Research connected to &quot;machine learning&quot;

Near-Optimal Regret Bounds for Contextual Combinatorial Semi-Bandits with Linear Payoff Functions

The contextual combinatorial semi-bandit problem with linear payoff functions is a decision-making problem in which a learner chooses a set of arms with the feature vectors in each round under given constraints so as to maximize the sum of rewards of arms. Several existing algorithms have regret bounds that are optimal with respect to the number of rounds $T$. However, there is a gap of $\tilde{O}(\max(\sqrt{d}, \sqrt{k}))$ between the current best upper and lower bounds, where $d$ is the dimension of the feature vectors, $k$ is the number of the chosen arms in a round, and $\tilde{O}(\cdot)$ ignores the logarithmic factors. The dependence of $k$ and $d$ is of practical importance because $k$ may be larger than $T$ in real-world applications such as recommender systems. In this paper, we fill the gap by improving the upper and lower bounds. More precisely, we show that the C${}^2$UCB algorithm proposed by Qin, Chen, and Zhu (2014) has the optimal regret bound $\tilde{O}(d\sqrt{kT} + dk)$ for the partition matroid constraints. For general constraints, we propose an algorithm that modifies the reward estimates of arms in the C${}^2$UCB algorithm and demonstrate that it enjoys the optimal regret bound for a more general problem that can take into account other objectives simultaneously. We also show that our technique would be applicable to related problems. Numerical experiments support our theoretical results and considerations.

preprint2025arXiv

Discrete Semantic States and Hamiltonian Dynamics in LLM Embedding Spaces

We investigate the structure of Large Language Model (LLM) embedding spaces using mathematical concepts, particularly linear algebra and the Hamiltonian formalism, drawing inspiration from analogies with quantum mechanical systems. Motivated by the observation that LLM embeddings exhibit distinct states, suggesting discrete semantic representations, we explore the application of these mathematical tools to analyze semantic relationships. We demonstrate that the L2 normalization constraint, a characteristic of many LLM architectures, results in a structured embedding space suitable for analysis using a Hamiltonian formalism. We derive relationships between cosine similarity and perturbations of embedding vectors, and explore direct and indirect semantic transitions. Furthermore, we explore a quantum-inspired perspective, deriving an analogue of zero-point energy and discussing potential connections to Koopman-von Neumann mechanics. While the interpretation warrants careful consideration, our results suggest that this approach offers a promising avenue for gaining deeper insights into LLMs and potentially informing new methods for mitigating hallucinations.

Contextual Decision Trees

Focusing on Random Forests, we propose a multi-armed contextual bandit recommendation framework for feature-based selection of a single shallow tree of the learned ensemble. The trained system, which works on top of the Random Forest, dynamically identifies a base predictor that is responsible for providing the final output. In this way, we obtain local interpretations by observing the rules of the recommended tree. The carried out experiments reveal that our dynamic method is superior to an independent fitted CART decision tree and comparable to the whole black-box Random Forest in terms of predictive performances.

Not Your Grandfathers Test Set: Reducing Labeling Effort for Testing

Building and maintaining high-quality test sets remains a laborious and expensive task. As a result, test sets in the real world are often not properly kept up to date and drift from the production traffic they are supposed to represent. The frequency and severity of this drift raises serious concerns over the value of manually labeled test sets in the QA process. This paper proposes a simple but effective technique that drastically reduces the effort needed to construct and maintain a high-quality test set (reducing labeling effort by 80-100% across a range of practical scenarios). This result encourages a fundamental rethinking of the testing process by both practitioners, who can use these techniques immediately to improve their testing, and researchers who can help address many of the open questions raised by this new approach.

preprint2024arXiv

Lower Difficulty and Better Robustness: A Bregman Divergence Perspective for Adversarial Training

In this paper, we investigate on improving the adversarial robustness obtained in adversarial training (AT) via reducing the difficulty of optimization. To better study this problem, we build a novel Bregman divergence perspective for AT, in which AT can be viewed as the sliding process of the training data points on the negative entropy curve. Based on this perspective, we analyze the learning objectives of two typical AT methods, i.e., PGD-AT and TRADES, and we find that the optimization process of TRADES is easier than PGD-AT for that TRADES separates PGD-AT. In addition, we discuss the function of entropy in TRADES, and we find that models with high entropy can be better robustness learners. Inspired by the above findings, we propose two methods, i.e., FAIT and MER, which can both not only reduce the difficulty of optimization under the 10-step PGD adversaries, but also provide better robustness. Our work suggests that reducing the difficulty of optimization under the 10-step PGD adversaries is a promising approach for enhancing the adversarial robustness in AT.

