Single-Pass Bi-Directional Passing

• Single-pass bi-directional information passing is a method where a system propagates data in both directions in one computational sweep.
• It underpins various applications such as neural networks for vision and language, database query execution, and Bayesian optimization.
• Empirical studies show improvements in efficiency and accuracy, reducing redundant computations while enhancing model performance.

Single-pass bi-directional information passing refers to computational processes or architectures that enable information to flow in both directions (e.g., forward and backward, past and future, upstream and downstream) within a system or model in a single computational pass, as opposed to the classical sequential or multi-pass approaches that restrict the flow or require multiple traversals. This capability has emerged as a critical design principle across diverse domains including neural network architectures for vision, language, database systems, Bayesian optimization, and more. The following sections synthesize the key principles, formal methodologies, technical innovations, empirical outcomes, and applications of this paradigm, as reflected in recent peer-reviewed literature.

1. Principles and Taxonomy of Bi-Directional Information Passing

Bi-directional information passing enables mutual communication along both directions of a computational graph, topology, or sequence in a single pass. This contrasts with unidirectional paradigms that pass messages or gradients only from left-to-right, bottom-up, or upstream, often requiring additional passes to obtain full context (e.g., forward and backward in Yannakakis’ algorithm for joins or classical RNN-based inference).

Major instantiations of the principle include:

• Graph Neural Networks (GNNs): Edge and node states can exchange information in both directions within each message passing step (e.g., DimeNet, MEGA-GNN).
• Neural Sequence Models: Decoders or encoders simultaneously access past and potential future information (e.g., SB-NMT (1905.04847), BiCTC (2110.03326)).
• Database Query Execution: Information about join keys or predicates is propagated both up and down the query plan in a single pass (e.g., Parachute (2506.13670)).
• Bayesian Optimization: Parent and child models in hierarchical frameworks exchange information in both directions per round (e.g., BIF-HGP (2505.11294)).
• Vision Models: Locally bi-directional state-space models aggregate context from both spatial directions within a single scan (e.g., LBMamba (2506.15976)).

A distinguishing feature is that the bidirectional flow is achieved in a single computational sweep or via fused operations, without the redundancy of separate forward and backward stages.

2. Formal and Algorithmic Frameworks

Designing single-pass bi-directional architectures requires reconciling computational efficiency, correctness, and expressivity. Approaches vary by application:

• Message Passing in Graphs:

DimeNet (2003.03123) updates edge-embedded messages using both incoming and outgoing directions and encodes angular relationships, ensuring that global context can be assembled via local bi-directional updates in a single pass. MEGA-GNN (2412.00241) employs two-stage aggregation: first over all edges (multi-edge aggregation) between node pairs, then over nodes, maintaining directional information and permutation equivariance.

• Sequence Models and Decoding:

SB-NMT (1905.04847) introduces synchronous bidirectional beam search, generating translations from both ends towards the center and fusing forward (history) and reverse (future) context at every step:

$$\overrightarrow{H} = \overrightarrow{H}^{history} + \lambda \cdot \tanh(\overrightarrow{H}^{future})$$

and corresponding for the opposite direction.

• Database Query Optimization:

Parachute (2506.13670) analyzes static query plans to identify blocked information flows, and injects precomputed, join-induced fingerprint columns into parent and child tables, enabling filters (semi-joins) to be enforced both up and down the join tree:

$$R \rightsquigarrow S :\Leftrightarrow (R \prec S) \wedge (R \leftrightarrow S) \wedge is\_probe(S)$$

• State Space Models for Vision:

LBMamba (2506.15976) performs a global forward scan and, within each segment, a local backward scan, combining both results for each token location in one forward pass:

$h_t = h_t^f + (h_t^b - B^f x_t)$

Achieving O(1) memory overhead and no global backward sweep.

• Hierarchical Gaussian Process Models:

BIF-HGP (2505.11294) averages child GP predictions upward for the parent prior and distributes parent observations downward via a softmax-based credit assignment:

$$y_s(x) = y_p(x) \cdot \frac{e^{c_s(x)}}{\sum_j e^{c_j(x)}}$$

enabling mutual refinement in every iteration.

3. Implementation and Efficiency Considerations

Single-pass bidirectional designs offer notable computational advantages:

• Reduced Redundancy: Fused scans eliminate the need for full data structure reversals (e.g., LBVim’s local backward scan avoids an extra global sweep, reducing memory and doubling throughput (2506.15976)).
• Static Optimization: Precomputing fingerprints or aggregate structures supports aggressive early filtering/pruning (e.g., Parachute, with 1.54x speedup vs. DuckDB (2506.13670)).
• Scalability: Parallel local bidirectionality is executed in register-level, thread-local memory, avoiding HBM bottlenecks (LBMamba).
• Data Movement: EM bidirectional compression (1907.03235) achieves both high throughput and low disk usage by restricting random accesses.

