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Discrete Choice Experiments (DCEs) investigate the attributes that influence individuals' choices when selecting among various options. To enhance the quality of the estimated choice models, researchers opt for Bayesian optimal designs that utilize existing information about the attributes' preferences. Given the nonlinear nature of choice models, the construction of an appropriate design requires efficient algorithms. Among these, the Coordinate-Exchange (CE) algorithm is most commonly employed for constructing designs based on the multinomial logit model. Since this is a hill-climbing algorithm, obtaining better designs necessitates multiple random starting designs. This approach increases the algorithm's run-time, but may not lead to a significant improvement in results. We propose the use of a Simulated Annealing (SA) algorithm to construct Bayesian D-optimal designs. This algorithm accepts both superior and inferior solutions, avoiding premature convergence and allowing a more thorough exploration of potential designs. Consequently, it ultimately obtains higher-quality choice designs within the same time-frame. Our work represents the first application of an SA algorithm in constructing Bayesian optimal designs for DCEs. Through computational experiments and a real-life case study, we demonstrate that the SA designs consistently outperform the CE designs in terms of Bayesian D-efficiency, especially when the prior preference information is highly uncertain.

Automated market makers (AMMs) allocate fee revenue proportional to the amount of liquidity investors deposit. In this paper, we study the economic consequences of the competition between passive liquidity providers (LPs) caused by this allocation rule. We employ a game-theoretic model in which $N$ strategic agents optimally provide liquidity. In this setting, we find that competition drives LPs to provide excess liquidity. In the limit, the excess liquidity converges to a constant that linearly increases with the amount of base demand, demand that is insensitive to trading costs. Providing excess liquidity is costly as more capital is exposed to adverse selection costs, leading to a loss in welfare. Our main result is that the price of anarchy, defined over the liquidity provider performance, is $O(N)$, implying that the welfare loss scales linearly with the number of liquidity providers. We show that this result is still observable when using richer aggregate demand models.

This paper revisits the convergence of Stochastic Mirror Descent (SMD) in the contemporary nonconvex optimization setting. Existing results for batch-free nonconvex SMD restrict the choice of the distance generating function (DGF) to be differentiable with Lipschitz continuous gradients, thereby excluding important setups such as Shannon entropy. In this work, we present a new convergence analysis of nonconvex SMD supporting general DGF, that overcomes the above limitations and relies solely on the standard assumptions. Moreover, our convergence is established with respect to the Bregman Forward-Backward envelope, which is a stronger measure than the commonly used squared norm of gradient mapping. We further extend our results to guarantee high probability convergence under sub-Gaussian noise and global convergence under the generalized Bregman Proximal Polyak-{\L}ojasiewicz condition. Additionally, we illustrate the advantages of our improved SMD theory in various nonconvex machine learning tasks by harnessing nonsmooth DGFs. Notably, in the context of nonconvex differentially private (DP) learning, our theory yields a simple algorithm with a (nearly) dimension-independent utility bound. For the problem of training linear neural networks, we develop provably convergent stochastic algorithms.

Self-supervised learning (SSL) approaches have achieved great success when the amount of labeled data is limited. Within SSL, models learn robust feature representations by solving pretext tasks. One such pretext task is contrastive learning, which involves forming pairs of similar and dissimilar input samples, guiding the model to distinguish between them. In this work, we investigate the application of contrastive learning to the domain of medical image analysis. Our findings reveal that MoCo v2, a state-of-the-art contrastive learning method, encounters dimensional collapse when applied to medical images. This is attributed to the high degree of inter-image similarity shared between the medical images. To address this, we propose two key contributions: local feature learning and feature decorrelation. Local feature learning improves the ability of the model to focus on the local regions of the image, while feature decorrelation removes the linear dependence among the features. Our experimental findings demonstrate that our contributions significantly enhance the model's performance in the downstream task of medical segmentation, both in the linear evaluation and full fine-tuning settings. This work illustrates the importance of effectively adapting SSL techniques to the characteristics of medical imaging tasks. The source code will be made publicly available at: //github.com/CAMMA-public/med-moco

We generalize the DeGroot model for opinion dynamics to better capture realistic social scenarios. We introduce a model where each agent has their own individual cognitive biases. Society is represented as a directed graph whose edges indicate how much agents influence one another. Biases are represented as the functions in the square region $[-1,1]^2$ and categorized into four sub-regions based on the potential reactions they may elicit in an agent during instances of opinion disagreement. Under the assumption that each bias of every agent is a continuous function within the region of receptive but resistant reactions ($\mathbf{R}$), we show that the society converges to a consensus if the graph is strongly connected. Under the same assumption, we also establish that the entire society converges to a unanimous opinion if and only if the source components of the graph-namely, strongly connected components with no external influence-converge to that opinion. We illustrate that convergence is not guaranteed for strongly connected graphs when biases are either discontinuous functions in $\mathbf{R}$ or not included in $\mathbf{R}$. We showcase our model through a series of examples and simulations, offering insights into how opinions form in social networks under cognitive biases.