Developing Multi-Task Recommendations with Long-Term Rewards via Policy Distilled Reinforcement Learning

With the explosive growth of online products and content, recommendation techniques have been considered as an effective tool to overcome information overload, improve user experience, and boost business revenue. In recent years, we have observed a new desideratum of considering long-term rewards of multiple related recommendation tasks simultaneously. The consideration of long-term rewards is strongly tied to business revenue and growth. Learning multiple tasks simultaneously could generally improve the performance of individual task due to knowledge sharing in multi-task learning. While a few existing works have studied long-term rewards in recommendations, they mainly focus on a single recommendation task. In this paper, we propose {\it PoDiRe}: a \underline{po}licy \underline{di}stilled \underline{re}commender that can address long-term rewards of recommendations and simultaneously handle multiple recommendation tasks. This novel recommendation solution is based on a marriage of deep reinforcement learning and knowledge distillation techniques, which is able to establish knowledge sharing among different tasks and reduce the size of a learning model. The resulting model is expe

GatedFWA: Linear Flash Windowed Attention with Gated Associative Memory

Modern autoregressive models rely on attention, yet the Softmax full attention in Transformers scales quadratically with sequence length. Sliding Window Attention (SWA) achieves linear-time encoding/decoding by constraining the attention pattern, but under an \textit{Associative Memory} interpretation, its difference-style update renders the training objective effectively \emph{unbounded}. In contrast, Softmax attention normalizes updates, leading to \emph{memory shrinkage and gradient vanishing}. We propose GatedFWA: a Memory-\underline{Gated} (\underline{F}lash) \underline{W}indowed \underline{A}ttention mechanism that preserves SWAs efficiency while stabilizing memory updates and making gradient flow controllable. In essence, GatedFWA accumulate a per-token/head gate into a decay bias added to the attention logits, acting as a learnable contraction in the memory recurrence. We implement a fused one-pass gate preprocessing and a FlashAttention-compatible kernel that injects the gate under a sliding mask, ensuring I/O efficiency and numerical stability. On language modelling benchmarks, GatedFWA delivers competitive throughput with negligible overhead and better use of global cont

Extreme Value Policy Optimization for Safe Reinforcement Learning

Ensuring safety is a critical challenge in applying Reinforcement Learning (RL) to real-world scenarios. Constrained Reinforcement Learning (CRL) addresses this by maximizing returns under predefined constraints, typically formulated as the expected cumulative cost. However, expectation-based constraints overlook rare but high-impact extreme value events in the tail distribution, such as black swan incidents, which can lead to severe constraint violations. To address this issue, we propose the Extreme Value policy Optimization (EVO) algorithm, leveraging Extreme Value Theory (EVT) to model and exploit extreme reward and cost samples, reducing constraint violations. EVO introduces an extreme quantile optimization objective to explicitly capture extreme samples in the cost tail distribution. Additionally, we propose an extreme prioritization mechanism during replay, amplifying the learning signal from rare but high-impact extreme samples. Theoretically, we establish upper bounds on expected constraint violations during policy updates, guaranteeing strict constraint satisfaction at a zero-violation quantile level. Further, we demonstrate that EVO achieves a lower probability of constr

