We explore the capability of transformers to address endogeneity in in-context linear regression. Our main finding is that transformers inherently possess a mechanism to handle endogeneity effectively using instrumental variables (IV). First, we demonstrate that the transformer architecture can emulate a gradient-based bi-level optimization procedure that converges to the widely used two-stage least squares $(\textsf{2SLS})$ solution at an exponential rate. Next, we propose an in-context pretraining scheme and provide theoretical guarantees showing that the global minimizer of the pre-training loss achieves a small excess loss. Our extensive experiments validate these theoretical findings, showing that the trained transformer provides more robust and reliable in-context predictions and coefficient estimates than the $\textsf{2SLS}$ method, in the presence of endogeneity.
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Port-Hamiltonian neural networks (pHNNs) are emerging as a powerful modeling tool that integrates physical laws with deep learning techniques. While most research has focused on modeling the entire dynamics of interconnected systems, the potential for identifying and modeling individual subsystems while operating as part of a larger system has been overlooked. This study addresses this gap by introducing a novel method for using pHNNs to identify such subsystems based solely on input-output measurements. By utilizing the inherent compositional property of the port-Hamiltonian systems, we developed an algorithm that learns the dynamics of individual subsystems, without requiring direct access to their internal states. On top of that, by choosing an output error (OE) model structure, we have been able to handle measurement noise effectively. The effectiveness of the proposed approach is demonstrated through tests on interconnected systems, including multi-physics scenarios, demonstrating its potential for identifying subsystem dynamics and facilitating their integration into new interconnected models.
Despite their widespread use, the mechanisms by which large language models (LLMs) represent and regulate uncertainty in next-token predictions remain largely unexplored. This study investigates two critical components believed to influence this uncertainty: the recently discovered entropy neurons and a new set of components that we term token frequency neurons. Entropy neurons are characterized by an unusually high weight norm and influence the final layer normalization (LayerNorm) scale to effectively scale down the logits. Our work shows that entropy neurons operate by writing onto an unembedding null space, allowing them to impact the residual stream norm with minimal direct effect on the logits themselves. We observe the presence of entropy neurons across a range of models, up to 7 billion parameters. On the other hand, token frequency neurons, which we discover and describe here for the first time, boost or suppress each token's logit proportionally to its log frequency, thereby shifting the output distribution towards or away from the unigram distribution. Finally, we present a detailed case study where entropy neurons actively manage confidence in the setting of induction, i.e. detecting and continuing repeated subsequences.
QUIC, a new and increasingly used transport protocol, addresses and resolves the limitations of TCP by offering improved security, performance, and features such as stream multiplexing and connection migration. These features, however, also present challenges for network operators who need to monitor and analyze web traffic. In this paper, we introduce VisQUIC, a labeled dataset comprising over 100,000 QUIC traces from more than 44,000 websites (URLs), collected over a four-month period. These traces provide the foundation for generating more than seven million images, with configurable parameters of window length, pixel resolution, normalization, and labels. These images enable an observer looking at the interactions between a client and a server to analyze and gain insights about QUIC encrypted connections. To illustrate the dataset's potential, we offer a use-case example of an observer estimating the number of HTTP/3 responses/requests pairs in a given QUIC, which can reveal server behavior, client--server interactions, and the load imposed by an observed connection. We formulate the problem as a discrete regression problem, train a machine learning (ML) model for it, and then evaluate it using the proposed dataset on an example use case.
We introduce a simple, stochastic, a-posteriori, turbulence closure model based on a reduced subgrid scale term. This subgrid scale term is tailor-made to capture the statistics of a small set of spatially-integrate quantities of interest (QoIs), with only one unresolved scalar time series per QoI. In contrast to other data-driven surrogates the dimension of the "learning problem" is reduced from an evolving field to one scalar time series per QoI. We use an a-posteriori, nudging approach to find the distribution of the scalar series over time. This approach has the advantage of taking the interaction between the solver and the surrogate into account. A stochastic surrogate parametrization is obtained by random sampling from the found distribution for the scalar time series. Compared to an a-priori trained convolutional neural network, evaluating the new method is computationally much cheaper and gives similar long-term statistics.
Embeddings have become a cornerstone in the functionality of large language models (LLMs) due to their ability to transform text data into rich, dense numerical representations that capture semantic and syntactic properties. These embedding vector databases serve as the long-term memory of LLMs, enabling efficient handling of a wide range of natural language processing tasks. However, the surge in popularity of embedding vector databases in LLMs has been accompanied by significant concerns about privacy leakage. Embedding vector databases are particularly vulnerable to embedding inversion attacks, where adversaries can exploit the embeddings to reverse-engineer and extract sensitive information from the original text data. Existing defense mechanisms have shown limitations, often struggling to balance security with the performance of downstream tasks. To address these challenges, we introduce Eguard, a novel defense mechanism designed to mitigate embedding inversion attacks. Eguard employs a transformer-based projection network and text mutual information optimization to safeguard embeddings while preserving the utility of LLMs. Our approach significantly reduces privacy risks, protecting over 95% of tokens from inversion while maintaining high performance across downstream tasks consistent with original embeddings.