With the rapid development of Large Language Models (LLMs), various explorations have arisen to utilize LLMs capability of context understanding on recommender systems. While pioneering strategies have primarily transformed traditional recommendation tasks into challenges of natural language generation, there has been a relative scarcity of exploration in the domain of session-based recommendation (SBR) due to its specificity. SBR has been primarily dominated by Graph Neural Networks, which have achieved many successful outcomes due to their ability to capture both the implicit and explicit relationships between adjacent behaviors. The structural nature of graphs contrasts with the essence of natural language, posing a significant adaptation gap for LLMs. In this paper, we introduce large language models with graphical Session-Based recommendation, named LLMGR, an effective framework that bridges the aforementioned gap by harmoniously integrating LLMs with Graph Neural Networks (GNNs) for SBR tasks. This integration seeks to leverage the complementary strengths of LLMs in natural language understanding and GNNs in relational data processing, leading to a more powerful session-based recommender system that can understand and recommend items within a session. Moreover, to endow the LLM with the capability to empower SBR tasks, we design a series of prompts for both auxiliary and major instruction tuning tasks. These prompts are crafted to assist the LLM in understanding graph-structured data and align textual information with nodes, effectively translating nuanced user interactions into a format that can be understood and utilized by LLM architectures. Extensive experiments on three real-world datasets demonstrate that LLMGR outperforms several competitive baselines, indicating its effectiveness in enhancing SBR tasks and its potential as a research direction for future exploration.

Multimodal learning seeks to utilize data from multiple sources to improve the overall performance of downstream tasks. It is desirable for redundancies in the data to make multimodal systems robust to missing or corrupted observations in some correlated modalities. However, we observe that the performance of several existing multimodal networks significantly deteriorates if one or multiple modalities are absent at test time. To enable robustness to missing modalities, we propose a simple and parameter-efficient adaptation procedure for pretrained multimodal networks. In particular, we exploit modulation of intermediate features to compensate for the missing modalities. We demonstrate that such adaptation can partially bridge performance drop due to missing modalities and outperform independent, dedicated networks trained for the available modality combinations in some cases. The proposed adaptation requires extremely small number of parameters (e.g., fewer than 0.7% of the total parameters) and applicable to a wide range of modality combinations and tasks. We conduct a series of experiments to highlight the missing modality robustness of our proposed method on 5 different datasets for multimodal semantic segmentation, multimodal material segmentation, and multimodal sentiment analysis tasks. Our proposed method demonstrates versatility across various tasks and datasets, and outperforms existing methods for robust multimodal learning with missing modalities.

The surge in popularity of Large Language Models (LLMs) has opened doors for new approaches to the creation of interactive agents. However, managing the temporal behavior of such agents over the course of an interaction remains challenging. The stateful, long-term horizon and quantitative reasoning required for coherent agent behavior does not fit well into the LLM paradigm. We propose a combination of formal logic-based program synthesis and LLM content generation to create generative agents that adhere to temporal constraints. Our approach uses Temporal Stream Logic (TSL) to generate an automaton that enforces a temporal structure on an agent and leaves the details of each action for a moment in time to an LLM. By using TSL, we are able to augment the generative agent where users have a higher level of guarantees on behavior, better interpretability of the system, and more ability to build agents in a modular way. We evaluate our approach on different tasks involved in creating a coherent interactive agent specialized for various application domains. We found that over all of the tasks, our approach using TSL achieves at least 96% adherence, whereas the pure LLM-based approach demonstrates as low as 14.67% adherence.

Recent work by Bravyi, Gosset, and Koenig showed that there exists a search problem that a constant-depth quantum circuit can solve, but that any constant-depth classical circuit with bounded fan-in cannot. They also pose the question: Can we achieve a similar proof of separation for an input-independent sampling task? In this paper, we show that the answer to this question is yes when the number of random input bits given to the classical circuit is bounded. We introduce a distribution $D_{n}$ over $\{0,1\}^n$ and construct a constant-depth uniform quantum circuit family $\{C_n\}_n$ such that $C_n$ samples from a distribution close to $D_{n}$ in total variation distance. For any $\delta < 1$ we also prove, unconditionally, that any classical circuit with bounded fan-in gates that takes as input $kn + n^\delta$ i.i.d. Bernouli random variables with entropy $1/k$ and produces output close to $D_{n}$ in total variation distance has depth $\Omega(\log \log n)$. This gives an unconditional proof that constant-depth quantum circuits can sample from distributions that can't be reproduced by constant-depth bounded fan-in classical circuits, even up to additive error. We also show a similar separation between constant-depth quantum circuits with advice and classical circuits with bounded fan-in and fan-out, but access to an unbounded number of i.i.d random inputs. The distribution $D_n$ and classical circuit lower bounds are inspired by work of Viola, in which he shows a different (but related) distribution cannot be sampled from approximately by constant-depth bounded fan-in classical circuits.

Graph Neural Networks (GNNs) have shown promising results on a broad spectrum of applications. Most empirical studies of GNNs directly take the observed graph as input, assuming the observed structure perfectly depicts the accurate and complete relations between nodes. However, graphs in the real world are inevitably noisy or incomplete, which could even exacerbate the quality of graph representations. In this work, we propose a novel Variational Information Bottleneck guided Graph Structure Learning framework, namely VIB-GSL, in the perspective of information theory. VIB-GSL advances the Information Bottleneck (IB) principle for graph structure learning, providing a more elegant and universal framework for mining underlying task-relevant relations. VIB-GSL learns an informative and compressive graph structure to distill the actionable information for specific downstream tasks. VIB-GSL deduces a variational approximation for irregular graph data to form a tractable IB objective function, which facilitates training stability. Extensive experimental results demonstrate that the superior effectiveness and robustness of VIB-GSL.