Towards Higher-order Topological Consistency for Unsupervised Network Alignment

Network alignment task, which aims to identify corresponding nodes in different networks, is of great significance for many subsequent applications. Without the need for labeled anchor links, unsupervised alignment methods have been attracting more and more attention. However, the topological consistency assumptions defined by existing methods are generally low-order and less accurate because only the edge-indiscriminative topological pattern is considered, which is especially risky in an unsupervised setting. To reposition the focus of the alignment process from low-order to higher-order topological consistency, in this paper, we propose a fully unsupervised network alignment framework named HTC. The proposed higher-order topological consistency is formulated based on edge orbits, which is merged into the information aggregation process of a graph convolutional network so that the alignment consistencies are transformed into the similarity of node embeddings. Furthermore, the encoder is trained to be multi-orbit-aware and then be refined to identify more trusted anchor links. Node correspondence is comprehensively evaluated by integrating all different orders of consistency. {In addition to sound theoretical analysis, the superiority of the proposed method is also empirically demonstrated through extensive experimental evaluation. On three pairs of real-world datasets and two pairs of synthetic datasets, our HTC consistently outperforms a wide variety of unsupervised and supervised methods with the least or comparable time consumption. It also exhibits robustness to structural noise as a result of our multi-orbit-aware training mechanism.

preprint2023arXiv

Attention-LSTM for Multivariate Traffic State Prediction on Rural Roads

Accurate traffic volume and speed prediction have a wide range of applications in transportation. It can result in useful and timely information for both travellers and transportation decision-makers. In this study, an Attention based Long Sort-Term Memory model (A-LSTM) is proposed to simultaneously predict traffic volume and speed in a critical rural road segmentation which connects Tehran to Chalus, the most tourist destination city in Iran. Moreover, this study compares the results of the A-LSTM model with the Long Short-Term Memory (LSTM) model. Both models show acceptable performance in predicting speed and flow. However, the A-LSTM model outperforms the LSTM in 5 and 15-minute intervals. In contrast, there is no meaningful difference between the two models for the 30-minute time interval. By comparing the performance of the models based on different time horizons, the 15-minute horizon model outperforms the others by reaching the lowest Mean Square Error (MSE) loss of 0.0032, followed by the 30 and 5-minutes horizons with 0.004 and 0.0051, respectively. In addition, this study compares the results of the models based on two transformations of temporal categorical input variables, one-hot or cyclic, for the 15-minute time interval. The results demonstrate that both LSTM and A-LSTM with cyclic feature encoding outperform those with one-hot feature encoding.

preprint2014arXiv

Simple Deep Random Model Ensemble

Representation learning and unsupervised learning are two central topics of machine learning and signal processing. Deep learning is one of the most effective unsupervised representation learning approach. The main contributions of this paper to the topics are as follows. (i) We propose to view the representative deep learning approaches as special cases of the knowledge reuse framework of clustering ensemble. (ii) We propose to view sparse coding when used as a feature encoder as the consensus function of clustering ensemble, and view dictionary learning as the training process of the base clusterings of clustering ensemble. (ii) Based on the above two views, we propose a very simple deep learning algorithm, named deep random model ensemble (DRME). It is a stack of random model ensembles. Each random model ensemble is a special k-means ensemble that discards the expectation-maximization optimization of each base k-means but only preserves the default initialization method of the base k-means. (iv) We propose to select the most powerful representation among the layers by applying DRME to clustering where the single-linkage is used as the clustering algorithm. Moreover, the DRME bas

preprint2016arXiv

Perturbed Iterate Analysis for Asynchronous Stochastic Optimization

We introduce and analyze stochastic optimization methods where the input to each gradient update is perturbed by bounded noise. We show that this framework forms the basis of a unified approach to analyze asynchronous implementations of stochastic optimization algorithms.In this framework, asynchronous stochastic optimization algorithms can be thought of as serial methods operating on noisy inputs. Using our perturbed iterate framework, we provide new analyses of the Hogwild! algorithm and asynchronous stochastic coordinate descent, that are simpler than earlier analyses, remove many assumptions of previous models, and in some cases yield improved upper bounds on the convergence rates. We proceed to apply our framework to develop and analyze KroMagnon: a novel, parallel, sparse stochastic variance-reduced gradient (SVRG) algorithm. We demonstrate experimentally on a 16-core machine that the sparse and parallel version of SVRG is in some cases more than four orders of magnitude faster than the standard SVRG algorithm.

