Peru tennis predictions tomorrow

Maria Silva vs. Laura Gomez

Maria Silva vem de uma série impressionante de vitórias em torneios locais, demonstrando uma técnica impecável e um jogo mental forte. Laura Gomez, por outro lado, é conhecida por sua habilidade em partidas decisivas e seu serviço poderoso.

• Forças de Maria Silva: Consistência no jogo de fundo de quadra e excelentes devoluções.
• Fraquezas de Laura Gomez: Pode ser inconsistente em jogos longos.

Juan Perez vs. Carlos Rodriguez

Juan Perez é um veterano com vasta experiência internacional, enquanto Carlos Rodriguez é um jovem talento com um estilo de jogo agressivo.

• Forças de Juan Perez: Estratégia inteligente e resistência física.
• Fraquezas de Carlos Rodriguez: Pode ter dificuldades em manter o foco durante os momentos críticos do jogo.

Sofia Alvarez vs. Ana Martinez

Sofia Alvarez é conhecida por seu jogo rápido e precisão nos fundamentos, enquanto Ana Martinez possui um backhand excepcional e uma defesa sólida.

• Forças de Sofia Alvarez: Velocidade e capacidade de adaptar-se rapidamente às mudanças do jogo.
• Fraquezas de Ana Martinez: Menor consistência em jogos contra tenistas agressivos.

Maria Silva vs. Laura Gomez

• Maria Silva tem uma taxa de acerto no primeiro saque de 70%, comparado aos 65% de Laura Gomez.
• Laura Gomez tem uma taxa superior na devolução do segundo saque, com 50% contra os 45% de Maria Silva.

Juan Perez vs. Carlos Rodriguez

• Juan Perez tem uma média de pontos ganhos por jogo na rede de 60%, enquanto Carlos tem 55%.
• O índice de erros não forçados é menor para Juan Perez (15%) comparado a Carlos Rodriguez (20%).

Sofia Alvarez vs. Ana Martinez

• Sofia Alvarez tem uma média superior em pontos ganhos em trocas rápidas (70%) contra os 65% de Ana Martinez.
• Ana Martinez possui uma defesa mais sólida com uma taxa de recuperação eficaz em bolas difíceis (80%).

Maria Silva vs. Laura Gomez

A especialista Carla Mendes sugere que Maria Silva tem mais chances de vencer o jogo. Ela destaca a consistência recente da Silva e sua habilidade em manter a calma sob pressão como fatores decisivos.

• Aposte na vitória direta da Maria Silva com odds favoráveis (1.85).
• Duas ou mais sets: Dada a habilidade defensiva da Gomez, apostar nessa opção pode ser vantajoso (2.10).

Juan Perez vs. Carlos Rodriguez

O analista Ricardo Santos aponta para a experiência internacional do Juan Perez como um diferencial crucial neste confronto. Ele recomenda que apostadores considerem a possibilidade da vitória dele em três sets ou mais, dada a resistência física demonstrada por Perez nas partidas passadas.

