Neural collapse (NC) refers to the surprising structure of the last layer of deep neural networks in the terminal phase of gradient descent training. Recently, an increasing amount of experimental evidence has pointed to the propagation of NC to earlier layers of neural networks. However, while the NC in the last layer is well studied theoretically, much less is known about its multi-layered counterpart - deep neural collapse (DNC). In particular, existing work focuses either on linear layers or only on the last two layers at the price of an extra assumption. Our work fills this gap by generalizing the established analytical framework for NC - the unconstrained features model - to multiple non-linear layers. Our key technical contribution is to show that, in a deep unconstrained features model, the unique global optimum for binary classification exhibits all the properties typical of DNC. This explains the existing experimental evidence of DNC. We also empirically show that (i) by optimizing deep unconstrained features models via gradient descent, the resulting solution agrees well with our theory, and (ii) trained networks recover the unconstrained features suitable for the occurrence of DNC, thus supporting the validity of this modeling principle.

However, existing theoretical results are restricted to special cases: linear models, only two layers or binary classification. In contrast, we focus on non-linear models of arbitrary depth in multi-class classification and reveal a surprising qualitative shift.

Memory-augmented neural networks (MANNs) can perform algorithmic tasks such as sorting. However, they often fail to generalise to input sequence lengths not encountered during training. We introduce two approaches that constrain the state space of the MANN's controller network: state compression and state regularisation. We empirically demonstrated that both approaches can improve generalisation to input sequences of out-of-distribution lengths for a specific type of MANN: the differentiable neural computer (DNC). The constrained DNC could process input sequences that were up to 2.3 times longer than those processed by an unconstrained baseline controller network. Notably, the applied constraints enabled the extension of the DNC's memory matrix without the need for retraining and thus allowed the processing of input sequences that were 10.4 times longer. However, the improvements were not consistent across all tested algorithmic tasks. Interestingly, solutions that performed better often had a highly structured state space, characterised by state trajectories exhibiting increased curvature and loop-like patterns. Our experimental work demonstrates that state-space constraints can enable the training of a DNC using shorter input sequences, thereby saving computational resources and facilitating training when acquiring long sequences is costly.

Multi-modal entity alignment (MMEA) aims to identify equivalent entities across heterogeneous multi-modal knowledge graphs (MMKGs), where each entity is described by attributes from various modalities. Existing methods typically assume that both intra-entity and inter-graph correspondences are faultless, which is often violated in real-world MMKGs due to the reliance on expert annotations. In this paper, we reveal and study a highly practical yet under-explored problem in MMEA, termed Dual-level Noisy Correspondence (DNC). DNC refers to misalignments in both intra-entity (entity-attribute) and inter-graph (entity-entity and attribute-attribute) correspondences. To address the DNC problem, we propose a robust MMEA framework termed RULE. RULE first estimates the reliability of both intra-entity and inter-graph correspondences via a dedicated two-fold principle. Leveraging the estimated reliabilities, RULE mitigates the negative impact of intra-entity noise during attribute fusion and prevents overfitting to noisy inter-graph correspondences during inter-graph discrepancy elimination. Beyond the training-time designs, RULE further incorporates a correspondence reasoning module that uncovers the underlying attribute-attribute connection across graphs, guaranteeing more accurate equivalent entity identification. Extensive experiments on five benchmarks verify the effectiveness of our method against the DNC compared with seven state-of-the-art methods.The code is available at \href{https://github.com/XLearning-SCU/RULE}{XLearning-SCU/RULE}

Neural collapse (NC) refers to the surprising structure of the last layer of deep neural networks in the terminal phase of gradient descent training. Recently, an increasing amount of experimental evidence has pointed to the propagation of NC to earlier layers of neural networks. However, while the NC in the last layer is well studied theoretically, much less is known about its multi-layered counterpart - deep neural collapse (DNC). In particular, existing work focuses either on linear layers or only on the last two layers at the price of an extra assumption. Our work fills this gap by generalizing the established analytical framework for NC - the unconstrained features model - to multiple non-linear layers.

