DualHyp Framework: Modular Multi-Source Inference

• DualHyp Framework is a modular methodology that separates independent signal streams, preserving modality-specific information for robust inference.
• It employs delayed fusion strategies at a high abstraction level, ensuring precision by deferring integration until the reasoning stage.
• The framework integrates reliability prompts and hyper-dual mathematical techniques to enable tractable uncertainty modeling and efficient parameter estimation.

The DualHyp Framework denotes a suite of methods in which hypothesis-level modularity is leveraged for multi-source signal processing and inference, spanning contemporary applications from generative error correction in audio-visual speech recognition to dual-parameterized modeling in particle physics and automatic differentiation. Paradigmatically, DualHyp frameworks maintain distinct streams for disparate sources—be they modalities in sensory input or sectors in theoretical physics—and defer fusion until a higher abstraction level, typically the output or reasoning space. This strategy enables robust compositional inference, tractable uncertainty modeling, and improved downstream performance under corruption or perturbation. Theoretical underpinnings incorporate mathematical constructions from multi-scale evolution and hyper-dual numbers, while instantiations in LLM-driven architectures have demonstrated marked empirical gains in complex, noisy environments.

1. Source and Modality Separation: Hypothesis Composition

A defining attribute of the DualHyp Framework is the maintenance of independent hypothesis streams. In audio-visual speech recognition (AVSR), this approach manifests as two recognition heads: one for automatic speech recognition (ASR) and another for visual speech recognition (VSR). Each head generates an N-best list of candidate textual hypotheses, $\mathcal{H}^{asr}$ and $\mathcal{H}^{vsr}$, which are composed into a dual hypothesis set, $$\mathcal{H}^{dual} = \mathcal{H}^{asr} \cup \mathcal{H}^{vsr}$$ (Kim et al., 15 Oct 2025). This strategy preserves modality-specific information and error profiles, enabling the subsequent fusion at the LLM stage to be precise and context-aware.

In multiparton scattering physics, the dual structure appears in the separation of double transverse-momentum dependent parton distribution functions (DTMDs) describing two independent hard processes, each with its own set of quantum numbers and evolution equations (Buffing, 2017). The factorization of soft radiation into sector-dependent kernels facilitates distinct, yet correlated, evolution strategies for multi-parton contributions.

2. Fusion Strategies: Delayed and Language-Space Integration

Unlike traditional frameworks that fuse features at early or intermediate stages, DualHyp defers integration until output space where a generative reasoning model (typically an LLM) operates (Kim et al., 15 Oct 2025). The LLM receives the union of ASR and VSR hypotheses and synthesizes an output transcription via:

$$\hat{y} = \operatorname{argmax}_y P(y \mid \mathcal{H}^{dual}; \theta_{LLM})$$

This delayed fusion avoids cross-modal feature contamination, allowing context-driven selection or synthesis of subsequences from either input. The approach adapts to noise and ambiguity by exploiting the redundancies of the dual streams.

A plausible implication is that such deferred reasoning is generalizable beyond AVSR—for instance, in physics, modular fusion of DTMDs via sector-specific kernels enables analytical tractability and precision in multi-scale phenomena (Buffing, 2017).

3. Reliability-Guided Reasoning: The RelPrompt Mechanism

The RelPrompt mechanism introduces a reliability-aware prompt to guide the LLM during hypothesis fusion (Kim et al., 15 Oct 2025). Signal quality is assessed for each segment (e.g., 0.4 s windows for audio and groups of video frames), and reliability tokens (Clean, Noisy, Mixed) are generated via lightweight models (1D CNNs):

• $m^a$: audio modality reliability mask
• $m^v$: visual modality reliability mask

These masks are prepended to the dual hypotheses, adapting the conditional generation strategy:

$$\hat{y} = \operatorname{argmax}_y P(y \mid \mathcal{H}^{dual}, m^a, m^v; \theta_{LLM})$$

By providing explicit guidance on modality trustworthiness, the framework enables dynamic attention allocation in the LLM at temporal precision commensurate with signal degradation.