When Prompts Interact: Assessing Prompt Arithmetic for Deconfounding under Distribution Shift

In classification tasks, models may rely on confounding variables to achieve strong in-distribution performance, capturing spurious features that fail under distribution shift. This shortcut behavior leads to substantial degradation in out-of-distribution settings. Task arithmetic offers a potential solution by removing unwanted signals via subtraction of secondary model updates, but it typically requires full fine-tuning, which is computationally expensive. Prompt tuning provides a parameter-efficient alternative by adapting models through a small set of trainable virtual tokens. Task arithmetic on the resulting prompts presents an appealing alternative to operations on entire models, but the extent to which this approach can limit reliance on spurious features remains to be established. In this work, we study whether composing soft prompts through task arithmetic improves robustness to confounding shifts. We propose Hybrid Prompt Arithmetic (HyPA), which combines task prompts with linearized confounder prompts to counteract spurious correlations. Across multiple benchmarks, HyPA consistently improves the robustness-performance trade-off relative to prompt-arithmetic baselines under distribution shift. We further analyze how HyPA affects hidden representations and find evidence consistent with it mitigating confounding either by reducing the influence of confounder signals on predictions or by suppressing them in the representation. These results establish HyPA as a parameter-efficient and promising approach for improving robustness under confounding shifts in the evaluated setting.

preprint2012arXiv

Directed Time Series Regression for Control

We propose directed time series regression, a new approach to estimating parameters of time-series models for use in certainty equivalent model predictive control. The approach combines merits of least squares regression and empirical optimization. Through a computational study involving a stochastic version of a well known inverted pendulum balancing problem, we demonstrate that directed time series regression can generate significant improvements in controller performance over either of the aforementioned alternatives.

Density estimation on low-dimensional manifolds: an inflation-deflation approach

Normalizing Flows (NFs) are universal density estimators based on Neural Networks. However, this universality is limited: the density's support needs to be diffeomorphic to a Euclidean space. In this paper, we propose a novel method to overcome this limitation without sacrificing universality. The proposed method inflates the data manifold by adding noise in the normal space, trains an NF on this inflated manifold, and, finally, deflates the learned density. Our main result provides sufficient conditions on the manifold and the specific choice of noise under which the corresponding estimator is exact. Our method has the same computational complexity as NFs and does not require computing an inverse flow. We also show that, if the embedding dimension is much larger than the manifold dimension, noise in the normal space can be well approximated by Gaussian noise. This allows using our method for approximating arbitrary densities on unknown manifolds provided that the manifold dimension is known.

A Survey of Explainable Reinforcement Learning

Explainable reinforcement learning (XRL) is an emerging subfield of explainable machine learning that has attracted considerable attention in recent years. The goal of XRL is to elucidate the decision-making process of learning agents in sequential decision-making settings. In this survey, we propose a novel taxonomy for organizing the XRL literature that prioritizes the RL setting. We overview techniques according to this taxonomy. We point out gaps in the literature, which we use to motivate and outline a roadmap for future work.

Quartet: Native FP4 Training Can Be Optimal for Large Language Models

Training large language models (LLMs) models directly in low-precision offers a way to address computational costs by improving both throughput and energy efficiency. For those purposes, NVIDIA's recent Blackwell architecture facilitates very low-precision operations using FP4 variants. Yet, current algorithms for training LLMs in FP4 precision face significant accuracy degradation and often rely on mixed-precision fallbacks. In this paper, we investigate hardware-supported FP4 training and introduce a new approach for accurate, end-to-end FP4 training with all the major computations (i.e., linear layers) in low precision. Through extensive evaluations on Llama-type models, we reveal a new low-precision scaling law that quantifies performance trade-offs across bit-widths and training setups. Guided by this investigation, we design an "optimal" technique in terms of accuracy-vs-computation, called Quartet. We implement Quartet using optimized CUDA kernels tailored for Blackwell, demonstrating that fully FP4-based training is a competitive alternative to FP16 half-precision and to FP8 training. Our code is available at https://github.com/IST-DASLab/Quartet.

