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Description

Editorial

Hyperdimensional Row Encoding Using Bind-Bundle Operations

MEDIUM20 pts

Hyperdimensional Computing (HDC) is an emerging computational paradigm inspired by how the human brain processes information. At its core, HDC represents data as high-dimensional vectors (typically thousands of dimensions) called hypervectors. These hypervectors have remarkable mathematical properties that enable efficient and robust symbolic reasoning.

In this problem, you will implement a fundamental HDC operation: encoding a structured data record (row) into a single composite hypervector. This encoding preserves the semantic relationships between feature names and their values while creating a holistic representation suitable for machine learning tasks.

Core HDC Operations

1. Hypervector Generation

Each element (feature name or value) is mapped to a unique bipolar hypervector (containing only -1 or +1 values). These base hypervectors are generated deterministically using random seeds.

2. Binding (⊗) - Associative Pairing

Binding creates a unique representation for a key-value pair. It uses element-wise multiplication:

$$\text{bound}{i} = \text{name_hv}{i} \times \text{value_hv}_{i}$$

The bound hypervector is quasi-orthogonal to both the name and value hypervectors, effectively creating a distinct "slot" for each feature-value association.

3. Bundling (⊕) - Aggregation

Bundling combines multiple hypervectors into a single composite representation using element-wise summation followed by bipolar normalization:

$$\text{composite}{i} = \text{sign}\left(\sum{k=1}^{K} \text{bound}^{(k)}_{i}\right)$$

Where the sign function maps non-negative values to +1 and negative values to -1.

Your Task

Implement the function encode_row_hypervector(row, dim, random_seeds) that:

For each feature in the row:
- Generate a hypervector for the feature name using the seed from random_seeds[feature_name]
- Generate a hypervector for the feature value using a deterministic combination of the seed and value (use hash(value) + seed as the combined seed)
- Bind these two hypervectors using element-wise multiplication
Bundle all bound hypervectors:
- Compute the element-wise sum across all bound hypervectors
- Normalize to bipolar values: values ≥ 0 become +1, values < 0 become -1
Return the final composite hypervector as a numpy array of shape (dim,)

Hypervector Generation Algorithm

To generate a deterministic bipolar hypervector of dimension dim with a given seed:

1. Set numpy random seed to the given seed value
2. Generate dim random values from uniform distribution [0, 1)
3. Map each value to bipolar: value < 0.5 → -1, value ≥ 0.5 → +1

Important Notes

Process features in the order they appear in the row dictionary
Use consistent seeding for reproducibility
The binding operation is commutative and associative
Zero values in the sum during bundling should map to +1 (non-negative rule)

Example

Input

row = {'FeatureA': 'value1', 'FeatureB': 'value2'}
dim = 5
random_seeds = {'FeatureA': 42, 'FeatureB': 7}

Output

[1, -1, 1, -1, 1]

Explanation

Step-by-step encoding process:

1. Process 'FeatureA':

Generate name_hv using seed 42: [-1, 1, 1, -1, 1] (example)
Generate value_hv using seed (hash('value1') + 42): [1, 1, -1, 1, 1] (example)
Bind: name_hv ⊗ value_hv = [-1×1, 1×1, 1×-1, -1×1, 1×1] = [-1, 1, -1, -1, 1]

2. Process 'FeatureB':

Generate name_hv using seed 7
Generate value_hv using seed (hash('value2') + 7)
Bind the two hypervectors

3. Bundle all bound hypervectors:

Sum element-wise across all bound hypervectors
Apply bipolar normalization (≥0 → 1, <0 → -1)

Result: [1, -1, 1, -1, 1] — a compact 5-dimensional representation encoding both features and their values.

Example

Input

row = {'Color': 'Red'}
dim = 8
random_seeds = {'Color': 100}

Output

[1, -1, -1, -1, -1, -1, 1, 1]

Explanation

Single feature encoding:

With only one feature, the encoding process is straightforward:

1. Generate hypervector for "Color" (seed 100) 2. Generate hypervector for "Red" (seed = hash("Red") + 100) 3. Bind the name and value hypervectors via element-wise multiplication 4. No bundling required since there's only one bound hypervector 5. Normalize to bipolar values

The result directly captures the association between the feature "Color" and its value "Red" in an 8-dimensional hypervector.

