While Large Language Models (LLMs) demonstrate strong performance across domains, their long-context capabilities are limited by transient neural activations causing information decay and unstructured feed-forward network (FFN) weights leading to semantic fragmentation. Inspired by the brain's working memory and cortical modularity, we propose PaceLLM, featuring two innovations: (1) a Persistent Activity (PA) Mechanism that mimics prefrontal cortex (PFC) neurons' persistent firing by introducing an activation-level memory bank to dynamically retrieve, reuse, and update critical FFN states, addressing contextual decay; and (2) Cortical Expert (CE) Clustering that emulates task-adaptive neural specialization to reorganize FFN weights into semantic modules, establishing cross-token dependencies and mitigating fragmentation.

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For the theoretical exposition, we first establish the following Lemmas. Lemma A.1 proves that the derivative of the function φis bounded in the `2-norm when the domain is restricted to the support of P. Lemma A.1. Lemma A.3 proves that the function fΘ, as a function of Θ, is Lipschitz with respect to the k k norm. Joint first authors contributed equally Corresponding author 35th Conference on Neural Information Processing Systems (NeurIPS 2021). Thus, from equation (1), h φ(PC(θ)) φ(θ),x PC(θ)i 0. (2) We now observe that, dφ(x,θ) dφ(x,PC(θ)) dφ(PC(θ),θ) = h φ(PC(θ)) φ(θ),x PC(θ)i 0. Hence the result.

Multi-view anchor graph clustering selects representative anchors to avoid full pair-wise similarities and therefore reduce the complexity of graph methods. Although widely applied in large-scale applications, existing approaches do not pay sufficient attention to establishing correct correspondences between the anchor sets across views. To be specific, anchor graphs obtained from different views are not aligned column-wisely. Such an Anchor-Unaligned Problem (AUP) would cause inaccurate graph fusion and degrade the clustering performance. Under multi-view scenarios, generating correct correspondences could be extremely difficult since anchors are not consistent in feature dimensions.

Unlike MI, some GEMINIs do not require regularisations when training.

Clustering, in particular k-means clustering, is a central topic in data analysis. Clustering with Bregman divergences is a recently proposed generalization of k-means clustering which has already been widely used in applications. In this paper we analyze theoretical properties of Bregman clustering when the number of the clusters k is large. We establish quantization rates and describe the limiting distribution of the centers as k, extending well-known results for k-means clustering.

Clustering and dimensionality reduction have been crucial topics in machine learning and computer vision. Clustering high-dimensional data has been challenging for a long time due to the curse of dimensionality. For that reason, a more promising direction is the joint learning of dimension reduction and clustering. In this work, we propose a Manifold Learning Framework that learns dimensionality reduction and clustering simultaneously. The proposed framework is able to jointly learn the parameters of a dimension reduction technique (e.g. linear projection or a neural network) and cluster the data based on the resulting features (e.g. under a Gaussian Mixture Model framework). The framework searches for the dimension reduction parameters and the optimal clusters by traversing a manifold,using Gradient Manifold Optimization. The obtained The proposed framework is exemplified with a Gaussian Mixture Model as one simple but efficient example, in a process that is somehow similar to unsupervised Linear Discriminant Analysis (LDA). We apply the proposed method to the unsupervised training of simulated data as well as a benchmark image dataset (i.e. MNIST). The experimental results indicate that our algorithm has better performance than popular clustering algorithms from the literature.

Differentially private $K$-means clustering enables releasing cluster centers derived from a dataset while protecting the privacy of the individuals. Non-interactive clustering techniques based on privatized histograms are attractive because the released data synopsis can be reused for other downstream tasks without additional privacy loss. The choice of the number of grids for discretizing the data points is crucial, as it directly controls the quantization bias and the amount of noise injected to preserve privacy. The widely adopted strategy selects a grid size that is independent of the number of clusters and also relies on empirical tuning. In this work, we revisit this choice and propose a refined grid-size selection rule derived by minimizing an upper bound on the expected deviation in the K-means objective function, leading to a more principled discretization strategy for non-interactive private clustering. Compared to prior work, our grid resolution differs both in its dependence on the number of clusters and in the scaling with dataset size and privacy budget. Extensive numerical results elucidate that the proposed strategy results in accurate clustering compared to the state-of-the-art techniques, even under tight privacy budgets.

We study the effects of center initialization on the performance of a family of distributed gradient-based clustering algorithms introduced in [1], that work over connected networks of users. In the considered scenario, each user contains a local dataset and communicates only with its immediate neighbours, with the aim of finding a global clustering of the joint data. We perform extensive numerical experiments, evaluating the effects of center initialization on the performance of our family of methods, demonstrating that our methods are more resilient to the effects of initialization, compared to centralized gradient clustering [2]. Next, inspired by the $K$-means++ initialization [3], we propose a novel distributed center initialization scheme, which is shown to improve the performance of our methods, compared to the baseline random initialization.

Clustering graphs under the Stochastic Block Model (SBM) and extensions are well studied. Guarantees of correctness exist under the assumption that the data is sampled from a model. In this paper, we propose a framework, in which we obtain "correctness" guarantees without assuming the data comes from a model. The guarantees we obtain depend instead on the statistics of the data that can be checked. We also show that this framework ties in with the existing model-based framework, and that we can exploit results in model-based recovery, as well as strengthen the results existing in that area of research.