We present a novel approach to feature labeling using gradient descent in token-space. While existing methods typically use language models to generate hypotheses about feature meanings, our method directly optimizes label representations by using a language model as a discriminator to predict feature activations. We formulate this as a multi-objective optimization problem in token-space, balancing prediction accuracy, entropy minimization, and linguistic naturalness. Our proof-of-concept experiments demonstrate successful convergence to interpretable single-token labels across diverse domains, including features for detecting animals, mammals, Chinese text, and numbers. Although our current implementation is constrained to single-token labels and relatively simple features, the results suggest that token-space gradient descent could become a valuable addition to the interpretability researcher's toolkit. Recent work in mechanistic interpretability has made significant progress in decomposing neural networks into interpretable features.

Theory of Mind (ToM) is a hallmark of human cognition, allowing individuals to reason about others' beliefs and intentions. Engineers behind recent advances in Artificial Intelligence (AI) have claimed to demonstrate comparable capabilities. This paper presents a model that surpasses traditional ToM tests designed for 3-year-old children, providing strong support for the presence of ToM in AI systems.

Deep neural networks learn structured features from complex, non-Gaussian inputs, but the mechanisms behind this process remain poorly understood. Our work is motivated by the observation that the first-layer filters learnt by deep convolutional neural networks from natural images resemble those learnt by independent component analysis (ICA), a simple unsupervised method that seeks the most non-Gaussian projections of its inputs. This similarity suggests that ICA provides a simple, yet principled model for studying feature learning. Here, we leverage this connection to investigate the interplay between data structure and optimisation in feature learning for the most popular ICA algorithm, FastICA, and stochastic gradient descent (SGD), which is used to train deep networks. We rigorously establish that FastICA requires at least $n\gtrsim d^4$ samples to recover a single non-Gaussian direction from $d$-dimensional inputs on a simple synthetic data model. We show that vanilla online SGD outperforms FastICA, and prove that the optimal sample complexity $n \gtrsim d^2$ can be reached by smoothing the loss, albeit in a data-dependent way. We finally demonstrate the existence of a search phase for FastICA on ImageNet, and discuss how the strong non-Gaussianity of said images compensates for the poor sample complexity of FastICA.

We investigate the problem of learning a Single Index Model (SIM)- a popular model for studying the ability of neural networks to learn features - from anisotropic Gaussian inputs by training a neuron using vanilla Stochastic Gradient Descent (SGD). While the isotropic case has been extensively studied, the anisotropic case has received less attention and the impact of the covariance matrix on the learning dynamics remains unclear. For instance, Mousavi-Hosseini et al. (2023b) proposed a spherical SGD that requires a separate estimation of the data covariance matrix, thereby oversimplifying the influence of covariance. In this study, we analyze the learning dynamics of vanilla SGD under the SIM with anisotropic input data, demonstrating that vanilla SGD automatically adapts to the data's covariance structure. Leveraging these results, we derive upper and lower bounds on the sample complexity using a notion of effective dimension that is determined by the structure of the covariance matrix instead of the input data dimension.

Distributionally robust optimization (DRO) is a powerful technique to train robust models against data distribution shift. This paper aims to solve regularized nonconvex DRO problems, where the uncertainty set is modeled by a so-called generalized Sinkhorn distance and the loss function is nonconvex and possibly unbounded. Such a distance allows to model uncertainty of distributions with different probability supports and divergence functions. For this class of regularized DRO problems, we derive a novel dual formulation taking the form of nested stochastic programming, where the dual variable depends on the data sample. To solve the dual problem, we provide theoretical evidence to design a nested stochastic gradient descent (SGD) algorithm, which leverages stochastic approximation to estimate the nested stochastic gradients. We study the convergence rate of nested SGD and establish polynomial iteration and sample complexities that are independent of the data size and parameter dimension, indicating its potential for solving large-scale DRO problems. We conduct numerical experiments to demonstrate the efficiency and robustness of the proposed algorithm.

Policy gradient methods are one of the most successful methods for solving challenging reinforcement learning problems. However, despite their empirical successes, many SOTA policy gradient algorithms for discounted problems deviate from the theoretical policy gradient theorem due to the existence of a distribution mismatch. In this work, we analyze the impact of this mismatch on the policy gradient methods. Specifically, we first show that in the case of tabular parameterizations, the methods under the mismatch remain globally optimal. Then, we extend this analysis to more general parameterizations by leveraging the theory of biased stochastic gradient descent. Our findings offer new insights into the robustness of policy gradient methods as well as the gap between theoretical foundations and practical implementations.