4. Theoretical Foundation: Evolution Equations and Hyper-Dual Numbers

The DualHyp concept is supported by rigorous mathematical formalisms. In particle phenomenology, the evolution equations for DTMDs

$$\frac{\partial}{\partial \ln \zeta} {}^R F_{a_1a_2}(...) = \frac{1}{2} \sum_{R'} {}^{RR'}K_{a_1a_2}(...) {}^{R'}F_{a_1a_2}(...)$$

and their solutions via matrix exponentials underpin scale-dependent resummation strategies (Buffing, 2017).

In the context of automatic differentiation, hyper-dual numbers of the form $$\hat{\hat{x}} = \langle x, \delta x_1, \delta x_2, \delta\delta x\rangle$$ encapsulate both first- and mixed second-order perturbations. Operator overloading on elementary and composite functions ensures correct propagation of derivatives, expressible as:

• Function value: $y = f(x)$
• First-order derivatives: $\delta y_1 = \nabla f(x)\cdot \delta x_1$, $\delta y_2 = \nabla f(x)\cdot \delta x_2$
• Second-order (mixed) derivative: $$\delta\delta y = \delta x_1^T\nabla^2 f(x)\delta x_2 + \nabla f(x)\cdot \delta\delta x$$ (Neuenhofen, 2018)

The correctness theorem (“Recursion of hyper-dual numbers”) guarantees that if all constituent functions/operators are overloaded according to these rules, final derivatives are rigorously computed.

5. Empirical Performance and Implementation

DualHyp frameworks have substantiated significant empirical gains in their target domains. In AVSR, DualHyp with RelPrompt achieves up to 57.7% error rate gain on the LRS2 benchmark versus Whisper-large‑v3, contrasting with only ~10% improvement for single-stream error correction (Kim et al., 15 Oct 2025). This robustness is attributed to selective trust in cleaner modalities and dynamic error adaptation.

In automatic differentiation, Matlab implementations of hyper-dual arithmetic (with interfaces HD_Jacobian_Call and HD_Hessian_Call) provide direct extraction of Jacobian and Hessian matrices from perturbed function calls, requiring only operator/function overloading and properly constructed inputs (Neuenhofen, 2018). This suggests efficient and mathematically certified derivative computation for optimization and sensitivity analysis.

6. Application Scope and Dataset Availability

DualHyp frameworks are instantiated in multiple domains:

Domain	Dual Structure	Reasoning/Output Stage
AVSR	ASR & VSR N-best hypotheses	LLM for correction
Parton Physics	DTMDs for two hard processes	Cross section resummation
Automatic Differentiation	Hyper-dual number components	Jacobian/Hessian computation

Publicly released code and datasets for DualHyp (AVSR) are available, including pre-generated ASR/VSR hypotheses across diverse corruption scenarios (Kim et al., 15 Oct 2025). This supports reproducibility and further exploration of hypothesis-level modular inference.

7. Cross-Domain Implications and Extensions

The DualHyp design principle—namely, modular dual-stream processing with deferred reasoning—facilitates tractable uncertainty quantification, preserves source-specific signal fidelity, and provides systematic mechanisms for performance gains under adverse conditions. This suggests applicability to broader multimodal fusion problems, hybrid physical modeling, and automatic inference frameworks beyond those currently published.

In multiparton theory, the clear separation of scales, factorized soft function structure, and robust matching to collinear inputs lend themselves to improved perturbative control and more precise phenomenological predictions, offering strategies to disentangle complex interactions and backgrounds (Buffing, 2017). In automatic differentiation, the correctness of hyper-dual number propagation promises robust higher-order sensitivity analysis.

A plausible implication is that future frameworks leveraging DualHyp principles will further generalize the modularity and reliability-aware reasoning for increasingly complex, multi-source inference and correction tasks.