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feature_matrix.shape # Initialize selection state selected_mask = np.zeros(num_items, dtype=bool) @@ -123,31 +123,52 @@ def _prepare_vectors(matrix: np.ndarray) -> np.ndarray: # Current residuals under the sliding window residual_matrix = feature_matrix.astype(np.float32, copy=True) - # Sliding window storage - basis_vectors: list[np.ndarray] = [] - projection_coefficients_per_basis: list[np.ndarray] = [] + # Incrementally maintained squared norms: residual_sq_norms[i] = ||residual_matrix[i]||^2 + residual_sq_norms: np.ndarray = np.einsum("ij,ij->i", residual_matrix, residual_matrix) + + # Pre-allocated circular buffer + basis_matrix = np.zeros((window_size, n_dims), dtype=np.float32) + coeff_matrix = np.zeros((window_size, num_items), dtype=np.float32) + window_count = 0 + window_head = 0 + + # Pre-allocated buffer for rank-1 updates + _outer_buf = np.empty((num_items, n_dims), dtype=np.float32) def _push_basis_vector(basis_vector: np.ndarray) -> None: """Add a new basis vector to the sliding window and update residuals/projections.""" - if len(basis_vectors) == window_size: - # Remove oldest basis and restore its contribution to residuals - oldest_basis = basis_vectors.pop(0) - oldest_coefficients = projection_coefficients_per_basis.pop(0) - mask_unselected = ~selected_mask - if np.any(mask_unselected): - residual_matrix[mask_unselected] += oldest_coefficients[mask_unselected, None] * oldest_basis - - denominator = float(basis_vector @ basis_vector) + EPS32 - basis_vectors.append(basis_vector.astype(np.float32, copy=False)) - - mask_unselected = ~selected_mask - coefficients = np.zeros(num_items, dtype=np.float32) - if np.any(mask_unselected): - projections = (residual_matrix[mask_unselected] @ basis_vector) / denominator - coefficients[mask_unselected] = projections - residual_matrix[mask_unselected] -= projections[:, None] * basis_vector - - projection_coefficients_per_basis.append(coefficients) + nonlocal window_count, window_head + + if window_count == window_size: + # Evict oldest: restore its contribution to residuals (full-array op). + # Zero out selected items so their residuals stay untouched. + oldest_slot = window_head + coeff_matrix[oldest_slot][selected_mask] = 0.0 + old_coeffs = coeff_matrix[oldest_slot] + old_basis = basis_matrix[oldest_slot] + old_basis_sq = float(old_basis @ old_basis) + # r_new = r + c * b → ||r_new||^2 = ||r||^2 + 2c(r·b) + c^2||b||^2 + dots_evict = residual_matrix @ old_basis + residual_sq_norms[:] += old_coeffs * (2.0 * dots_evict + old_coeffs * old_basis_sq) + np.outer(old_coeffs, old_basis, out=_outer_buf) + np.add(residual_matrix, _outer_buf, out=residual_matrix) + else: + window_count += 1 + + basis_sq = float(basis_vector @ basis_vector) + denominator = basis_sq + EPS32 + basis_matrix[window_head] = basis_vector + dots = residual_matrix @ basis_vector + coefficients = dots / denominator + coefficients[selected_mask] = 0.0 + coeff_matrix[window_head] = coefficients + # r_new = r - c * b → ||r_new||^2 = ||r||^2 - 2c(r·b) + c^2||b||^2 + # = ||r||^2 - c(2·dot - c·basis_sq) + residual_sq_norms[:] -= coefficients * (2.0 * dots - coefficients * basis_sq) + np.maximum(residual_sq_norms, 0.0, out=residual_sq_norms) + np.outer(coefficients, basis_vector, out=_outer_buf) + np.subtract(residual_matrix, _outer_buf, out=residual_matrix) + window_head = (window_head + 1) % window_size # Seed with recent context (oldest → newest) if provided seeded_bases = 0 @@ -156,7 +177,9 @@ def _push_basis_vector(basis_vector: np.ndarray) -> None: context = context[-window_size:] # keep only the latest `window_size` items for context_vector in context: residual_context = context_vector.copy() - for basis in basis_vectors: + for slot_offset in range(window_count): + slot_idx = (window_head - window_count + slot_offset) % window_size + basis = basis_matrix[slot_idx] denominator_b = float(basis @ basis) + EPS32 residual_context -= float(residual_context @ basis) / denominator_b * basis _push_basis_vector(residual_context) @@ -165,7 +188,7 @@ def _push_basis_vector(basis_vector: np.ndarray) -> None: # Decide what to select first if seeded_bases > 0: # Use combined scores with diversity from seeded context - residual_norms = np.linalg.norm(residual_matrix, axis=1) + residual_norms = np.sqrt(residual_sq_norms) combined_scores = theta * relevance_scores + (1.0 - theta) * gamma * residual_norms combined_scores[selected_mask] = -np.inf first_index = int(np.argmax(combined_scores)) @@ -186,14 +209,12 @@ def _push_basis_vector(basis_vector: np.ndarray) -> None: # Main loop for step in range(1, top_k): - # Find best candidate among unselected items - available_indices = np.where(~selected_mask)[0] - # Residual norms measure novelty relative to the last `window` selections/context - residual_norms = np.linalg.norm(residual_matrix[available_indices], axis=1) - combined_scores = theta * relevance_scores[available_indices] + (1.0 - theta) * gamma * residual_norms - local_best = int(np.argmax(combined_scores)) - best_index = int(available_indices[local_best]) - best_score = float(combined_scores[local_best]) + # Compute scores using incrementally maintained squared norms + residual_norms = np.sqrt(residual_sq_norms) + combined_scores = theta * relevance_scores + (1.0 - theta) * gamma * residual_norms + combined_scores[selected_mask] = -np.inf + best_index = int(np.argmax(combined_scores)) + best_score = float(combined_scores[best_index]) # Update selection state selected_mask[best_index] = True From 742d073b260639beebcf125c816fe96dee810506 Mon Sep 17 00:00:00 2001 From: Pringled Date: Fri, 30 Jan 2026 09:53:26 +0100 Subject: [PATCH 2/6] Improved comments and variable names --- src/pyversity/strategies/ssd.py | 61 +++++++++++++++++++-------------- 1 file changed, 35 insertions(+), 26 deletions(-) diff --git a/src/pyversity/strategies/ssd.py b/src/pyversity/strategies/ssd.py index 42a4026..5e50fc6 100644 --- a/src/pyversity/strategies/ssd.py +++ b/src/pyversity/strategies/ssd.py @@ -123,51 +123,60 @@ def _prepare_vectors(matrix: np.ndarray) -> np.ndarray: # Current residuals under the sliding window residual_matrix = feature_matrix.astype(np.float32, copy=True) - # Incrementally maintained squared norms: residual_sq_norms[i] = ||residual_matrix[i]||^2 + # Squared residual norms, maintained incrementally to avoid recomputing from the full matrix residual_sq_norms: np.ndarray = np.einsum("ij,ij->i", residual_matrix, residual_matrix) - # Pre-allocated circular buffer + # Circular buffer for sliding window of basis vectors and their projection coefficients basis_matrix = np.zeros((window_size, n_dims), dtype=np.float32) coeff_matrix = np.zeros((window_size, num_items), dtype=np.float32) window_count = 0 window_head = 0 - # Pre-allocated buffer for rank-1 updates - _outer_buf = np.empty((num_items, n_dims), dtype=np.float32) + # Re-used buffer for rank-1 matrix updates (avoids allocating a new n×d array each step) + update_buffer = np.empty((num_items, n_dims), dtype=np.float32) def _push_basis_vector(basis_vector: np.ndarray) -> None: """Add a new basis vector to the sliding window and update residuals/projections.""" nonlocal window_count, window_head if window_count == window_size: - # Evict oldest: restore its contribution to residuals (full-array op). - # Zero out selected items so their residuals stay untouched. + # Evict the oldest basis and restore its contribution to residuals. + # Skip selected items so their residuals stay untouched. oldest_slot = window_head coeff_matrix[oldest_slot][selected_mask] = 0.0 - old_coeffs = coeff_matrix[oldest_slot] - old_basis = basis_matrix[oldest_slot] - old_basis_sq = float(old_basis @ old_basis) - # r_new = r + c * b → ||r_new||^2 = ||r||^2 + 2c(r·b) + c^2||b||^2 - dots_evict = residual_matrix @ old_basis - residual_sq_norms[:] += old_coeffs * (2.0 * dots_evict + old_coeffs * old_basis_sq) - np.outer(old_coeffs, old_basis, out=_outer_buf) - np.add(residual_matrix, _outer_buf, out=residual_matrix) + evicted_coefficients = coeff_matrix[oldest_slot] + evicted_basis = basis_matrix[oldest_slot] + evicted_basis_sq_norm = float(evicted_basis @ evicted_basis) + + # Update squared norms to reflect the restored residuals + projections = residual_matrix @ evicted_basis + residual_sq_norms[:] += evicted_coefficients * ( + 2.0 * projections + evicted_coefficients * evicted_basis_sq_norm + ) + + # Restore residuals by adding back the evicted projection + np.outer(evicted_coefficients, evicted_basis, out=update_buffer) + np.add(residual_matrix, update_buffer, out=residual_matrix) else: window_count += 1 - basis_sq = float(basis_vector @ basis_vector) - denominator = basis_sq + EPS32 + basis_sq_norm = float(basis_vector @ basis_vector) + denominator = basis_sq_norm + EPS32 basis_matrix[window_head] = basis_vector - dots = residual_matrix @ basis_vector - coefficients = dots / denominator + + # Project each item's residual onto the new basis vector + projections = residual_matrix @ basis_vector + coefficients = projections / denominator coefficients[selected_mask] = 0.0 coeff_matrix[window_head] = coefficients - # r_new = r - c * b → ||r_new||^2 = ||r||^2 - 2c(r·b) + c^2||b||^2 - # = ||r||^2 - c(2·dot - c·basis_sq) - residual_sq_norms[:] -= coefficients * (2.0 * dots - coefficients * basis_sq) + + # Update squared norms to reflect the removed projection + residual_sq_norms[:] -= coefficients * (2.0 * projections - coefficients * basis_sq_norm) np.maximum(residual_sq_norms, 0.0, out=residual_sq_norms) - np.outer(coefficients, basis_vector, out=_outer_buf) - np.subtract(residual_matrix, _outer_buf, out=residual_matrix) + + # Subtract projection from residuals + np.outer(coefficients, basis_vector, out=update_buffer) + np.subtract(residual_matrix, update_buffer, out=residual_matrix) window_head = (window_head + 1) % window_size # Seed with recent context (oldest → newest) if provided @@ -180,8 +189,8 @@ def _push_basis_vector(basis_vector: np.ndarray) -> None: for slot_offset in range(window_count): slot_idx = (window_head - window_count + slot_offset) % window_size basis = basis_matrix[slot_idx] - denominator_b = float(basis @ basis) + EPS32 - residual_context -= float(residual_context @ basis) / denominator_b * basis + denominator = float(basis @ basis) + EPS32 + residual_context -= float(residual_context @ basis) / denominator * basis _push_basis_vector(residual_context) seeded_bases += 1 @@ -209,7 +218,7 @@ def _push_basis_vector(basis_vector: np.ndarray) -> None: # Main loop for step in range(1, top_k): - # Compute scores using incrementally maintained squared norms + # Residual norms measure novelty relative to the sliding window of recent selections/context residual_norms = np.sqrt(residual_sq_norms) combined_scores = theta * relevance_scores + (1.0 - theta) * gamma * residual_norms combined_scores[selected_mask] = -np.inf From 8c1be37baf4e917075adc244e8b5b07afb26e505 Mon Sep 17 00:00:00 2001 From: Pringled Date: Fri, 30 Jan 2026 09:58:51 +0100 Subject: [PATCH 3/6] Updated readme --- README.