove the surprising fact that, in general, this is not the case. We adopt, instead, a feature-centric viewpoint on transfer learning and establish a number of theoretical results that demonstrate that when the target task is well represented by the feature space of the pre-trained model, transfer learning outperforms training from scratch. We study deep linear networks as a minimal model of transfer learning in which we can analytically characterize the transferability phase diagram as a function of the target dataset size and the feature space overlap. For this model, we establish rigorously that when the feature space overlap between the source and target tasks is sufficiently strong, both linear transfer and fine-tuning improve performance, especially in the low data limit. These results build on an emerging understanding of feature learning dynamics in deep linear networks, and we demonstrate numerically that the rigorous results we derive for the linear case also apply to nonlinear networks.
Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning
Authors: Amrith Setlur, Chirag Nagpal, Adam Fisch, Xinyang Geng, Jacob Eisenstein, Rishabh Agarwal, Alekh Agarwal, Jonathan Berant, Aviral Kumar
Date: 2024-10-10 00:00:00
Tasks: Reinforcement Learning (RL)

A promising approach for improving reasoning in large language models is to use process reward models (PRMs). PRMs provide feedback at each step of a multi-step reasoning trace, potentially improving credit assignment over outcome reward models (ORMs) that only provide feedback at the final step. However, collecting dense, per-step human labels is not scalable, and training PRMs from automatically-labeled data has thus far led to limited gains. To improve a base policy by running search against a PRM or using it as dense rewards for reinforcement learning (RL), we ask: "How should we design process rewards?". Our key insight is that, to be effective, the process reward for a step should measure progress: a change in the likelihood of producing a correct response in the future, before and after taking the step, corresponding to the notion of step-level advantages in RL. Crucially, this progress should be measured under a prover policy distinct from the base policy. We theoretically characterize the set of good provers and our results show that optimizing process rewards from such provers improves exploration during test-time search and online RL. In fact, our characterization shows that weak prover policies can substantially improve a stronger base policy, which we also observe empirically. We validate our claims by training process advantage verifiers (PAVs) to predict progress under such provers, and show that compared to ORMs, test-time search against PAVs is $>8\%$ more accurate, and $1.5-5\times$ more compute-efficient. Online RL with dense rewards from PAVs enables one of the first results with $5-6\times$ gain in sample efficiency, and $>6\%$ gain in accuracy, over ORMs.
Think Beyond Size: Adaptive Prompting for More Effective Reasoning
Authors: Kamesh R
Date: 2024-10-10 00:00:00
Tasks: Arithmetic Reasoning, Computational Efficiency, GSM8K, Logical Reasoning

Pretrained large language models (LLMs) are increasingly utilized across a wide range of natural language processing (NLP) tasks due to their impressive capabilities as few-shot learners. Recent techniques, such as chain-of-thought (CoT) prompting, have significantly advanced multi-step reasoning by introducing step-by-step decomposition, achieving state-of-the-art results on complex reasoning benchmarks. However, these approaches often rely on static prompting templates that do not adapt to task complexity or errors during the reasoning process. In this work, we introduce Adaptive Prompting, a dynamic and iterative framework designed to enhance reasoning by incorporating real-time adjustments to prompt structures and validation mechanisms.Experimental results demonstrate that Adaptive Prompting significantly improves performance on diverse reasoning benchmarks, including arithmetic reasoning (GSM8K, MultiArith), logical reasoning and commonsense tasks, achieving substantial accuracy gains compared to static prompting baselines. By integrating guided prompts, intermediate validation, and self-corrective steps, our approach enables smaller models to achieve competitive performance with larger counterparts, such as GPT-4, while maintaining computational efficiency. The framework achieves this without requiring fine-tuning or task-specific training data, highlighting the untapped potential of iterative reasoning methods.
Generalizing Stochastic Smoothing for Differentiation and Gradient Estimation
Authors: Felix Petersen, Christian Borgelt, Aashwin Mishra, Stefano Ermon
Date: 2024-10-10 00:00:00
Tasks: Pose Estimation

