The existing low-memory BLS implementation proposed recently avoids the need for storing and inverting large matrices, to achieve efficient usage of memories. However, the existing low-memory BLS implementation sacrifices the testing accuracy as a price for efficient usage of memories, since it can no longer obtain the generalized inverse or ridge solution for the output weights during incremental learning, and it cannot work under the very small ridge parameter that is utilized in the original BLS. Accordingly, it is required to develop the low-memory BLS implementations, which can work under very small ridge parameters and compute the generalized inverse or ridge solution for the output weights in the process of incremental learning. In this paper, firstly we propose the low-memory implementations for the recently proposed recursive and square-root BLS algorithms on added inputs and the recently proposed squareroot BLS algorithm on added nodes, by simply processing a batch of inputs or nodes in each recursion. Since the recursive BLS implementation includes the recursive updates of the inverse matrix that may introduce numerical instabilities after a large number of iterations, and needs the extra computational load to decompose the inverse matrix into the Cholesky factor when cooperating with the proposed low-memory implementation of the square-root BLS algorithm on added nodes, we only improve the low-memory implementations of the square-root BLS algorithms on added inputs and nodes, to propose the full lowmemory implementation of the square-root BLS algorithm. All the proposed low-memory BLS implementations compute the ridge solution for the output weights in the process of incremental learning, and most of them can work under very small ridge parameters.
翻译:现有的低模量 BLS 实施最近建议的现有低模量 BLS 实施避免需要存储和颠倒大型矩阵,以实现对记忆的高效使用。然而,现有的低模量 BLS 实施会牺牲测试精度作为高效使用记忆的一种价格,因为它无法在增量学习中为产出权重再获得通用反向或脊柱解决方案, 也无法在原始 BLS 中使用的非常小的脊脊参数下工作。 因此, 需要开发低模量的 BLS 实施, 它可以在非常小的脊脊柱参数下工作, 并计算增量学习过程中产出权重的普遍反向或峰值。 首先, 我们建议对最近提出的对增量投入的递增和正根的 BLS 算法进行低模效执行, 只需处理一系列投入或每递增量的正数, 递归性 BLS 的低精度执行包含对低精度矩阵的递增性更新, 在进行大量计算后, 将最小递增量的递增性递增性递增的 RNS, 递增性 递增性 递增性 递增性 递增性 递增性 递增性 递增性 递增性 递增性 递增性 递增性 递增性 递增性 递增性 递增性 递增性 递增性 递增性 递减 性 性 性 性 递增性 的 RLSLSLSLSLSLSLSLSLSLSLS