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/README.md b/README.md index 273b129..63fca26 100644 --- a/README.md +++ b/README.md @@ -77,6 +77,8 @@ The papers linked in [references](#references) provide more details on each stra | **COVER** (Facility-Location) | Ensures selected items collectively represent the full dataset's structure. | **O(k · n²)** | Great for topic coverage or clustering scenarios, but slower for large `n`. | | **SSD** (Sliding Spectrum Decomposition) | Sequence‑aware diversification: rewards novelty relative to recently shown items. | **O(k · n · d)** | Great for content feeds & infinite scroll where users consume sequentially. Recommended `diversity`: 0.6–0.9 | +Where **k** = number of items to select, **n** = number of candidates, **d** = embedding dimensionality. + ## Benchmarks All strategies are evaluated across 4 recommendation datasets. Full methodology and detailed results can be found in [`benchmarks`](benchmarks/). From 3205c21b13aaf992aed002a53fc617281419d009 Mon Sep 17 00:00:00 2001 From: Pringled Date: Fri, 30 Jan 2026 10:09:41 +0100 Subject: [PATCH 4/6] Updated plot and table, relaxed dependencies --- benchmarks/README.md | 10 +- benchmarks/results/latency.png | Bin 85404 -> 87947 bytes pyproject.toml | 4 +- uv.lock | 199 ++++++--------------------------- 4 files changed, 39 insertions(+), 174 deletions(-) diff --git a/benchmarks/README.md b/benchmarks/README.md index 07dd171..c7b6777 100644 --- a/benchmarks/README.md +++ b/benchmarks/README.md @@ -92,14 +92,14 @@ All strategies are fast. Even with 10,000 candidates, all complete in <100ms. Th - **Typical use case** (100 candidates): all strategies complete in <1ms - **MMR/MSD/DPP** are same order of magnitude; DPP is modestly slower at scale -- **SSD** is slower due to Gram-Schmidt orthogonalization, which scales with embedding dimension +- **SSD** is moderately slower due to per-step residual matrix updates | Strategy | 100 candidates | 1,000 candidates | 10,000 candidates | |----------|----------------|------------------|-------------------| -| MMR | ~0.1ms | ~1ms | ~10ms | -| MSD | ~0.1ms | ~1ms | ~10ms | -| DPP | ~0.1ms | ~2ms | ~20ms | -| SSD | ~0.5ms | ~5ms | ~80ms | +| MMR | ~0.1ms | ~0.2ms | ~2ms | +| MSD | ~0.1ms | ~0.2ms | ~2ms | +| DPP | ~0.1ms | ~0.3ms | ~2ms | +| SSD | ~0.3ms | ~1ms | ~12ms | *Measured with k=10 items selected, d=256 dimensional embeddings. 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## Latency -All strategies are fast. Even with 10,000 candidates, all complete in <100ms. The plot below shows latency scaling measured on a **separate synthetic benchmark** (k=10, d=256 embeddings, typical for modern embedding models): +All strategies are fast. Even with 10,000 candidates, all complete in <15ms. The plot below shows latency scaling measured on a **separate synthetic benchmark** (k=10, d=256 embeddings): ![Latency vs Candidates](results/latency.png) - **Typical use case** (100 candidates): all strategies complete in <1ms -- **MMR/MSD/DPP** are same order of magnitude; DPP is modestly slower at scale +- **MMR/MSD/DPP** are same order of magnitude - **SSD** is moderately slower due to per-step residual matrix updates | Strategy | 100 candidates | 1,000 candidates | 10,000 candidates | @@ -101,8 +101,6 @@ All strategies are fast. Even with 10,000 candidates, all complete in <100ms. Th | DPP | ~0.1ms | ~0.3ms | ~2ms | | SSD | ~0.3ms | ~1ms | ~12ms | -*Measured with k=10 items selected, d=256 dimensional embeddings. Note: main benchmarks use d=64; latency benchmark uses d=256 to reflect modern embedding model dimensions.* - ## Detailed Results
From 90e0c8f6f90fd50e10858081a93adc9e9ce6e20e Mon Sep 17 00:00:00 2001 From: Pringled Date: Fri, 30 Jan 2026 10:12:16 +0100 Subject: [PATCH 6/6] Bumped version --- src/pyversity/version.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/pyversity/version.py b/src/pyversity/version.py index be4dce4..6036609 100644 --- a/src/pyversity/version.py +++ b/src/pyversity/version.py @@ -1,2 +1,2 @@ -__version_triple__ = (0, 1, 1) +__version_triple__ = (0, 2, 0) __version__ = ".".join(map(str, __version_triple__))