Example

Input

row = {'Height': '170', 'Weight': '65', 'Age': '25'}
dim = 10
random_seeds = {'Height': 1, 'Weight': 2, 'Age': 3}

Output

[-1, 1, -1, -1, 1, -1, 1, 1, 1, -1]

Explanation

Multi-feature encoding with bundling:

1. Process each feature-value pair:

('Height', '170'): Generate and bind hypervectors using seeds 1 and hash('170')+1
('Weight', '65'): Generate and bind hypervectors using seeds 2 and hash('65')+2
('Age', '25'): Generate and bind hypervectors using seeds 3 and hash('25')+3

2. Bundle the three bound hypervectors:

For each dimension i, sum the values from all three bound hypervectors
Example: if position 0 has values [-1, 1, -1] from the three bound HVs, sum = -1
Apply sign: sum = -1 → output = -1

3. Result: A 10-dimensional bipolar hypervector that holistically represents this data record with height 170, weight 65, and age 25.

Key insight: The bundled representation preserves approximate similarity — records with similar feature values will produce similar hypervectors, enabling efficient nearest-neighbor searches and classification.

Accepted0/0·0% Acceptance

Constraints

1 ≤ len(row) ≤ 100 (number of features)
1 ≤ dim ≤ 10,000 (hypervector dimensionality)
All feature names in row will have corresponding entries in random_seeds
Feature values can be strings, integers, or floats
Seeds in random_seeds are non-negative integers < 2³¹
Feature names are non-empty strings
The function should be deterministic given the same inputs

Code

Visualizer

Solutions

14px

Test Cases3

Results

Submissions

dim =

row =

{"FeatureA":"value1","FeatureB":"value2"}

random_seeds =

{"FeatureA":42,"FeatureB":7}

Core HDC Operations

1. Hypervector Generation

Each element (feature name or value) is mapped to a unique bipolar hypervector (containing only -1 or +1 values). These base hypervectors are generated deterministically using random seeds.

2. Binding (⊗) - Associative Pairing

Binding creates a unique representation for a key-value pair. It uses element-wise multiplication:

$$\text{bound}{i} = \text{name_hv}{i} \times \text{value_hv}_{i}$$

The bound hypervector is quasi-orthogonal to both the name and value hypervectors, effectively creating a distinct "slot" for each feature-value association.

3. Bundling (⊕) - Aggregation

Bundling combines multiple hypervectors into a single composite representation using element-wise summation followed by bipolar normalization:

$$\text{composite}{i} = \text{sign}\left(\sum{k=1}^{K} \text{bound}^{(k)}_{i}\right)$$

Where the sign function maps non-negative values to +1 and negative values to -1.

Your Task

Implement the function encode_row_hypervector(row, dim, random_seeds) that:

For each feature in the row:

Generate a hypervector for the feature name using the seed from random_seeds[feature_name]
Generate a hypervector for the feature value using a deterministic combination of the seed and value (use hash(value) + seed as the combined seed)
Bind these two hypervectors using element-wise multiplication

Bundle all bound hypervectors:

Compute the element-wise sum across all bound hypervectors
Normalize to bipolar values: values ≥ 0 become +1, values < 0 become -1

Return the final composite hypervector as a numpy array of shape (dim,)

Hyperdimensional Row Encoding Using Bind-Bundle Operations

Core HDC Operations

1. Hypervector Generation

2. Binding (⊗) - Associative Pairing

3. Bundling (⊕) - Aggregation

Your Task

Hypervector Generation Algorithm

Important Notes

Hints

Hyperdimensional Row Encoding Using Bind-Bundle Operations

Core HDC Operations

1. Hypervector Generation

2. Binding (⊗) - Associative Pairing

3. Bundling (⊕) - Aggregation

Your Task

Hypervector Generation Algorithm

Important Notes

Hints