基于机器学习的填字游戏求解：约束融入与替代方法问询

Absolutely—with a large enough dataset of solved crossword puzzles, you absolutely can build a machine learning model to tackle this problem. Let’s dive into your specific questions:

Integrating Constraints Like Word Length and Shared Letters #

The paper you referenced focuses on semantic matching between clues and words, but to solve crosswords effectively, we need to weave in structural constraints. Here are some practical approaches:

• Hard constraints in training and inference:

  • For word length: Add it as an explicit feature to your model. For example, when training the dictionary embedding model, concatenate the word length (encoded as a numerical or one-hot vector) with the clue/word embeddings. This lets the model learn to associate clues not just with semantic meaning, but also with expected word lengths. During inference, you can immediately filter out any candidates that don’t match the required length before even running the semantic matching.
  • For shared letters: Treat the crossword grid as a graph where each word slot is a node, and edges represent overlapping letters. You can model this as a constraint satisfaction problem (CSP). After generating initial semantic candidates for each slot, use a solver (like a backtracking algorithm with pruning) to find a combination where all overlapping letters match. To make this more efficient, rank candidates by semantic score first, so the solver prioritizes higher-quality options.

• Joint modeling of semantics and constraints:

  • Use a Conditional Random Field (CRF) where each word slot is a random variable. Define two types of features: observation features (semantic matching score between clue and candidate word) and transition features (penalties if overlapping letters between adjacent slots don’t match). The CRF will learn to select candidates that maximize both semantic fit and constraint compliance.
  • For modern large language models (LLMs), frame the crossword as a structured prompt. Include the grid state (e.g., "Across 1: [3 letters] Clue: 'Morning drink', intersects with Down 1 at position 2 which is 'O'") in the prompt, and the LLM will naturally learn to generate words that fit both the clue and the constraints—many LLMs already have implicit knowledge of word structure and cross-word rules from training data.

Beyond Nearest Neighbor for Candidate Filtering #

Nearest neighbor is a solid baseline, but there are more direct, integrated methods:

• End-to-end generative models:

  • Fine-tune a sequence model (like T5, GPT-4, or Llama) on solved crossword data. Format the input to include all clues, grid positions, and any filled letters, and train the model to directly generate the correct words for each slot. The model will learn to incorporate constraints (length, shared letters) as part of its generation logic, eliminating the need for a separate filtering step.

• Constraint-aware ranking models:

  • Instead of generating a pool of candidates first, train a ranking model that takes the clue, target slot’s constraints (length, overlapping letters), and a candidate word, then outputs a "fit score". This score combines semantic matching (like the dictionary embedding approach) and constraint compliance (e.g., a heavy penalty if the word length is wrong, or overlapping letters don’t match). You can then select the candidate with the highest score directly.

• Reinforcement Learning (RL):

  • Treat solving the crossword as a sequential decision problem. An RL agent selects words for each slot one by one, with a reward function that penalizes invalid constraints (wrong length, mismatched letters) and rewards correct semantic matches. Over time, the agent learns to prioritize candidates that fit both the clue and the evolving grid state.

A Note on Extending the Dictionary Embedding Paper #

To build on Learning to Understand Phrases by Embedding the Dictionary, you can:

• Modify the embedding space to include word length as a dimension, so semantically similar words of the correct length are closer together.
• Add a post-processing step that re-ranks the top semantic candidates by constraint compliance (length, overlapping letters) before selecting the final word.

内容的提问来源于stack exchange，提问作者user2149631