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README.md

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+---
+language: en
+license: mit
+tags:
+- pointer-networks
+- efficient-transformers
+- long-range-modeling
+- linear-complexity
+- sequence-modeling
+- interpretability
+library_name: pytorch
+pipeline_tag: text-generation
+---
+
+# Pointer: Linear-Complexity Long-Range Modeling without Pre-training
+
+<div align="center">
+  <img src="paper_figure1_efficiency.png" alt="Efficiency Comparison" width="600"/>
+  <p><i>Pointer maintains linear scaling while Transformer shows quadratic growth</i></p>
+</div>
+
+## Model Description
+
+**Pointer** is a novel neural architecture that achieves **linear O(NK) complexity** for long-range sequence modeling through explicit layer-wise pointer chaining, eliminating the quadratic bottleneck of standard attention mechanisms.
+
+Unlike attention-based approaches that compute O(N²) pairwise interactions, Pointer creates structured long-distance connections via pointer chains where each layer's selection depends on previous layers' pointer positions.
+
+### Key Features
+
+- **Linear Complexity**: O(NK) operations where K ≪ N, providing **2-10× speedup** on sequences of length 2048+ compared to standard transformers
+- **No Pre-training Required**: Learns structured patterns from scratch, eliminating reliance on large-scale pre-training
+- **Interpretable Architecture**: Pointer heatmaps reveal hierarchical processing strategies with clear layer specialization
+- **Exact Computation**: Unlike approximation methods, Pointer computes exact structured connections
+
+## Architecture Innovation
+
+### Layer-wise Pointer Chaining
+
+Each position `i` selects exactly one target position `p_i^(ℓ)` per layer, with subsequent layers building upon these selections to form dependency paths:
+
+```
+p_i^(ℓ) = argmax_j Score(h_i^(ℓ), h_j^(ℓ), p_i^(ℓ-1))
+```
+
+This creates a dependency chain where each layer's pointer decisions influence subsequent layers, enabling the formation of structured long-range connections.
+
+### Complexity Analysis
+
+- **Computational**: O(NK) vs O(N²d) for standard attention
+- **Memory**: O(N) pointer indices vs O(N²) attention weights
+- **Scaling**: For N=8192, d=512: ~4M operations vs ~34B for attention (**~10,000× reduction**)
+
+<div align="center">
+  <img src="paper_figure2_longrange.png" alt="Long-range Performance" width="500"/>
+  <p><i>Consistent accuracy across increasing distances (512-2048 tokens)</i></p>
+</div>
+
+## Performance
+
+### Efficiency Benchmarks
+
+| Sequence Length | 256 | 512 | 1024 | 2048 |
+|----------------|-----|-----|------|------|
+| **Training Time (s)** |
+| Pointer | 0.35 | 0.29 | 0.55 | 1.45 |
+| Vanilla Transformer | 0.17 | 0.35 | 1.04 | 3.55 |
+| **Speedup** | 0.48× | 0.83× | 1.89× | **2.45×** |
+| **Throughput (tokens/s)** |
+| Pointer | 14,446 | 34,914 | 37,189 | 28,268 |
+| Vanilla Transformer | 30,320 | 29,427 | 19,703 | 11,549 |
+
+### Long-Range Dependency Modeling
+
+Copy task accuracy across variable-length gaps:
+
+| Distance | 512 | 1024 | 1536 | 2048 |
+|----------|-----|------|------|------|
+| Pointer | 4.38% | 5.50% | 5.38% | 5.25% |
+| Vanilla Transformer | 5.38% | 4.25% | 4.88% | 4.75% |
+
+Training loss decreased from 3.13 to 2.99 across distances, demonstrating effective learning.
+
+## Interpretability
+
+<div align="center">
+  <img src="paper_figure3_interpretability.png" alt="Interpretability Analysis" width="500"/>
+  <p><i>Pointer patterns reveal hierarchical processing across layers</i></p>
+</div>
+
+### Layer Specialization
+
+- **Early layers (0-2)**: Focus on local patterns (average hop distance ~47-58 tokens)
+- **Later layers (3-5)**: Establish long-range connections (up to 483 tokens)
+- **Emergent hierarchy**: Local → global processing arises through gradient-based learning
+
+<div align="center">
+  <img src="trained_pointer_heatmap_0.png" alt="Pointer Heatmap" width="400"/>
+  <p><i>Detailed pointer heatmap showing learned attention patterns</i></p>
+</div>
+
+### Structured Patterns
+
+- **Self-loops**: Information retention across layers
+- **Local clusters**: Capturing phrasal structure
+- **Long jumps**: Bridging distant contexts
+
+## Use Cases
+
+Pointer is particularly effective for:
+
+- **Long-context processing**: Sequences beyond attention's practical limits (4K-8K tokens)
+- **Edge deployment**: Reduced memory and compute requirements for on-device inference
+- **Low-resource domains**: No pre-training dependency makes it accessible without massive corpora
+- **Structured reasoning tasks**: Retrieval, copying, explicit dependency modeling
+- **Interpretable AI**: Clear visualization of learned dependency patterns
+
+## Model Configuration
+
+```python
+# Example configuration (3.2M parameters)
+config = {
+    "num_layers": 6,
+    "num_heads": 8,
+    "hidden_dim": 256,
+    "vocab_size": 10000,
+    "max_seq_length": 2048,
+    "pointer_temperature": 1.0,  # Gumbel-Softmax temperature
+}
+```
+
+## Training
+
+### Differentiable Pointer Selection
+
+During training, Gumbel-Softmax enables differentiable pointer selection:
+
+```python
+# Gumbel-Softmax for training
+s_tilde = (s + gumbel_noise) / temperature
+alpha = softmax(s_tilde)
+
+# Hard selection for inference
+p = argmax(s)
+```
+
+### Training Tips
+
+- Start with higher temperature (τ=1.0) and anneal during training
+- Use teacher forcing for sequence generation tasks
+- Monitor pointer hop distances to ensure long-range learning
+- Visualize pointer heatmaps to verify structured pattern emergence
+
+## Limitations
+
+- **Task specificity**: Excels on tasks with clear dependency paths; may underperform on dense semantic composition
+- **Evaluation scope**: Current results focus on controlled synthetic tasks (copy tasks)
+- **Generation quality**: Metrics measure teacher-forcing accuracy rather than autoregressive generation quality
+- **Single pointer per position**: Current implementation selects one target; multi-head variants could capture more complex patterns
+
+## Citation
+
+```bibtex
+@article{li2025pointer,
+  title={Pointer: Linear-Complexity Long-Range Modeling without Pre-training},
+  author={Li, Zixi},
+  journal={arXiv preprint},
+  year={2025},
+  institution={Noesis Lab, Sun Yat-sen University}
+}
+```
+
+## Related Work
+
+This work is part of broader research on adjacency-structured parallel propagation (ASPP):
+
+- **TreeGPT**: Bidirectional TreeFFN processing for visual reasoning
+- **Asterisk Operator**: Formal ASPP framework with universality theorems
+- **Pointer**: Dynamic graph construction through learned pointer chains
+
+## License
+
+MIT License
+
+## Contact
+
+- **Author**: Zixi Li
+- **Institution**: Noesis Lab (Independent Research Group), Sun Yat-sen University
+- **Email**: lizx93@mail2.sysu.edu.cn
+
+---
+
+<div align="center">
+  <p><b>Note</b>: Model weights are not currently available. This card documents the architecture and experimental results from the research paper.</p>
+</div>