Super-resolving 2D stress tensor field conserving equilibrium constraints using physics informed U-Net

In a finite element analysis, using a large number of grids is important to obtain accurate results, but is a resource-consuming task. Aiming to real-time simulation and optimization, it is desired to obtain fine grid analysis results within a limited resource. This paper proposes a super-resolution method that predicts a stress tensor field in a high-resolution from low-resolution contour plots by utilizing a U-Net-based neural network which is called PI-UNet. In addition, the proposed model minimizes the residual of the equilibrium constraints so that it outputs a physically reasonable solution. The proposed network is trained with FEM results of simple shapes, and is validated with a complicated realistic shape to evaluate generalization capability. Although ESRGAN is a standard model for image super-resolution, the proposed U-Net based model outperforms ESRGAN model in the stress tensor prediction task.

Preprocessing Reward Functions for Interpretability

In many real-world applications, the reward function is too complex to be manually specified. In such cases, reward functions must instead be learned from human feedback. Since the learned reward may fail to represent user preferences, it is important to be able to validate the learned reward function prior to deployment. One promising approach is to apply interpretability tools to the reward function to spot potential deviations from the user's intention. Existing work has applied general-purpose interpretability tools to understand learned reward functions. We propose exploiting the intrinsic structure of reward functions by first preprocessing them into simpler but equivalent reward functions, which are then visualized. We introduce a general framework for such reward preprocessing and propose concrete preprocessing algorithms. Our empirical evaluation shows that preprocessed rewards are often significantly easier to understand than the original reward.

Measurement error models: from nonparametric methods to deep neural networks

The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose an efficient neural network design for estimating measurement error models, in which we use a fully connected feed-forward neural network (FNN) to approximate the regression function $f(x)$, a normalizing flow to approximate the prior distribution of $X$, and an inference network to approximate the posterior distribution of $X$. Our method utilizes recent advances in variational inference for deep neural networks, such as the importance weight autoencoder, doubly reparametrized gradient estimator, and non-linear independent components estimation. We conduct an extensive numerical study to compare the neural network approach with classical nonparametric methods and observe that the neural network approach is more flexible in accommodating different classes of regression functions and performs superior or comparable to the best available method in nearly all settings.

preprint2013arXiv

Active and passive learning of linear separators under log-concave distributions

We provide new results concerning label efficient, polynomial time, passive and active learning of linear separators. We prove that active learning provides an exponential improvement over PAC (passive) learning of homogeneous linear separators under nearly log-concave distributions. Building on this, we provide a computationally efficient PAC algorithm with optimal (up to a constant factor) sample complexity for such problems. This resolves an open question concerning the sample complexity of efficient PAC algorithms under the uniform distribution in the unit ball. Moreover, it provides the first bound for a polynomial-time PAC algorithm that is tight for an interesting infinite class of hypothesis functions under a general and natural class of data-distributions, providing significant progress towards a longstanding open question. We also provide new bounds for active and passive learning in the case that the data might not be linearly separable, both in the agnostic case and and under the Tsybakov low-noise condition. To derive our results, we provide new structural results for (nearly) log-concave distributions, which might be of independent interest as well.

MARLeME: A Multi-Agent Reinforcement Learning Model Extraction Library

Multi-Agent Reinforcement Learning (MARL) encompasses a powerful class of methodologies that have been applied in a wide range of fields. An effective way to further empower these methodologies is to develop libraries and tools that could expand their interpretability and explainability. In this work, we introduce MARLeME: a MARL model extraction library, designed to improve explainability of MARL systems by approximating them with symbolic models. Symbolic models offer a high degree of interpretability, well-defined properties, and verifiable behaviour. Consequently, they can be used to inspect and better understand the underlying MARL system and corresponding MARL agents, as well as to replace all/some of the agents that are particularly safety and security critical.

preprint2016arXiv

Simple one-pass algorithm for penalized linear regression with cross-validation on MapReduce

