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.

We study the scaling properties of latent diffusion models (LDMs) with an emphasis on their sampling efficiency. While improved network architecture and inference algorithms have shown to effectively boost sampling efficiency of diffusion models, the role of model size -- a critical determinant of sampling efficiency -- has not been thoroughly examined. Through empirical analysis of established text-to-image diffusion models, we conduct an in-depth investigation into how model size influences sampling efficiency across varying sampling steps. Our findings unveil a surprising trend: when operating under a given inference budget, smaller models frequently outperform their larger equivalents in generating high-quality results. Moreover, we extend our study to demonstrate the generalizability of the these findings by applying various diffusion samplers, exploring diverse downstream tasks, evaluating post-distilled models, as well as comparing performance relative to training compute. These findings open up new pathways for the development of LDM scaling strategies which can be employed to enhance generative capabilities within limited inference budgets.

Abstract: Coarse-coded symbol memories have appeared in several neural network symbol processing models. In order to determine how these models would scale, one must first have some understanding of the mathematics of coarse-coded representa(cid:173) tions. We define the general structure of coarse-coded symbol memories and derive mathematical relationships among their essential parameters: memory 8ize, 8ymbol-8et size and capacity. The computed capacity of one of the schemes agrees well with actual measurements oC tbe coarse-coded working memory of DCPS, Touretzky and Hinton's distributed connectionist production system.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

Network data appear in a number of applications, such as online social networks and biological networks, and there is growing interest in both developing models for networks as well as studying the properties of such data. Since individual network datasets continue to grow in size, it is necessary to develop models that accurately represent the real-life scaling properties of networks. One behavior of interest is having a power law in the degree distribution. However, other types of power laws that have been observed empirically and considered for applications such as clustering and feature allocation models have not been studied as frequently in models for graph data. In this paper, we enumerate desirable asymptotic behavior that may be of interest for modeling graph data, including sparsity and several types of power laws. We outline a general framework for graph generative models using completely random measures; by contrast to the pioneering work of Caron and Fox (2015), we consider instantiating more of the existing atoms of the random measure as the dataset size increases rather than adding new atoms to the measure. We see that these two models can be complementary; they respectively yield interpretations as (1) time passing among existing members of a network and (2) new individuals joining a network. We detail a particular instance of this framework and show simulated results that suggest this model exhibits some desirable asymptotic power-law behavior.

DCPS' memory scheme is a modified version of the Random Receptors method [5]. The symbol space is the set of all triples over a 25 letter alphabet. Units have fixed-size receptive fields organized as 6 x 6 x 6 subspaces. Patterns are manipulated to minimize the variance in pattern size across symbols.

DCPS' memory scheme is a modified version of the Random Receptors method [5]. The symbol space is the set of all triples over a 25 letter alphabet. Units have fixed-size receptive fields organized as 6 x 6 x 6 subspaces. Patterns are manipulated to minimize the variance in pattern size across symbols.

DCPS' memory scheme is a modified version of the Random Receptors method [5]. The symbol space is the set of all triples over a 25 letter alphabet. Units have fixed-size receptive fields organized as 6 x 6 x 6 subspaces. Patterns are manipulated to minimize the variance in pattern size across symbols.