In contrast to the classic formulation of partial monitoring, linear partial monitoring can model infinite outcome spaces, while imposing a linear structure on both the losses and the observations. This setting can be viewed as a generalization of linear bandits where loss and feedback are decoupled in a flexible manner. In this work, we address a nonstochastic (adversarial), finite-actions version of the problem through a simple instance of the exploration-by-optimization method that is amenable to efficient implementation. We derive regret bounds that depend on the game structure in a more transparent manner than previous theoretical guarantees for this paradigm. Our bounds feature instance-specific quantities that reflect the degree of alignment between observations and losses, and resemble known guarantees in the stochastic setting. Notably, they achieve the standard T rate in easy (locally observable) games and T2/3 in hard (globally observable) games, where T is the time horizon. We instantiate these bounds in a selection of old and new partial information settings subsumed by this model, and illustrate that the achieved dependence on the game structure can be tight in interesting cases.

A.1 Dataset Examples450 In this section of the appendix, we present a detailed overview of several representative tasks from451 each category included in REASONINGGYM. For each task, we describe its structure, complexity452 parameters, and provide examples.453 A.1.1 complex_arithmetic(Algebra)454 Find the solution of an arithmetic operation involving complex numbers.455 The spiral order is clockwise, starting from the top-left corner. Predict the corresponding output grid by applying the rule you found.

In off-policy policy evaluation (OPE) tasks within reinforcement learning, Temporal Difference Learning(TD) and Fitted Q-Iteration (FQI) have traditionally been viewed as differing in the number of updates toward the target value function: TD makes one update, FQI makes an infinite number, and Partial Fitted Q-Iteration (PFQI) performs a finite number. We show that this view is not accurate, and provide a new mathematical perspective under linear value function approximation that unifies these methods as a single iterative method solving the same linear system, but using different matrix splitting schemes and preconditioners. We show that increasing the number of updates under the same target value function, i.e., the target network technique, is a transition from using a constant preconditioner to using a data-feature adaptive preconditioner. This elucidates, for the first time, why TD convergence does not necessarily imply FQI convergence, and establishes tight convergence connections among TD, PFQI, and FQI. Our framework enables sharper theoretical results than previous work and characterization of the convergence conditions for each algorithm, without relying on assumptions about the features (e.g., linear independence). We also provide an encoder-decoder perspective to better understand the convergence conditions of TD, and prove, for the first time, that when a large learning rate doesn't work, trying a smaller one may help. Our framework also leads to the discovery of new crucial conditions on features for convergence, and shows how common assumptions about features influence convergence, e.g., the assumption of linearly independent features can be dropped without compromising the convergence guarantees of stochastic TD in the on-policy setting. This paper is also the first to introduce matrix splitting into the convergence analysis of these algorithms.

We provide a unified theoretical analysis of Linear Discriminant Analysis with simultaneous multilabel scatter matrix formulations and Stiefel orthogonality constraints. Our contributions span both algebraic structure and statistical guarantees. On the algebraic side, we characterize the rank of the multilabel between-class scatter matrix, showing that the effective discriminant dimensionality can strictly exceed the classical single-label bound of $C-1$; we establish a multilabel partition of variance and prove that all four Fisher objectives are equivalent under the $W^\top S_t^{ML} W = I_r$ constraint while characterizing their divergence under the Stiefel constraint; and we prove a two-sided label-distance preservation bound relating projected distances to Hamming distances in label space. On the statistical side, we establish a finite-sample $O(k_{\max}\sqrt{d\log d/n}/gap_r)$ bound on the subspace estimation error under sub-Gaussian noise with a matching $Ω(σ^2 d/(n\,gap_r))$ minimax lower bound, establishing a near-minimax-optimal rate (matching up to logarithmic and $k_{\max}$ factors) for multilabel discriminant subspace estimation. We further provide high-probability distance concentration, robustness guarantees under label interactions, and a regularization analysis preserving the spectral structure when $d \gg n$. All results are verified numerically on synthetic data generated from the linear label-effect model, covering both the algebraic identities and the multilabel-specific quantities ($k_{\max}$, $κ(S_t^{ML})$, $\|Γ/n\|_2$, $Δ_r$) that govern the statistical bounds. The numerical experiments are designed as a sanity check for the theorems rather than as an empirical benchmark; evaluation on real multilabel datasets is left to future work targeting application-oriented venues.

We set the patch size to be 8. Our model is optimized by AdamW optimizer [3] with a learning rate2 of 0.0004, 250k training steps, linearly warm-up of 5000 steps and an exponentially weight-decaying3 schedule. The gradient norm is clipped at 1. We use Pytorch automatic mixed-precision and data4 paralleling for training acceleration. All models are trained on 4 Nvidia RTXA5000 GPUs with a5 total batch size of 128.

Learning object-centric representations from complex natural environments enables both humans and machines with reasoning abilities from low-level perceptual features. To capture compositional entities of the scene, we proposed cyclic walks between perceptual features extracted from vision transformers and object entities. First, a slot-attention module interfaces with these perceptual features and produces a finite set of slot representations. These slots can bind to any object entities in the scene via inter-slot competitions for attention. Next, we establish entity-feature correspondence with cyclic walks along high transition probability based on the pairwise similarity between perceptual features (aka "parts") and slot-binded object representations (aka "whole").

Federated Learning (FL) [1]provides acommunication-efficient andprivacypreserving means to learn from data distributed across clients such as cell phones, autonomous vehicles, and hospitals. FL aims for each client to benefit from collaborating in the learning process without sacrificing data privacy or paying a substantial communication cost. Federated Averaging (FedAvg) [1] is the predominant FL algorithm.

However,batch-splitting suffers from problems including the inability to train very large models (due to memory constraints), high latency, and inefficiency at small batch sizes. All of these can be solved by more general distribution strategies (model-parallelism). Unfortunately,efficient model-parallel algorithms tend tobe complicated todiscover, describe, and to implement, particularly on large clusters.

Consider a data-generation process that transforms low-dimensional latent causally-related variables to high-dimensional observed variables. Causal representation learning (CRL) is the process of using the observed data to recover the latent causal variables and the causal structure among them.