This paper proposes a representational model for grid cells. In this model, the 2D self-position of the agent is represented by a high-dimensional vector, and the 2D self-motion or displacement of the agent is represented by a matrix that transforms the vector. Each component of the vector is a unit or a cell. The model consists of the following three sub-models. (1) Vector-matrix multiplication. The movement from the current position to the next position is modeled by matrix-vector multiplication, i.e., the vector of the next position is obtained by multiplying the matrix of the motion to the vector of the current position. (2) Magnified local isometry. The angle between two nearby vectors equals the Euclidean distance between the two corresponding positions multiplied by a magnifying factor. (3) Global adjacency kernel. The inner product between two vectors measures the adjacency between the two corresponding positions, which is defined by a kernel function of the Euclidean distance between the two positions. Our representational model has explicit algebra and geometry. It can learn hexagon patterns of grid cells, and it is capable of error correction, path integral and path planning.
Similar to word2vec @cite_18 , the vector representation in our method may be called a place2vec. In word2vec, the inner product of two vectors measures the similarity of the words. In place2vec, the inner product of two vectors measures the adjacency of two positions.
@cite_18
2509219942 1241017059 2525183655 2336585117
Vector-based word representations can help to improve a document classifier.The information of word2vec vectors and bags of words are very complementary.The combination of word2vec and BOW word representations obtains the best results.Word2vec is much more stable than bag of words models in cross-domain experiments. In this paper we show how a vector-based word representation obtained via word2vec can help to improve the results of a document classifier based on bags of words. Both models allow obtaining numeric representations from texts, but they do it very differently. The bag of words model can represent documents by means of widely dispersed vectors in which the indices are words or groups of words. word2vec generates word level representations building vectors that are much more compact, where indices implicitly contain information about the context of word occurrences. Bags of words are very effective for document classification and in our experiments no representation using only word2vec vectors is able to improve their results. However, this does not mean that the information provided by word2vec is not useful for the classification task. When this information is used in combination with the bags of words, the results are improved, showing its complementarity and its contribution to the task. We have also performed cross-domain experiments in which word2vec has shown much more stable behavior than bag of words models. We present a novel word level vector representation based on symmetric patterns (SPs). For this aim we automatically acquire SPs (e.g., “X and Y”) from a large corpus of plain text, and generate vectors where each coordinate represents the cooccurrence in SPs of the represented word with another word of the vocabulary. Our representation has three advantages over existing alternatives: First, being based on symmetric word relationships, it is highly suitable for word similarity prediction. Particularly, on the SimLex999 word similarity dataset, our model achieves a Spearman’s score of 0.517, compared to 0.462 of the state-of-the-art word2vec model. Interestingly, our model performs exceptionally well on verbs, outperforming stateof-the-art baselines by 20.2‐41.5 . Second, pattern features can be adapted to the needs of a target NLP application. For example, we show that we can easily control whether the embeddings derived from SPs deem antonym pairs (e.g. (big,small)) as similar or dissimilar, an important distinction for tasks such as word classification and sentiment analysis. Finally, we show that a simple combination of the word similarity scores generated by our method and by word2vec results in a superior predictive power over that of each individual model, scoring as high as 0.563 in Spearman’s on SimLex999. This emphasizes the differences between the signals captured by each of the models. We propose a framework of word-vector adaptation, which makes vectors of visually similar concepts close to each other. Here, word vectors are real-valued vector representation of words, e.g., word2vec representation. Our basic idea is to assume that each concept has some hypernyms that are important to determine its visual features. For example, for a concept Swallow with hypernyms Bird, Animal and Entity, we believe Bird is the most important since birds have common visual features with their feathers etc. Adapted word vectors are obtained for each word by taking a weighted sum of a given original word vector and its hypernym word vectors. Our weight optimization makes vectors of visually similar concepts close to each other, by giving a large weight for such important hypernyms. We apply the adapted word vectors to zero-shot learning on the TRECVID 2014 semantic indexing dataset. We achieved 0.083 of Mean Average Precision, which is the best performance without using TRECVID training data to the best of our knowledge. The vector representations of fixed dimensionality for words (in text) offered by Word2Vec have been shown to be very useful in many application scenarios, in particular due to the semantic information they carry. This paper proposes a parallel version, the Audio Word2Vec. It offers the vector representations of fixed dimensionality for variable-length audio segments. These vector representations are shown to describe the sequential phonetic structures of the audio segments to a good degree, with very attractive real world applications such as query-by-example Spoken Term Detection (STD). In this STD application, the proposed approach significantly outperformed the conventional Dynamic Time Warping (DTW) based approaches at significantly lower computation requirements. We propose unsupervised learning of Audio Word2Vec from audio data without human annotation using Sequence-to-sequence Audoencoder (SA). SA consists of two RNNs equipped with Long Short-Term Memory (LSTM) units: the first RNN (encoder) maps the input audio sequence into a vector representation of fixed dimensionality, and the second RNN (decoder) maps the representation back to the input audio sequence. The two RNNs are jointly trained by minimizing the reconstruction error. Denoising Sequence-to-sequence Autoencoder (DSA) is furthered proposed offering more robust learning.