In this paper, we propose a one-pass algorithm on MapReduce for penalized linear regression \[f_λ(α, β) = \|Y - α\mathbf{1} - Xβ\|_2^2 + p_λ(β)\] where $α$ is the intercept which can be omitted depending on application; $β$ is the coefficients and $p_λ$ is the penalized function with penalizing parameter $λ$. $f_λ(α, β)$ includes interesting classes such as Lasso, Ridge regression and Elastic-net. Compared to latest iterative distributed algorithms requiring multiple MapReduce jobs, our algorithm achieves huge performance improvement; moreover, our algorithm is exact compared to the approximate algorithms such as parallel stochastic gradient decent. Moreover, what our algorithm distinguishes with others is that it trains the model with cross validation to choose optimal $λ$ instead of user specified one. Key words: penalized linear regression, lasso, elastic-net, ridge, MapReduce

DINO: A Conditional Energy-Based GAN for Domain Translation

Domain translation is the process of transforming data from one domain to another while preserving the common semantics. Some of the most popular domain translation systems are based on conditional generative adversarial networks, which use source domain data to drive the generator and as an input to the discriminator. However, this approach does not enforce the preservation of shared semantics since the conditional input can often be ignored by the discriminator. We propose an alternative method for conditioning and present a new framework, where two networks are simultaneously trained, in a supervised manner, to perform domain translation in opposite directions. Our method is not only better at capturing the shared information between two domains but is more generic and can be applied to a broader range of problems. The proposed framework performs well even in challenging cross-modal translations, such as video-driven speech reconstruction, for which other systems struggle to maintain correspondence.

Implications on Feature Detection when using the Benefit-Cost Ratio

In many practical machine learning applications, there are two objectives: one is to maximize predictive accuracy and the other is to minimize costs of the resulting model. These costs of individual features may be financial costs, but can also refer to other aspects, like for example evaluation time. Feature selection addresses both objectives, as it reduces the number of features and can improve the generalization ability of the model. If costs differ between features, the feature selection needs to trade-off the individual benefit and cost of each feature. A popular trade-off choice is the ratio of both, the BCR (benefit-cost ratio). In this paper we analyze implications of using this measure with special focus to the ability to distinguish relevant features from noise. We perform a simulation study for different cost and data settings and obtain detection rates of relevant features and empirical distributions of the trade-off ratio. Our simulation study exposed a clear impact of the cost setting on the detection rate. In situations with large cost differences and small effect sizes, the BCR missed relevant features and preferred cheap noise features. We conclude that a trade-of

A Framework of Learning Through Empirical Gain Maximization

We develop in this paper a framework of empirical gain maximization (EGM) to address the robust regression problem where heavy-tailed noise or outliers may present in the response variable. The idea of EGM is to approximate the density function of the noise distribution instead of approximating the truth function directly as usual. Unlike the classical maximum likelihood estimation that encourages equal importance of all observations and could be problematic in the presence of abnormal observations, EGM schemes can be interpreted from a minimum distance estimation viewpoint and allow the ignorance of those observations. Furthermore, it is shown that several well-known robust nonconvex regression paradigms, such as Tukey regression and truncated least square regression, can be reformulated into this new framework. We then develop a learning theory for EGM, by means of which a unified analysis can be conducted for these well-established but not fully-understood regression approaches. Resulting from the new framework, a novel interpretation of existing bounded nonconvex loss functions can be concluded. Within this new framework, the two seemingly irrelevant terminologies, the well-known Tukey's biweight loss for robust regression and the triweight kernel for nonparametric smoothing, are closely related. More precisely, it is shown that the Tukey's biweight loss can be derived from the triweight kernel. Similarly, other frequently employed bounded nonconvex loss functions in machine learning such as the truncated square loss, the Geman-McClure loss, and the exponential squared loss can also be reformulated from certain smoothing kernels in statistics. In addition, the new framework enables us to devise new bounded nonconvex loss functions for robust learning.