We show that the behavior of stochastic gradient descent is related to Bayesian statistics by showing that SGD is effectively diffusion on a fractal landscape, where the fractal dimension can be accounted for in a purely Bayesian way. By doing this we show that SGD can be regarded as a modified Bayesian sampler which accounts for accessibility constraints induced by the fractal structure of the loss landscape. We verify our results experimentally by examining the diffusion of weights during training. These results offer insight into the factors which determine the learning process, and seemingly answer the question of how SGD and purely Bayesian sampling are related.

Abstract--Federated learning has emerged as an attractive approach to protect data privacy by eliminating the need for sharing clients' data while reducing communication costs compared with centralized machine learning algorithms. However, recent studies have shown that federated learning alone does not guarantee privacy, as private data may still be inferred from the uploaded parameters to the central server. In order to successfully avoid data leakage, adopting differential privacy (DP) in the local optimization process or in the local update aggregation process has emerged as two feasible ways for achieving sample-level or user-level privacy guarantees respectively, in federated learning models. However, compared to their non-private equivalents, these approaches suffer from a poor utility . T o improve the privacy-utility trade-off, we present a modification to these vanilla differentially private algorithms based on a Haar wavelet transformation step and a novel noise injection scheme that significantly lowers the asymptotic bound of the noise variance. We also present a holistic convergence analysis of our proposed algorithm, showing that our method yields better convergence performance than the vanilla DP algorithms. Numerical experiments on real-world datasets demonstrate that our method outperforms existing approaches in model utility while maintaining the same privacy guarantees. Machine learning (ML) has become an essential tool to analyze this data and extract valuable insights for various applications, including facial recognition, data analytics, weather prediction, and speech recognition, among others [1], [2], [3], [4], [5]. However, in real-world settings, data -- particularly personal data -- is often created and stored on end-user devices. The majority of traditional ML algorithms require the centralization of these training data, which involves collecting and processing data at a potent cloud-based server [6], [7]. This process carries significant risks to data integrity and privacy, particularly when it comes to personal data. Kanishka Ranaweera is with School of Engineering and Built Environment, Deakin University, Waurn Ponds, VIC 3216, Australia, and also with the Data61, CSIRO, Eveleigh, NSW 2015, Australia. Dinh C. Nguyen is with the Department of Electrical and Computer Engineering, The University of Alabama in Huntsville Alabama, USA. Pubudu N. Pathirana is with School of Engineering and Built Environment, Deakin University, Waurn Ponds, VIC 3216, Australia.

--The skip-gram model (SGM), which employs a neural network to generate node vectors, serves as the basis for numerous popular graph embedding techniques. However, since the training datasets contain sensitive linkage information, the parameters of a released SGM may encode private information and pose significant privacy risks. Differential privacy (DP) is a rigorous standard for protecting individual privacy in data analysis. Nevertheless, when applying differential privacy to skip-gram in graphs, it becomes highly challenging due to the complex link relationships, which potentially result in high sensitivity and necessitate substantial noise injection. T o tackle this challenge, we present AdvSGM, a differentially private skip-gram for graphs via adversarial training. Our core idea is to leverage adversarial training to privatize skip-gram while improving its utility. T owards this end, we develop a novel adversarial training module by devising two optimizable noise terms that correspond to the parameters of a skip-gram. By fine-tuning the weights between modules within AdvSGM, we can achieve differentially private gradient updates without additional noise injection. Extensive experimental results on six real-world graph datasets show that AdvSGM preserves high data utility across different downstream tasks. Graph embedding, which has attracted increasing research attention, represents nodes by low-dimensional vectors while preserving the inherent properties and structures of the graph. In this way, well-studied machine learning algorithms can be easily applied for further mining tasks like clustering, classification, and prediction. Skip-gram models (SGMs) are a popular class of graph embedding models thanks to their simplicity and effectiveness, including DeepWalk [1], LINE [2], and node2vec [3]. However, SGMs, which capture not only general data characteristics but also specific details about individual data, are vulnerable to adversarial attacks, particularly user-linkage attacks [4] that exploit the linkage information between nodes to infer whether an individual is present in the training dataset. Therefore, node embeddings need to be sanitized with privacy guarantees before they can be released to the public. Differential privacy (DP) [5] is a well studied statistical privacy model recognized for its rigorous mathematical underpinnings. In this paper, we study the problem of achieving privacy-preserving skip-gram for graphs under differential privacy.

We analyze the ability of computational units to retain past responses after parameter updates, a key property for system-wide continual learning. Neural networks trained with gradient descent lack this capability, prompting us to propose Modelleyen, an alternative approach with inherent response preservation. We demonstrate through experiments on modeling the dynamics of a simple environment and on MNIST that, despite increased computational complexity and some representational limitations at its current stage, Modelleyen achieves continual learning without relying on sample replay or predefined task boundaries.