Many recent state-of-the-art results in language tasks were achieved using compound systems that perform multiple Language Model (LM) calls and aggregate their responses. However, there is little understanding of how the number of LM calls - e.g., when asking the LM to answer each question multiple times and taking a majority vote - affects such a compound system's performance. In this paper, we initiate the study of scaling properties of compound inference systems. We analyze, theoretically and empirically, how the number of LM calls affects the performance of Vote and Filter-Vote, two of the simplest compound system designs, which aggregate LM responses via majority voting, optionally applying LM filters. We find, surprisingly, that across multiple language tasks, the performance of both Vote and Filter-Vote can first increase but then decrease as a function of the number of LM calls. Our theoretical results suggest that this non-monotonicity is due to the diversity of query difficulties within a task: more LM calls lead to higher performance on "easy" queries, but lower performance on "hard" queries, and nonmonotone behavior can emerge when a task contains both types of queries. This insight then allows us to compute, from a small number of samples, the number of LM calls that maximizes system performance, and define an analytical scaling model for both systems. Experiments show that our scaling model can accurately predict the performance of Vote and Filter-Vote systems and thus find the optimal number of LM calls to make.

We thank the reviewers for their extensive comments. Where is the novelty (R2+R4) / What is the point of the new proofs (R2)? However, our primary result is to show why it works. Newton's method with a more stable trust-region based method gave rise to a more stable fixed-point (line 131), and Given this, partial derivatives and full derivatives coincide. This mischaracterisation by R6 is our fault; we had intended to cite Fitzgibbon's later We emphasise that we're modifying a baseline [24] that was published independently All issues raised by the reviewers will be clarified. 'network' instead of'parameters of the energy function' in the pose experiment; we agree the name should be changed.

Neural representations for 3D scenes have made substantial advancements recently, yet object removal remains a challenging yet practical issue, due to the absence of multi-view supervision over occluded areas. Diffusion Models (DMs), trained on extensive 2D images, show diverse and high-fidelity generative capabilities in the 2D domain. However, due to not being specifically trained on 3D data, their application to multi-view data often exacerbates inconsistency, hence impacting the overall quality of the 3D output. To address these issues, we introduce "In-N-Out", a novel approach that begins by inpainting a prior, i.e., the occluded area from a single view using DMs, followed by outstretching it to create multi-view inpaintings via latents alignments. Our analysis identifies that the variability in DMs' outputs mainly arises from initially sampled latents and intermediate latents predicted in the denoising process. We explicitly align of initial latents using a Neural Radiance Field (NeRF) to establish a consistent foundational structure in the inpainted area, complemented by an implicit alignment of intermediate latents through cross-view attention during the denoising phases, enhancing appearance consistency across views. To further enhance rendering results, we apply a patchbased hybrid loss to optimize NeRF. We demonstrate that our techniques effectively mitigate the challenges posed by inconsistencies in DMs and substantially improve the fidelity and coherence of inpainted 3D representations.

This work studies the global convergence and implicit bias of Gauss Newton's (GN) when optimizing over-parameterized one-hidden layer networks in the mean-field regime. We first establish a global convergence result for GN in the continuous-time limit exhibiting a faster convergence rate compared to GD due to improved conditioning. We then perform an empirical study on a synthetic regression task to investigate the implicit bias of GN's method. While GN is consistently faster than GD in finding a global optimum, the learned model generalizes well on test data when starting from random initial weights with a small variance and using a small step size to slow down convergence. Specifically, our study shows that such a setting results in a hidden learning phenomenon, where the dynamics are able to recover features with good generalization properties despite the model having sub-optimal training and test performances due to an under-optimized linear layer. This study exhibits a trade-off between the convergence speed of GN and the generalization ability of the learned solution.

Learning-based simulators show great potential for simulating particle dynamics when 3D groundtruth is available, but per-particle correspondences are not always accessible. The development of neural rendering presents a new solution to this field to learn 3D dynamics from 2D images by inverse rendering. However, existing approaches still suffer from ill-posed natures resulting from the 2D to 3D uncertainty, for example, specific 2D images can correspond with various 3D particle distributions. To mitigate such uncertainty, we consider a conventional, mechanically interpretable framework as the physical priors and extend it to a learning-based version. In brief, we incorporate the learnable graph kernels into the classic Discrete Element Analysis (DEA) framework to implement a novel mechanics-integrated learning system. In this case, the graph network kernels are only used for approximating some specific mechanical operators in the DEA framework rather than the whole dynamics mapping. By integrating the strong physics priors, our methods can effectively learn the dynamics of various materials from the partial 2D observations in a unified manner. Experiments show that our approach outperforms other learned simulators by a large margin in this context and is robust to different renderers, fewer training samples, and fewer camera views.

Language-image pre-training is an effective technique for learning powerful representations in general domains. However, when directly turning to person representation learning, these general pre-training methods suffer from unsatisfactory performance. The reason is that they neglect critical person-related characteristics, i.e., fine-grained attributes and identities. To address this issue, we propose a novel language-image pre-training framework for person representation learning, termed PLIP. Specifically, we elaborately design three pretext tasks: 1) Text-guided Image Colorization, aims to establish the correspondence between the person-related image regions and the fine-grained color-part textual phrases.

We study the Combinatorial Group Testing (CGT) problem in a novel gametheoretic framework, with a solution concept of Adversarial Equilibrium (AE). In this new framework, we have n selfish autonomous agents, corresponding to the elements of the universe [n] = {0, 1,..., n 1}, and a hidden set K [n] of active agents of size |K| = k n. In each round of the game, each active agent decides if it is present in a query Q [n], and all agents receive some limited feedback on Q K. The goal of each active agent is to ensure that its id could be revealed from the feedback as early as possible. We present a comprehensive set of results for this new game, where we design and analyze adaptive algorithmic strategies of agents which are AE's. In particular, if k is known to the agents, then we show adaptive AE strategies with provably near-optimal maximum revealing time of O(k log(n/k)).

Existing state-of-the-art dense object detection techniques tend to produce a large number of false positive detections on difficult images with complex scenes because they focus on ensuring a high recall. To improve the detection accuracy, we propose an Adaptive Important Region Selection (AIRS) framework guided by Evidential Q-learning coupled with a uniquely designed reward function. Inspired by human visual attention, our detection model conducts object search in a top-down, hierarchical fashion. It starts from the top of the hierarchy with the coarsest granularity and then identifies the potential patches likely to contain objects of interest. It then discards non-informative patches and progressively moves downward on the selected ones for a fine-grained search. The proposed evidential Q-learning systematically encodes epistemic uncertainty in its evidential-Q value to encourage the exploration of unknown patches, especially in the early phase of model training. In this way, the proposed model dynamically balances exploration-exploitation to cover both highly valuable and informative patches. Theoretical analysis and extensive experiments on multiple datasets demonstrate that our proposed framework outperforms the SOTA models.