Physics-constrained Unsupervised Learning of Partial Differential Equations using Meshes

Enhancing neural networks with knowledge of physical equations has become an efficient way of solving various physics problems, from fluid flow to electromagnetism. Graph neural networks show promise in accurately representing irregularly meshed objects and learning their dynamics, but have so far required supervision through large datasets. In this work, we represent meshes naturally as graphs, process these using Graph Networks, and formulate our physics-based loss to provide an unsupervised learning framework for partial differential equations (PDE). We quantitatively compare our results to a classical numerical PDE solver, and show that our computationally efficient approach can be used as an interactive PDE solver that is adjusting boundary conditions in real-time and remains sufficiently close to the baseline solution. Our inherently differentiable framework will enable the application of PDE solvers in interactive settings, such as model-based control of soft-body deformations, or in gradient-based optimization methods that require a fully differentiable pipeline.

Expert2Coder: Capturing Divergent Brain Regions Using Mixture of Regression Experts

fMRI semantic category understanding using linguistic encoding models attempts to learn a forward mapping that relates stimuli to the corresponding brain activation. State-of-the-art encoding models use a single global model (linear or non-linear) to predict brain activation given the stimulus. However, the critical assumption in these methods is that a priori different brain regions respond the same way to all the stimuli, that is, there is no modularity or specialization assumed for any region. This goes against the modularity theory, supported by many cognitive neuroscience investigations suggesting that there are functionally specialized regions in the brain. In this paper, we achieve this by clustering similar regions together and for every cluster we learn a different linear regression model using a mixture of linear experts model. The key idea here is that each linear expert captures the behaviour of similar brain regions. Given a new stimulus, the utility of the proposed model is twofold (i) predicts the brain activation as a weighted linear combination of the activations of multiple linear experts and (ii) to learn multiple experts corresponding to different brain regions.

Improving the Euclidean Diffusion Generation of Manifold Data by Mitigating Score Function Singularity

Euclidean diffusion models have achieved remarkable success in generative modeling across diverse domains, and they have been extended to manifold cases in recent advances. Instead of explicitly utilizing the structure of special manifolds as studied in previous works, in this paper we investigate direct sampling of the Euclidean diffusion models for general manifold-structured data. We reveal the multiscale singularity of the score function in the ambient space, which hinders the accuracy of diffusion-generated samples. We then present an elaborate theoretical analysis of the singularity structure of the score function by decomposing it along the tangential and normal directions of the manifold. To mitigate the singularity and improve the sampling accuracy, we propose two novel methods: (1) Niso-DM, which reduces the scale discrepancies in the score function by utilizing a non-isotropic noise, and (2) Tango-DM, which trains only the tangential component of the score function using a tangential-only loss function. Numerical experiments demonstrate that our methods achieve superior performance on distributions over various manifolds with complex geometries.

Latent Variable Models for Bayesian Causal Discovery

Learning predictors that do not rely on spurious correlations involves building causal representations. However, learning such a representation is very challenging. We, therefore, formulate the problem of learning a causal representation from high dimensional data and study causal recovery with synthetic data. This work introduces a latent variable decoder model, Decoder BCD, for Bayesian causal discovery and performs experiments in mildly supervised and unsupervised settings. We present a series of synthetic experiments to characterize important factors for causal discovery and show that using known intervention targets as labels helps in unsupervised Bayesian inference over structure and parameters of linear Gaussian additive noise latent structural causal models.

Deep Linear Discriminant Analysis Revisited

We show that for unconstrained Deep Linear Discriminant Analysis (LDA) classifiers, maximum-likelihood training admits pathological solutions in which class means drift together, covariances collapse, and the learned representation becomes almost non-discriminative. Conversely, cross-entropy training yields excellent accuracy but decouples the head from the underlying generative model, leading to highly inconsistent parameter estimates. To reconcile generative structure with discriminative performance, we introduce the \emph{Discriminative Negative Log-Likelihood} (DNLL) loss, which augments the LDA log-likelihood with a simple penalty on the mixture density. DNLL can be interpreted as standard LDA NLL plus a term that explicitly discourages regions where several classes are simultaneously likely. Deep LDA trained with DNLL produces clean, well-separated latent spaces, matches the test accuracy of softmax classifiers on synthetic data and standard image benchmarks, and yields substantially better calibrated predictive probabilities, restoring a coherent probabilistic interpretation to deep discriminant models.