We deal with the problem of gradient estimation for stochastic differentiable relaxations of algorithms, operators, simulators, and other non-differentiable functions. Stochastic smoothing conventionally perturbs the input of a non-differentiable function with a differentiable density distribution with full support, smoothing it and enabling gradient estimation. Our theory starts at first principles to derive stochastic smoothing with reduced assumptions, without requiring a differentiable density nor full support, and we present a general framework for relaxation and gradient estimation of non-differentiable black-box functions $f:\mathbb{R}^n\to\mathbb{R}^m$. We develop variance reduction for gradient estimation from 3 orthogonal perspectives. Empirically, we benchmark 6 distributions and up to 24 variance reduction strategies for differentiable sorting and ranking, differentiable shortest-paths on graphs, differentiable rendering for pose estimation, as well as differentiable cryo-ET simulations.
On Barycenter Computation: Semi-Unbalanced Optimal Transport-based Method on Gaussians
Authors: Ngoc-Hai Nguyen, Dung Le, Hoang-Phi Nguyen, Tung Pham, Nhat Ho
Date: 2024-10-10 00:00:00

We explore a robust version of the barycenter problem among $n$ centered Gaussian probability measures, termed Semi-Unbalanced Optimal Transport (SUOT)-based Barycenter, wherein the barycenter remains fixed while the others are relaxed using Kullback-Leibler divergence. We develop optimization algorithms on Bures-Wasserstein manifold, named the Exact Geodesic Gradient Descent and Hybrid Gradient Descent algorithms. While the Exact Geodesic Gradient Descent method is based on computing the exact closed form of the first-order derivative of the objective function of the barycenter along a geodesic on the Bures manifold, the Hybrid Gradient Descent method utilizes optimizer components when solving the SUOT problem to replace outlier measures before applying the Riemannian Gradient Descent. We establish the theoretical convergence guarantees for both methods and demonstrate that the Exact Geodesic Gradient Descent algorithm attains a dimension-free convergence rate. Finally, we conduct experiments to compare the normal Wasserstein Barycenter with ours and perform an ablation study.
Noether's razor: Learning Conserved Quantities
Authors: Tycho F. A. van der Ouderaa, Mark van der Wilk, Pim de Haan
Date: 2024-10-10 00:00:00
Tasks: Model Selection

Symmetries have proven useful in machine learning models, improving generalisation and overall performance. At the same time, recent advancements in learning dynamical systems rely on modelling the underlying Hamiltonian to guarantee the conservation of energy. These approaches can be connected via a seminal result in mathematical physics: Noether's theorem, which states that symmetries in a dynamical system correspond to conserved quantities. This work uses Noether's theorem to parameterise symmetries as learnable conserved quantities. We then allow conserved quantities and associated symmetries to be learned directly from train data through approximate Bayesian model selection, jointly with the regular training procedure. As training objective, we derive a variational lower bound to the marginal likelihood. The objective automatically embodies an Occam's Razor effect that avoids collapse of conservation laws to the trivial constant, without the need to manually add and tune additional regularisers. We demonstrate a proof-of-principle on $n$-harmonic oscillators and $n$-body systems. We find that our method correctly identifies the correct conserved quantities and U($n$) and SE($n$) symmetry groups, improving overall performance and predictive accuracy on test data.
Gaussian Process Thompson Sampling via Rootfinding
Authors: Taiwo A. Adebiyi, Bach Do, Ruda Zhang
Date: 2024-10-10 00:00:00
Tasks: Bayesian Optimization, Decision Making, global-optimization, Thompson Sampling