• Aposta na vitória em três sets ou mais (2.25).
None: [23]: super().__init__(vocab) [24]: self._embedding_dim = embedding_dim [25]: self._similarity_function = similarity_function [26]: # We will create our own embeddings for the first and second words in the pair. [27]: self._embedding_1 = nn.Embedding(vocab.get_vocab_size(), embedding_dim) [28]: self._embedding_2 = nn.Embedding(vocab.get_vocab_size(), embedding_dim) [29]: # We will learn a matrix to project the similarity scores into the desired embedding dimension. [30]: self._projection_layer = nn.Linear(1, embedding_dim) [31]: def forward( [32]: self, [33]: tokens_1: torch.LongTensor, [34]: tokens_2: torch.LongTensor, [35]: token_type_ids: Optional[ [36]: torch.LongTensor [37]: ] = None, # pylint: disable=unused-argument [38]: ) -> torch.FloatTensor: [39]: """ [40]: # Parameters [41]: tokens_1 : `torch.LongTensor`, required. [42]: A tensor of shape `(batch_size, num_tokens)` representing the words in the [43]: first of two paired sequences of tokens in a batch. [44]: Each token should be an index into the vocabulary. [45]: tokens_2 : `torch.LongTensor`, required. [46]: A tensor of shape `(batch_size, num_tokens)` representing the words in the [47]: second of two paired sequences of tokens in a batch. [48]: Each token should be an index into the vocabulary. [49]: token_type_ids : `torch.LongTensor`, optional (default = `None`). [50]: A tensor of shape `(batch_size, num_tokens)` representing the type of each token within the model. [51]: This will be used to add differentially weighted embeddings for each token type. [52]: If `token_type_ids` is not passed then this will default to zeros. [53]: This is not used by this class but we include it so that we can use this class as a drop-in replacement for other classes. [54]: # Returns [55]: `torch.FloatTensor` [56]: An embedded representation of shape `(batch_size, num_tokens, embedding_dim)` [57]: representing the embedded representation of the input tokens. [58]: Each embedded vector is the dot product of two word embeddings followed by a learned linear projection. **Shape**: `(batch_size * num_tokens,)` **Type**: `torch.LongTensor` **Shape**: `(batch_size * num_tokens,)` If not passed this defaults to a tensor of zeros with shape `(batch_size * num_tokens,)`. **Shape**: `(batch_size * num_tokens, embedding_dim)` The output will have shape `(batch_size * num_tokens, embedding_dim)`. ***** Tag Data ***** ID: 2 description: Forward method for computing embeddings using dot products and linear projections. start line: 31 end line: 38 dependencies: - type: Class name: DotProductEmbedder start line: 13 end line: 16 context description: The forward method implements the core functionality of the DotProductEmbedder, calculating embeddings by performing dot products on word embeddings and projecting them using a learned linear layer. algorithmic depth: 4 algorithmic depth external: N obscurity: 3 advanced coding concepts: 3 interesting for students: 5 self contained: N ************ ## Challenging Aspects ### Challenging aspects in above code: 1. **Handling Variable Input Sizes:** The function must handle variable batch sizes and sequence lengths (`num_tokens`). This requires careful handling to ensure that operations are correctly applied across different dimensions without errors. 2. **Efficient Tensor Operations:** Performing dot products and subsequent projections efficiently on potentially large tensors is non-trivial. Ensuring optimal performance while maintaining correctness is crucial. 3. **Optional Parameters Handling:** The `token_type_ids` parameter is optional and may or may not be provided. The function needs to handle cases where this parameter is `None` gracefully without introducing bugs or inefficiencies. 4. **Dimensionality Management:** Ensuring that tensor dimensions align correctly throughout various operations is critical to avoid runtime errors or incorrect results. 5. **Memory Management:** Efficiently managing memory usage when dealing with large tensors is important to prevent out-of-memory errors and to maintain performance. ### Extension: 1. **Dynamic Vocabulary Handling:** Extend functionality to handle dynamically changing vocabularies where new words can be added during runtime and embeddings need to be updated accordingly. 2. **Contextual Embeddings:** Incorporate context-aware embeddings that adjust based on surrounding words within sequences rather than static embeddings. 3. **Multi-head Attention Mechanism:** Introduce multi-head attention mechanisms that allow parallel computation over multiple attention heads for better capturing dependencies in sequences. ## Exercise: ### Exercise Prompt: You are tasked with extending the functionality of the given [SNIPPET] to include additional features and optimizations while maintaining efficient and correct tensor operations. #### Requirements: 1. **Dynamic Vocabulary Handling:** Modify the `DotProductEmbedder` class to handle dynamic vocabulary updates where new words can be added during runtime without restarting or retraining from scratch. 2. **Contextual Embeddings:** Implement context-aware embeddings where each word's embedding considers its surrounding context within sequences. 3. **Multi-head Attention Mechanism:** Integrate multi-head attention mechanisms into your implementation to enhance capturing dependencies within sequences. ### Provided Code Snippet: python class DotProductEmbedder(TokenEmbedder): """ An embedder which computes an embedding by taking the dot product of two word embeddings. """ def forward( self, tokens_1: torch.LongTensor, tokens_2: torch.LongTensor, token_type_ids: Optional[ torch.LongTensor] = None, ) -> torch.FloatTensor: ## Solution: ### Step-by-step Solution: #### Step 1: Dynamic Vocabulary Handling Modify the initialization method and add methods to update vocabulary dynamically: python class DotProductEmbedder(TokenEmbedder): def __init__(self, vocab_size, embed_dim): super().__init__() self.vocab_size = vocab_size self.embed_dim = embed_dim # Initialize embeddings with initial vocab size self.embedding_matrix = nn.Embedding(self.vocab_size, self.embed_dim) def update_vocab(self, new_words): """Update vocabulary dynamically with new words.""" new_vocab_size = self.vocab_size + len(new_words) new_embedding_matrix = nn.Embedding(new_vocab_size, self.embed_dim) # Copy old weights into new embedding matrix and initialize new weights randomly new_embedding_matrix.weight.data[:self.vocab_size] = self.embedding_matrix.weight.data.clone() # Update internal state with new vocab size and embedding matrix self.vocab_size = new_vocab_size self.embedding_matrix = new_embedding_matrix #### Step 2: Contextual Embeddings Implement context-aware embeddings: python import torch.nn.functional as F class ContextualDotProductEmbedder(DotProductEmbedder): def __init__(self, vocab_size, embed_dim): super().__init__(vocab_size, embed_dim) def forward( self, tokens_1: torch.LongTensor, tokens_2: torch.LongTensor, token_type_ids: Optional[ torch.LongTensor] = None, ) -> torch.FloatTensor: # Get embeddings for both sets of tokens embeds_1 = self.embedding_matrix(tokens_1) embeds_2 = self.embedding_matrix(tokens_2) # Compute contextual representations using convolutional layers or other context-aware mechanisms contextual_embeds_1 = F.relu(self.contextual_layer(embeds_1)) contextual_embeds_2 = F.relu(self.contextual_layer(embeds_2)) # Compute dot products between contextual representations dot_products = (contextual_embeds_1 * contextual_embeds_2).sum(dim=-1) # Project results using learned linear layer return self.projection_layer(dot_products.unsqueeze(-1)).squeeze(-1) #### Step 3: Multi-head Attention Mechanism Integrate multi-head attention mechanism: python class MultiHeadDotProductEmbedder(ContextualDotProductEmbedder): def __init__(self, vocab_size, embed_dim, num_heads): super().__init__(vocab_size, embed_dim) assert embed_dim % num_heads == 0 self.num_heads = num_heads self.head_dim = embed_dim // num_heads # Define multi-head attention components self.query_layers = nn.ModuleList([nn.Linear(embed_dim, self.head_dim) for _ in range(num_heads)]) self.key_layers = nn.ModuleList([nn.Linear(embed_dim, self.head_dim) for _ in range(num_heads)]) self.value_layers = nn.ModuleList([nn.Linear(embed_dim, self.head_dim) for _ in range(num_heads)]) def forward( self, tokens_1: torch.LongTensor, tokens_2: torch.LongTensor, token_type_ids: Optional[ torch.LongTensor] = None, ) -> torch.FloatTensor: # Get base embeddings embeds_1 = super().forward(tokens_1=tokens_1) embeds_2 = super().forward(tokens_2=tokens_2)