Deep Neural Collapse (DNC) refers to the surprisingly rigid structure of the data representations in the final layers of Deep Neural Networks (DNNs). Though the phenomenon has been measured in a wide variety of settings, its emergence is only partially understood. In this work, we provide substantial evidence that DNC formation occurs primarily through deep feature learning with the average gradient outer product (AGOP). This takes a step further compared to efforts that explain neural collapse via feature-agnostic approaches, such as the unconstrained features model. We proceed by providing evidence that the right singular vectors and values of the weights are responsible for the majority of within-class variability collapse in DNNs. As shown in recent work, this singular structure is highly correlated with that of the AGOP. We then establish experimentally and theoretically that AGOP induces neural collapse in a randomly initialized neural network. In particular, we demonstrate that Deep Recursive Feature Machines, a method originally introduced as an abstraction for AGOP feature learning in convolutional neural networks, exhibits DNC.

Large discrete action spaces (LDAS) remain a central challenge in reinforcement learning. Existing solution approaches can handle unstructured LDAS with up to a few million actions. However, many real-world applications in logistics, production, and transportation systems have combinatorial action spaces, whose size grows well beyond millions of actions, even on small instances. Fortunately, such action spaces exhibit structure, e.g., equally spaced discrete resource units. With this work, we focus on handling structured LDAS (SLDAS) with sizes that cannot be handled by current benchmarks: we propose Dynamic Neighborhood Construction (DNC), a novel exploitation paradigm for SLDAS. We present a scalable neighborhood exploration heuristic that utilizes this paradigm and efficiently explores the discrete neighborhood around the continuous proxy action in structured action spaces with up to $10^{73}$ actions. We demonstrate the performance of our method by benchmarking it against three state-of-the-art approaches designed for large discrete action spaces across two distinct environments. Our results show that DNC matches or outperforms state-of-the-art approaches while being computationally more efficient. Furthermore, our method scales to action spaces that so far remained computationally intractable for existing methodologies.

A Differentiable Neural Computer (DNC) is a neural network with an external memory which allows for iterative content modification via read, write and delete operations. We show that information theoretic properties of the memory contents play an important role in the performance of such architectures. We introduce a novel concept of memory demon to DNC architectures which modifies the memory contents implicitly via additive input encoding. The goal of the memory demon is to maximize the expected sum of mutual information of the consecutive external memory contents.

A key feature of intelligent behaviour is the ability to learn abstract strategies that scale and transfer to unfamiliar problems. An abstract strategy solves every sample from a problem class, no matter its representation or complexity -- like algorithms in computer science. Neural networks are powerful models for processing sensory data, discovering hidden patterns, and learning complex functions, but they struggle to learn such iterative, sequential or hierarchical algorithmic strategies. Extending neural networks with external memories has increased their capacities in learning such strategies, but they are still prone to data variations, struggle to learn scalable and transferable solutions, and require massive training data. We present the Neural Harvard Computer (NHC), a memory-augmented network based architecture, that employs abstraction by decoupling algorithmic operations from data manipulations, realized by splitting the information flow and separated modules. This abstraction mechanism and evolutionary training enable the learning of robust and scalable algorithmic solutions. On a diverse set of 11 algorithms with varying complexities, we show that the NHC reliably learns algorithmic solutions with strong generalization and abstraction: perfect generalization and scaling to arbitrary task configurations and complexities far beyond seen during training, and being independent of the data representation and the task domain.

A differentiable neural computer (DNC) is a memory augmented neural network devised to solve a wide range of algorithmic and question answering tasks and it showed promising performance in a variety of domains. However, its single memory-based operations are not enough to store and retrieve diverse informative representations existing in many tasks. Furthermore, DNC does not explicitly consider the memorization itself as a target objective, which inevitably leads to a very slow learning speed of the model. To address those issues, we propose a novel distributed memory-based self-supervised DNC architecture for enhanced memory augmented neural network performance. We introduce (i) a multiple distributed memory block mechanism that stores information independently to each memory block and uses stored information in a cooperative way for diverse representation and (ii) a self-supervised memory loss term which ensures how well a given input is written to the memory. Our experiments on algorithmic and question answering tasks show that the proposed model outperforms all other variations of DNC in a large margin, and also matches the performance of other state-of-the-art memory-based network models.