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DOLPHIN: A Programmable Framework for Scalable Neurosymbolic Learning
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Introduces DOLPHIN, a PyTorch-integrated neurosymbolic framework that runs symbolic logic on CPU while vectorizing probabilistic computation and gradients on GPU, with vectorized DAMP and DTKP-AM provenances.
Problem
Neurosymbolic learning does not scale to complex symbolic programs (recursion, black-box functions) or large datasets; existing frameworks either run symbolic computation on CPU without batching or ground everything on GPU and run out of memory.
Approach
Decouple symbols (arbitrary Python objects, processed on CPU) from tags (batched PyTorch tensors of probabilities, processed on GPU) via a Distribution abstraction with apply/filter/apply_if/union/get_probs primitives, plus vectorized provenance semirings (DAMP and an add-mult approximation of top-k proofs, DTKP-AM).
Key results
- Across 13 benchmarks, DOLPHIN matches baseline accuracy on simpler tasks while being 1.71x to 62x faster, and converges on complex benchmarks (larger HWF, Path, Mugen) where Scallop, ISED, and IndeCateR+ time out at 10 hours.
- On CLUTRR-3 and CLUTRR-4, DOLPHIN takes about 13 and 15 minutes, roughly 5x and 8.5x faster than Scallop, though its CLUTRR accuracy is slightly lower than Scallop's.
- Average speedup of 13.95x across baselines and benchmarks; DTKP-AM reaches up to 20% accuracy gain on HWF and 33% on Path over the second-best method on the largest versions.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DOLPHIN instead of Scallop | neurosymbolic training · SumN-5 through Mugen-5K | training time: 1.71x to 47.18x faster | Helped |
| Use DOLPHIN instead of LTN, ISED, or IndeCateR+ | SumN and HWF · SumN and HWF | training time: 1.72x to 62.41x faster | Helped |
| Use DOLPHIN rather than Scallop | complex benchmarks · HWF, PathFinder, and Mugen | convergence within 10 hours | Helped |
| Use DOLPHIN rather than Scallop | CLUTRR · CLUTRR | accuracy | Hurt |
| Use DAMP instead of DTKP-AM (ablation) | DOLPHIN · SumN | accuracy: 72% points on average | Helped |
| Use DTKP-AM instead of DAMP (ablation) | DOLPHIN · HWF | accuracy: 42.2% points on average | Helped |
| Use DAMP rather than DTKP-AM (ablation) | DOLPHIN · PathFinder, CLUTRR, and Mugen | accuracy | No clear effect |
| Increase DTKP-AM top-K (ablation) | DOLPHIN · Sum-15, Path-256, CLUTRR-4, and Mugen-5K | accuracy | No clear effect |
| Increase DTKP-AM top-K (ablation) | DOLPHIN · HWF-19 | accuracy: 8.94; 99.15; 96.89; 95.75 | Mixed |
| Increase DTKP-AM top-K (ablation) | DOLPHIN · Sum-15, HWF-19, Path-256, CLUTRR-4, and Mugen-5K | training time per epoch: 37.21; 47.70; 53.52; 58.54; 1.21e3; 1.40e3; 1.33e3; 1.46e3; 1.97e3; 2.34e3; 2.10e3; 2.12e3; 240.50; 257.89; 261.31; 257. | Mixed |
| Parallelize tag computations on GPU over batches instead of running all computations sequentially on CPU (ablation) | DOLPHIN HWF forward pass · HWF | total time (s): 497.26 -> 89.25 | Helped |
Surprising findings
- DAMP outperforms DTKP-AM by about 72 percentage points on SumN, since top-k proofs cannot capture all digit-sum combinations.
- DTKP-AM outperforms DAMP on HWF by about 42 percentage points on average.
Limitations
- Users must write programs in a batched manner, which may be restrictive for newcomers.
- Representations needed by generative models such as causal LLMs have not been investigated.
- No support for non-deterministic symbolic programs.
Experimental setup
Datasets: MNIST HWF PathFinder CLUTRR Mugen
Benchmarks: MNIST SumN HWF PathFinder CLUTRR Mugen
Metrics: accuracy training time to convergence scaling factor alpha
Baselines: Scallop ISED IndeCateR+ Logic Tensor Networks
Builds on: Scallop DTKP DAMP Logic Tensor Networks DeepProbLog
Closest papers by meaning
- Right for the Right Reasons: Avoiding Reasoning Shortcuts via Prototypical Neurosymbolic AI (NeurIPS 2025 · similarity 0.88)
- CTSketch: Compositional Tensor Sketching for Scalable Neurosymbolic Learning (NeurIPS 2025 · similarity 0.88)
- Position: The Road to Generalizable Neuro-Symbolic Learning Should be Paved with Foundation Models (NeurIPS 2026 · similarity 0.86)
- Verification Learning: Make Unsupervised Neuro-Symbolic System Feasible (ICML 2025 · similarity 0.86)
- Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Models (NeurIPS 2026 · similarity 0.86)
- Convex and Bilevel Optimization for Neural-Symbolic Inference and Learning (ICML 2024 · similarity 0.85)
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