Thompson sampling (TS) is a simple, effective stochastic policy in Bayesian decision making. It samples the posterior belief about the reward profile and optimizes the sample to obtain a candidate decision. In continuous optimization, the posterior of the objective function is often a Gaussian process (GP), whose sample paths have numerous local optima, making their global optimization challenging. In this work, we introduce an efficient global optimization strategy for GP-TS that carefully selects starting points for gradient-based multi-start optimizers. It identifies all local optima of the prior sample via univariate global rootfinding, and optimizes the posterior sample using a differentiable, decoupled representation. We demonstrate remarkable improvement in the global optimization of GP posterior samples, especially in high dimensions. This leads to dramatic improvements in the overall performance of Bayesian optimization using GP-TS acquisition functions, surprisingly outperforming alternatives like GP-UCB and EI.
VerifierQ: Enhancing LLM Test Time Compute with Q-Learning-based Verifiers
Authors: Jianing Qi, Hao Tang, Zhigang Zhu
Date: 2024-10-10 00:00:00
Tasks: Mathematical Reasoning, Q-Learning, Reinforcement Learning (RL)

Recent advancements in test time compute, particularly through the use of verifier models, have significantly enhanced the reasoning capabilities of Large Language Models (LLMs). This generator-verifier approach closely resembles the actor-critic framework in reinforcement learning (RL). However, current verifier models in LLMs often rely on supervised fine-tuning without temporal difference learning such as Q-learning. This paper introduces VerifierQ, a novel approach that integrates Offline Q-learning into LLM verifier models. We address three key challenges in applying Q-learning to LLMs: (1) handling utterance-level Markov Decision Processes (MDPs), (2) managing large action spaces, and (3) mitigating overestimation bias. VerifierQ introduces a modified Bellman update for bounded Q-values, incorporates Implicit Q-learning (IQL) for efficient action space management, and integrates a novel Conservative Q-learning (CQL) formulation for balanced Q-value estimation. Our method enables parallel Q-value computation and improving training efficiency. While recent work has explored RL techniques like MCTS for generators, VerifierQ is among the first to investigate the verifier (critic) aspect in LLMs through Q-learning. This integration of RL principles into verifier models complements existing advancements in generator techniques, potentially enabling more robust and adaptive reasoning in LLMs. Experimental results on mathematical reasoning tasks demonstrate VerifierQ's superior performance compared to traditional supervised fine-tuning approaches, with improvements in efficiency, accuracy and robustness. By enhancing the synergy between generation and evaluation capabilities, VerifierQ contributes to the ongoing evolution of AI systems in addressing complex cognitive tasks across various domains.
Generalization Bounds and Model Complexity for Kolmogorov-Arnold Networks
Authors: Xianyang Zhang, Huijuan Zhou
Date: 2024-10-10 00:00:00
Tasks: Generalization Bounds, Kolmogorov-Arnold Networks

Kolmogorov-Arnold Network (KAN) is a network structure recently proposed by Liu et al. (2024) that offers improved interpretability and a more parsimonious design in many science-oriented tasks compared to multi-layer perceptrons. This work provides a rigorous theoretical analysis of KAN by establishing generalization bounds for KAN equipped with activation functions that are either represented by linear combinations of basis functions or lying in a low-rank Reproducing Kernel Hilbert Space (RKHS). In the first case, the generalization bound accommodates various choices of basis functions in forming the activation functions in each layer of KAN and is adapted to different operator norms at each layer. For a particular choice of operator norms, the bound scales with the $l_1$ norm of the coefficient matrices and the Lipschitz constants for the activation functions, and it has no dependence on combinatorial parameters (e.g., number of nodes) outside of logarithmic factors. Moreover, our result does not require the boundedness assumption on the loss function and, hence, is applicable to a general class of regression-type loss functions. In the low-rank case, the generalization bound scales polynomially with the underlying ranks as well as the Lipschitz constants of the activation functions in each layer. These bounds are empirically investigated for KANs trained with stochastic gradient descent on simulated and real data sets. The numerical results demonstrate the practical relevance of these bounds.
Non-transferable Pruning
Authors: Ruyi Ding, Lili Su, Aidong Adam Ding, Yunsi Fei
Date: 2024-10-10 00:00:00
Tasks: Self-Supervised Learning, Transfer Learning