Hierarchical sorting is a fundamental task for programmable matter, inspired by the spontaneous formation of interfaces and membranes in nature. The task entails particles of different types, present in fixed densities, sorting into corresponding regions of a space that are themselves organized. By analyzing the Gibbs distribution of a general fixed-magnetization model of equilibrium statistical mechanics, we prove that particles moving stochastically according to local affinities solve the hierarchical sorting task. The analysis of fixed-magnetization models is notoriously difficult, and approaches that have led to recent breakthroughs in sampling the low-temperature regime only work in the variable-magnetization setting by default. To overcome this barrier, we introduce a new approach for comparing the partition functions of fixed- and variable-magnetization models. The core technique identifies a special class of configurations that contribute comparably to the two partition functions, which then serves as a bridge between the fixed- and variable-magnetization settings. Our main result is an estimate of the Gibbs distribution that unifies existing and new results for models at fixed magnetization, including the Ising, Potts, and Blume--Capel models, and leads to stochastic distributed algorithms for hierarchical sorting and other self-organizing tasks, like compression and separation.
We develop a new approach for approximating large independent sets when the input graph is a one-sided spectral expander - that is, the uniform random walk matrix of the graph has its second eigenvalue bounded away from 1. Consequently, we obtain a polynomial time algorithm to find linear-sized independent sets in one-sided expanders that are almost $3$-colorable or are promised to contain an independent set of size $(1/2-\epsilon)n$. Our second result above can be refined to require only a weaker vertex expansion property with an efficient certificate. In a surprising contrast to our algorithmic result, we observe that the analogous task of finding a linear-sized independent set in almost $4$-colorable one-sided expanders (even when the second eigenvalue is $o_n(1)$) is NP-hard, assuming the Unique Games Conjecture. All prior algorithms that beat the worst-case guarantees for this problem rely on bottom eigenspace enumeration techniques (following the classical spectral methods of Alon and Kahale) and require two-sided expansion, meaning a bounded number of negative eigenvalues of magnitude $\Omega(1)$. Such techniques naturally extend to almost $k$-colorable graphs for any constant $k$, in contrast to analogous guarantees on one-sided expanders, which are Unique Games-hard to achieve for $k \geq 4$. Our rounding builds on the method of simulating multiple samples from a pseudo-distribution introduced by Bafna et. al. for rounding Unique Games instances. The key to our analysis is a new clustering property of large independent sets in expanding graphs - every large independent set has a larger-than-expected intersection with some member of a small list - and its formalization in the low-degree sum-of-squares proof system.
The key challenge of image manipulation detection is how to learn generalizable features that are sensitive to manipulations in novel data, whilst specific to prevent false alarms on authentic images. Current research emphasizes the sensitivity, with the specificity overlooked. In this paper we address both aspects by multi-view feature learning and multi-scale supervision. By exploiting noise distribution and boundary artifact surrounding tampered regions, the former aims to learn semantic-agnostic and thus more generalizable features. The latter allows us to learn from authentic images which are nontrivial to be taken into account by current semantic segmentation network based methods. Our thoughts are realized by a new network which we term MVSS-Net. Extensive experiments on five benchmark sets justify the viability of MVSS-Net for both pixel-level and image-level manipulation detection.
Domain shift is a fundamental problem in visual recognition which typically arises when the source and target data follow different distributions. The existing domain adaptation approaches which tackle this problem work in the closed-set setting with the assumption that the source and the target data share exactly the same classes of objects. In this paper, we tackle a more realistic problem of open-set domain shift where the target data contains additional classes that are not present in the source data. More specifically, we introduce an end-to-end Progressive Graph Learning (PGL) framework where a graph neural network with episodic training is integrated to suppress underlying conditional shift and adversarial learning is adopted to close the gap between the source and target distributions. Compared to the existing open-set adaptation approaches, our approach guarantees to achieve a tighter upper bound of the target error. Extensive experiments on three standard open-set benchmarks evidence that our approach significantly outperforms the state-of-the-arts in open-set domain adaptation.
Image-to-image translation aims to learn the mapping between two visual domains. There are two main challenges for many applications: 1) the lack of aligned training pairs and 2) multiple possible outputs from a single input image. In this work, we present an approach based on disentangled representation for producing diverse outputs without paired training images. To achieve diversity, we propose to embed images onto two spaces: a domain-invariant content space capturing shared information across domains and a domain-specific attribute space. Our model takes the encoded content features extracted from a given input and the attribute vectors sampled from the attribute space to produce diverse outputs at test time. To handle unpaired training data, we introduce a novel cross-cycle consistency loss based on disentangled representations. Qualitative results show that our model can generate diverse and realistic images on a wide range of tasks without paired training data. For quantitative comparisons, we measure realism with user study and diversity with a perceptual distance metric. We apply the proposed model to domain adaptation and show competitive performance when compared to the state-of-the-art on the MNIST-M and the LineMod datasets.
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