Potential trade-offs:

• Additional space may be required for precomputed columns or artificial nodes (Parachute, MEGA-GNN).
• Approximate pruning or fingerprinting may allow some false positives, though instance-optimality can often be approached.
• Effectiveness can vary depending on architectural details—e.g., in NMT, model design and masking may limit bi-directional gains in high-resource settings (2011.12165).

4. Empirical Outcomes and Applications

Bi-directional single-pass paradigms consistently yield empirical improvements:

• Pose Estimation: BGSIM (1805.00603) achieves 62.9 mAP (COCO), 77.6 mAP (MPII), outperforming prior methods especially in crowded/occluded scenes by aggregating information across all joints in both directions.
• Machine Translation: SB-NMT (1905.04847) surpasses Transformer by +3.9 BLEU (Chinese-English), +1.5 BLEU (English-German), leveraging both history and predicted future context at each step.
• Speech Recognition: Bidirectional CTC decoding (2110.03326) reduces character error rate over traditional methods, especially at sequence beginnings, by integrating future context in a single pass.
• Database Performance: Parachute (2506.13670) achieves up to 1.54x execution speedup and 8.79x reduction in dangling tuples, with a moderate (~15%) storage overhead.
• Graph Learning: MEGA-GNN (2412.00241) outperforms SOTA on AML data by up to 13% F1; sustains permutation equivariance and rich expressivity for multigraphs.
• Vision: LBVim (2506.15976) consistently improves top-1 accuracy (by 0.8–1.6%) and throughput (up to 83%) in ImageNet classification relative to bi-directional global scan counterparts.

Applications span multi-person pose estimation, natural language translation, offline/online speech recognition, financial transaction graph analysis, image and sequence classification, query optimization in OLAP/OLTP environments, and multi-agent path execution.

5. Technical Innovations and Theoretical Guarantees

Key technical advances enabling efficient single-pass bi-directional passing include:

• Dynamic root/base point selection in graph models (BGSIM), adapting information flow per-instance.
• Hybrid local-global bi-directionality: Local window backward scans (LBMamba) plus alternated direction stacking for full global context.
• Pre-attached join-induced fingerprints in databases (Parachute), supporting predicate translation across join boundaries.
• Synchronous, interactive attention fusion (SB-NMT), where each generated token conditions on both its own history and “future” tokens from the complementary direction.
• Statistically orthogonal basis coding (DimeNet), enabling parameter-efficient directional representation via spherical Bessel and harmonics.
• Bidirectional sample-efficient Bayesian updating (BIF-HGP), with formal credit assignment.

Theoretical analysis supports the claim that under mild assumptions, single-pass bi-directional representations retain higher mutual information and effective dimension compared to unidirectional ones, leading to improved downstream performance (2506.00859).

6. Comparative Assessment and Ongoing Challenges

Comparing single-pass bi-directional with classical two-pass or instance-optimal algorithms reveals important trade-offs:

Feature	Single-Pass Bi-Directional	Multi-Pass/Unidirectional
Efficiency	Higher	Lower/Redundant scans
Storage Overhead	Modest/Adjustable	None or high (full indexes)
Expressivity	High, global and local	Variable, context-limited
Deadlock/Coverage Guarantees	Maintained with analysis	Guaranteed (but more costly)
Practicality in Production	High (OLAP/DB, GPU)	Often impractical

Challenges remain in tuning the space-accuracy trade-off (as in Parachute), generalizing full-bidirectionality to arbitrary graphs with cycles, and managing the memory overhead of maintaining richer edge or fingerprint structures. Applicability to streaming or online/real-time settings may require further engineering.

7. Future Research Directions

Areas of ongoing or future investigation include:

• Scalability: More efficient local-global bi-directional schemes for very large graphs or tensors.
• Learning-based heuristics: For dynamic fingerprint design or cycle-breaking in real-world physical and data systems.
• Extensions to continuous or asynchronous environments: For example, handling continuous-time MAPF or streaming query processing.
• Deeper integration of decision-theoretic and probabilistic inference paradigms: As seen in bidirectional deliberation reasoning (2407.06112).

A plausible implication is that single-pass bi-directional information passing is likely to become a foundational principle for scalable, robust, and accurate inference and decision-making across a spectrum of machine learning, optimization, and data management systems.