We are unable to provide the monkey data as .

However, since this decoder effectively approximates thenth derivative of the input vector, it is very sensitive to noise. In our framework, the input is often very noisy, since it corresponds to the converging points of different learning traces. In this section we describe two linear decoders that differ from that in [35] and are more noise-resilient. A.9 and A.10 is crucial for long temporal horizons, since regularization causes the overall magnitude of the recoveredτ-space to decrease asτ increases3. Normalization amends thedecreasing magnitude problem bymaking theτ-space to sum to 1 for everyτ.

In neural network literature, angular similarity between feature vectors is frequently used for interpreting or re-using learned representations. However, the inner product in neural networks partially disperses information over the scales and angles of the involved input vectors and weight vectors. Therefore, when using only angular similarity on representations trained with the inner product, information loss occurs in downstream methods, which limits their performance. In this paper, we proposed the $\textit{spherization layer}$ to represent all information on angular similarity. The layer 1) maps the pre-activations of input vectors into the specific range of angles, 2) converts the angular coordinates of the vectors to Cartesian coordinates with an additional dimension, and 3) trains decision boundaries from hyperplanes, without bias parameters, passing through the origin. This approach guarantees that representation learning always occurs on the hyperspherical surface without the loss of any information unlike other projection-based methods. Furthermore, this method can be applied to any network by replacing an existing layer. We validate the functional correctness of the proposed method in a toy task, retention ability in well-known image classification tasks, and effectiveness in word analogy test and few-shot learning.

Past efforts to map the Medline database have been limited to small subsets of the available data because of the exponentially increasing memory and processing demands of existing algorithms. We designed a novel algorithm for sparse matrix multiplication that allowed us to apply a self-organizing map to the entire Medline dataset, allowing for a more complete map of existing medical knowledge. The algorithm also increases the feasibility of refining the self-organizing map to account for changes in the dataset over time.

Raul Rojas Department of Mathemanullcs and Stanullsnullcs University of Nevada Reno October 2025 Abstract This paper shows how a mulnulllayer perceptron with two hidden layers, which has been designed to classify two classes of data points, can easily be transformed into a deep neural network with one - gate layers and skip connecnullons. As shown in [1], deep one - gate per layer networks can perfectly separate points belonging to two classes in an n - dimensional space. Here, I present an alternanullve proof that may be easier to understand. This proof shows that classical neural networks that separate two classes can be transformed into deep one - gate - per - layer networks with skip connecnullons. A perceptron receives a vector input and divides input space into two subspaces: the posinullve and neganullve half - spaces (Figure 1a).

Hierarchical feed-forward networks have been successfully applied in object recognition. At each level of the hierarchy, features are extracted and encoded, followed by a pooling step. Within this processing pipeline, the common trend is to learn the feature coding templates, often referred as codebook entries, filters, or over-complete basis. Recently, an approach that apparently does not use templates has been shown to obtain very promising results. This is the second-order pooling (O2P) [1, 2, 3, 4, 5]. In this paper, we analyze O2P as a coding-pooling scheme. We find that at testing phase, O2P automatically adapts the feature coding templates to the input features, rather than using templates learned during the training phase. From this finding, we are able to bring common concepts of coding-pooling schemes to O2P, such as feature quantization. This allows for significant accuracy improvements of O2P in standard benchmarks of image classification, namely Caltech101 and VOC07.

We consider the problem of estimating the mean of a set of vectors, which are stored in a distributed system.

Personal use of this material is permitted. Abstract --This work introduces an automated testing approach that employs agents controlling game characters to detect potential bugs within a game level. Harnessing the power of Bayesian Optimization (BO) to execute sample-efficient search, the method determines the next sampling point by analyzing the data collected so far and calculates the data point that will maximize information acquisition. T o support the BO process, we introduce a game testing-specific model built on top of a grid map, that features the smoothness and uncertainty estimation required by BO, however and most importantly, it does not suffer the scalability issues that traditional models carry. The experiments demonstrate that the approach significantly improves map coverage capabilities in both time efficiency and exploration distribution. There is a spectrum of issues that can be encountered in a game, ranging from the low-level of abstraction, e.g., the related to collisions detection, game mechanics, performance, crash states, all the way to the high-level end problems like game balance, or player experience [1], [2].

For the low-rank RNNs (section 3.1), we trained the