Pretrained Deep Neural Networks (DNNs), developed from extensive datasets to integrate multifaceted knowledge, are increasingly recognized as valuable intellectual property (IP). To safeguard these models against IP infringement, strategies for ownership verification and usage authorization have emerged. Unlike most existing IP protection strategies that concentrate on restricting direct access to the model, our study addresses an extended DNN IP issue: applicability authorization, aiming to prevent the misuse of learned knowledge, particularly in unauthorized transfer learning scenarios. We propose Non-Transferable Pruning (NTP), a novel IP protection method that leverages model pruning to control a pretrained DNN's transferability to unauthorized data domains. Selective pruning can deliberately diminish a model's suitability on unauthorized domains, even with full fine-tuning. Specifically, our framework employs the alternating direction method of multipliers (ADMM) for optimizing both the model sparsity and an innovative non-transferable learning loss, augmented with Fisher space discriminative regularization, to constrain the model's generalizability to the target dataset. We also propose a novel effective metric to measure the model non-transferability: Area Under the Sample-wise Learning Curve (SLC-AUC). This metric facilitates consideration of full fine-tuning across various sample sizes. Experimental results demonstrate that NTP significantly surpasses the state-of-the-art non-transferable learning methods, with an average SLC-AUC at $-0.54$ across diverse pairs of source and target domains, indicating that models trained with NTP do not suit for transfer learning to unauthorized target domains. The efficacy of NTP is validated in both supervised and self-supervised learning contexts, confirming its applicability in real-world scenarios.
Time Can Invalidate Algorithmic Recourse
Authors: Giovanni De Toni, Stefano Teso, Bruno Lepri, Andrea Passerini
Date: 2024-10-10 00:00:00
Tasks: counterfactual, valid

Algorithmic Recourse (AR) aims to provide users with actionable steps to overturn unfavourable decisions made by machine learning predictors. However, these actions often take time to implement (e.g., getting a degree can take years), and their effects may vary as the world evolves. Thus, it is natural to ask for recourse that remains valid in a dynamic environment. In this paper, we study the robustness of algorithmic recourse over time by casting the problem through the lens of causality. We demonstrate theoretically and empirically that (even robust) causal AR methods can fail over time, except in the -- unlikely -- case that the world is stationary. Even more critically, unless the world is fully deterministic, counterfactual AR cannot be solved optimally. To account for this, we propose a simple yet effective algorithm for temporal AR that explicitly accounts for time under the assumption of having access to an estimator approximating the stochastic process. Our simulations on synthetic and realistic datasets show how considering time produces more resilient solutions to potential trends in the data distribution.
More Experts Than Galaxies: Conditionally-overlapping Experts With Biologically-Inspired Fixed Routing
Authors: Sagi Shaier, Francisco Pereira, Katharina von der Wense, Lawrence E Hunter, Matt Jones
Date: 2024-10-10 00:00:00
Tasks: image-classification, Image Classification, Language Modeling, Language Modelling, Mixture-of-Experts, Transfer Learning

The evolution of biological neural systems has led to both modularity and sparse coding, which enables energy efficiency and robustness across the diversity of tasks in the lifespan. In contrast, standard neural networks rely on dense, non-specialized architectures, where all model parameters are simultaneously updated to learn multiple tasks, leading to interference. Current sparse neural network approaches aim to alleviate this issue but are hindered by limitations such as 1) trainable gating functions that cause representation collapse, 2) disjoint experts that result in redundant computation and slow learning, and 3) reliance on explicit input or task IDs that limit flexibility and scalability. In this paper we propose Conditionally Overlapping Mixture of ExperTs (COMET), a general deep learning method that addresses these challenges by inducing a modular, sparse architecture with an exponential number of overlapping experts. COMET replaces the trainable gating function used in Sparse Mixture of Experts with a fixed, biologically inspired random projection applied to individual input representations. This design causes the degree of expert overlap to depend on input similarity, so that similar inputs tend to share more parameters. This results in faster learning \rev{per update step} and improved \rev{out-of-sample} generalization. We demonstrate the effectiveness of COMET on a range of tasks, including image classification, language modeling, and regression, using several popular deep learning architectures.