Given M with (M) < 1andanunsatur (M)

ThepolytopeP(X,L) is in fact a "twisted sum" of a finite number of lattice polytopes fibering overP(F,L| F) .

Recent studies have revealed that properties of training trajectories can be indicative of generalization.

Conventional wisdom attributes the mysterious generalization abilities of overparameterized neural networks to gradient descent (and its variants). The recent volume hypothesis challenges this view: it posits that these generalization abilities persist even when gradient descent is replaced by Guess & Check (G&C), i.e., by drawing weight settings until one that fits the training data is found. The validity of the volume hypothesis for wide and deep neural networks remains an open question. In this paper, we theoretically investigate this question for matrix factorization (with linear and non-linear activation)--a common testbed in neural network theory. We first prove that generalization under G&C deteriorates with increasing width, establishing what is, to our knowledge, the first case where G&C is provably inferior to gradient descent. Conversely, we prove that generalization under G&C improves with increasing depth, revealing a stark contrast between wide and deep networks, which we further validate empirically. These findings suggest that even in simple settings, there may not be a simple answer to the question of whether neural networks need gradient descent to generalize well.

In a standard view of the reinforcement learning problem, an agent's goal is to efficiently identify a policy that maximizes long-term reward. However, this perspective is based on a restricted view of learning as finding a solution, rather than treating learning as endless adaptation. In contrast, continual reinforcement learning refers to the setting in which the best agents never stop learning. Despite the importance of continual reinforcement learning, the community lacks a simple definition of the problem that highlights its commitments and makes its primary concepts precise and clear. To this end, this paper is dedicated to carefully defining the continual reinforcement learning problem.

In this paper we investigate which subsets of the real plane are realisable as the set of points on which a one-layer ReLU neural network takes a positive value. In the case of cones we give a full characterisation of such sets. Furthermore, we give a necessary condition for any subset of $\mathbb R^d$. We give various examples of such one-layer neural networks.

We tackle the task of long-form music generation--particularly the challenging \textbf{lyrics-to-song} problem--by introducing YuE, a family of open foundation models based on the LLaMA2 architecture. Specifically, YuE scales to trillions of tokens and generates up to five minutes of music while maintaining lyrical alignment, coherent musical structure, and engaging vocal melodies with appropriate accompaniment. It achieves this through (1) track-decoupled next-token prediction to overcome dense mixture signals, (2) structural progressive conditioning for long-context lyrical alignment, and (3) a multitask, multiphase pre-training recipe to converge and generalize. In addition, we redesign the in-context learning technique for music generation, enabling versatile style transfer (e.g., converting Japanese city pop into an English rap while preserving the original accompaniment) and bidirectional generation. Through extensive evaluation, we demonstrate that YuE matches or even surpasses some of the proprietary systems in musicality and vocal agility. In addition, fine-tuning YuE enables additional controls and enhanced support for tail languages. Furthermore, beyond generation, we show that YuE's learned representations can perform well on music understanding tasks, where the results of YuE match or exceed state-of-the-art methods on the MARBLE benchmark. Keywords: lyrics2song, song generation, long-form, foundation model, music generation

Emotional support dialogue systems aim to reduce help-seekers' distress and help them overcome challenges. While human values$\unicode{x2013}$core beliefs that shape an individual's priorities$\unicode{x2013}$are increasingly emphasized in contemporary psychological therapy for their role in fostering internal transformation and long-term emotional well-being, their integration into emotional support systems remains underexplored. To bridge this gap, we present a value-driven method for training emotional support dialogue systems designed to reinforce positive values in seekers. Our model learns to identify which values to reinforce at each turn and how to do so, by leveraging online support conversations from Reddit. The model demonstrated superior performance in emotional support capabilities, outperforming various baselines. Notably, it more effectively explored and elicited values from seekers. Expert assessments by therapists highlighted two key strengths of our model: its ability to validate users' challenges and its effectiveness in emphasizing positive aspects of their situations$\unicode{x2013}$both crucial elements of value reinforcement. Our work validates the effectiveness of value reinforcement for emotional support systems and establishes a foundation for future research.