# Q4a · Lexical and vector semantics Subject: Natural Language Processing Exam: TEE Reader: https://deep-learning-study-room.vercel.app/nlp/#tee/papers/legacy-f23/q4a Canonical: https://deep-learning-study-room.vercel.app/read/nlp/tee/papers/legacy-f23--q4a/ Previous examination · complete worked answers **Question. Explain lexical semantics and vector semantics with suitable examples.** [10 marks] ### Answer **A lexical relation connects words or senses by a meaning relationship.** State the relation and its direction before giving the example. | Relation | Exam definition | Examples and direction | | --- | --- | --- | | Homonymy | The same form has unrelated meanings. | bank: financial institution / river edge; bat: animal / sports implement | | Polysemy | One lexical item has multiple related senses. | head: body part / head of a department; paper: material / article | | Synonymy | Different words have identical or closely similar meanings in a specified sense. | sofa / couch; automobile / car | | Antonymy | Words have opposite meanings. | hot / cold; alive / dead; buy / sell | | Hyponymy | A more specific concept is a type of a more general one. | rose is a flower; car is a vehicle | | Hypernymy | A broader concept includes a more specific one. | flower is a hypernym of rose | | Meronymy | A concept is a part of another concept. | wheel is part of car; finger is part of hand | | Holonymy | A concept is the whole containing a part. | car is a holonym of wheel | ### How to distinguish the commonly confused pairs For homonymy versus polysemy, ask whether the senses share an identifiable meaning. A river bank and a financial bank are unrelated. A financial bank and a blood bank share a repository/storage idea, illustrating polysemy in the supplied notes. For hyponymy versus meronymy, use the sentence test: **“X is a kind of Y”** indicates hyponymy; **“X is part of Y”** indicates meronymy. A wheel is not a type of car. | Expression | Correct relation | Reason | | --- | --- | --- | | sparrow → bird | Hyponymy | A sparrow is a kind of bird | | bird → sparrow | Hypernymy | Bird is the broader category | | keyboard → computer | Meronymy | Keyboard is a component | | computer → keyboard | Holonymy | Computer is the containing whole | | mouth of a person / mouth of a river | Polysemy | Both senses share the idea of an opening; the river use is a related extension | Synonyms are not always interchangeable in every context or register. “Big mistake” and “large mistake” can sound different even though big and large overlap in meaning. Antonyms can be gradable (hot/cold), complementary (alive/dead) or relational converses (buy/sell). HYPO = specific type; HYPER = bigger category. MERO = part; HOLO = whole. **The distributional hypothesis states that words occurring in similar contexts tend to have similar meanings or semantic behaviour.** “Cat” and “dog” often occur near pet, feed and animal. Their context patterns can therefore be represented and compared numerically. A **vector** is an ordered list of numbers. Each position must have a fixed meaning. For context order [pet, food, road], cat=[4,3,0] means four co-occurrences with pet, three with food, none with road. A **matrix** stacks vectors as rows in a table. A **word–context co-occurrence matrix** records how often a target word occurs with each context word under a specified context definition. A window may be a sentence, document, or a fixed number of neighbouring tokens. State its width, direction and whether targets count themselves. Choose target words → Choose context/window → Count co-occurrences → Store each row as a vector → Compare vectors **Question. Build the symmetric co-occurrence matrix for “cats eat fish” using a window of one token on either side, no self-counts and vocabulary [cats,eat,fish].** #### Given One sentence, one occurrence of each token. Left and right adjacent tokens are contexts. #### To find A 3×3 target-by-context count matrix. #### Formula and why it applies $$ X_{ij} $$ counts the number of times context word $$ j $$ occurs within the chosen window of target $$ i $$ . #### Step 1. Target cats Only eat is adjacent. Row cats = [0,1,0]. #### Step 2. Target eat cats is left and fish is right. Row eat = [1,0,1]. #### Step 3. Target fish Only eat is adjacent. Row fish = [0,1,0]. #### Step 4. Assemble the matrix | Target / context | cats | eat | fish | | --- | --- | --- | --- | | cats | 0 | 1 | 0 | | eat | 1 | 0 | 1 | | fish | 0 | 1 | 0 | **Answer.** Rows are [0,1,0], [1,0,1], [0,1,0]. The symmetry follows from the symmetric window. **Question. Build a target–context matrix for sentences “cats eat fish” and “dogs eat fish”. Target words are cats and dogs; context columns [eat,fish]; use the entire sentence excluding the target.** #### Given Each sentence contains one target. Count context token occurrences. #### To find Two context vectors. #### Formula and why it applies Count each context word in every sentence containing the target. #### Step 1. Count cats contexts In its sentence: eat occurs once, fish once → [1,1]. #### Step 2. Count dogs contexts In its sentence: eat occurs once, fish once → [1,1]. #### Step 3. Compare Both targets have identical observed context patterns in this very small corpus. **Answer.** cats=[1,1], dogs=[1,1]. This corpus supplies no context evidence to distinguish them. **Question. For “a b a”, use a right-only window of one token. Build the matrix with rows/columns [a,b].** #### Given Count directed target→next-word events, not both directions. #### To find The co-occurrence matrix. #### Formula and why it applies $$ X_{ij}=C(\text{target }i\text{ immediately followed by }j) $$ . #### Step 1. First target a Next token is b → add 1 to X(a,b). #### Step 2. Target b Next token is a → add 1 to X(b,a). #### Step 3. Final a No following token → no addition. #### Step 4. Write matrix | Target / next | a | b | | --- | --- | --- | | a | 0 | 1 | | b | 1 | 0 | **Answer.** a=[0,1], b=[1,0]. A different context window would produce a different matrix. Word ka meaning: uske aas-paas kaunse words kitni baar aaye, uski number-list.