BetterTogether Framework

• BetterTogether Framework is a collection of strategies that integrate statistical, computational, and algorithmic modules for robust inference and effective decision making.
• It employs modularization with restricted information flow to shield well-specified modules from error propagation, ensuring more reliable performance.
• The framework leverages alternating optimization for joint tuning of prompt templates and neural weights, achieving significant accuracy gains in tasks like multi-hop QA.

The BetterTogether Framework encompasses a family of strategies and methodologies aiming to integrate heterogeneous modules—either statistical, computational, or algorithmic—into cohesive systems optimized for inference, prediction, decision making, or other downstream tasks. Across recent literature, "BetterTogether" has come to refer specifically to two related threads: the modularization of statistical models for robust inference under misspecification, and the joint optimization of prompt templates and neural LLM weights in modular NLP pipelines. Both leverage the alternating optimization or restricted information flow between modules to attain superior empirical performance compared to unstructured end-to-end training or fully factored Bayesian updates.

1. Modularization and the Rationale for Restricted Information Flow

Modern inference tasks frequently require the assimilation of multiple data modalities (e.g., observational data, experimental measurements, behavioral logs) best represented as separable but connected "modules." Each module, with its own likelihood, parameterization, and prior knowledge, maps to a subgraph in a larger graphical model. The BetterTogether paradigm, as articulated in (Jacob et al., 2017), formalizes joint inference via

$$\bar{\pi}(\theta_1,\theta_2|Y_1,Y_2) = \frac{p_1(Y_1|\theta_1)\,p_2(Y_2|\theta_1,\theta_2)\,p_1(\theta_1)\,p_2(\theta_2|\theta_1)}{\bar{\pi}(Y_1,Y_2)}$$

for a two-module system. When modules may be misspecified or bear unequal trust, practitioners may instead employ a "cut" distribution:

$$\pi^{\text{cut}}(\theta_1,\theta_2|Y_1,Y_2) = \bar{\pi}(\theta_2|\theta_1,Y_2)\,\bar{\pi}(\theta_1|Y_1)$$

This effectively restricts information propagation, protecting well-specified modules from error feedback, which is crucial in high-dimensional or multi-domain settings susceptible to systematic bias or structural model error.

2. Graphical Representation and Inference Architecture

The framework promotes explicit use of graphical models: nodes represent parameters and data associated with a module, and edges represent dependencies across modules. These serve dual functions:

• Information Propagation: The explicit graphical structure enables directed or weighted propagation of uncertainty and data influence, facilitating control over where misspecification-induced "feedback" is permitted.
• Uncertainty Quantification: By modular separation, practitioners can analyze the residual posterior uncertainty traceable to trusted versus suspect modules, as visualized by the structure of the dependency graph.

This architecture not only aids in model organization but is central to evaluating and justifying partial or asymmetric updates in compound models.

3. Optimization Strategy: Joint, Modular, and Alternating Algorithms

Within the NLP domain, the BetterTogether approach (Soylu et al., 15 Jul 2024) targets the joint optimization of LM pipelines composed of several modules, each defined by a prompt template (π) and model weights (θ). The central objective is

$$\underset{\theta, \pi}{\arg\max}\ \frac{1}{|X|}\sum_{(x, m)\in X} \mu(\Phi_{(\theta, \pi)}(x), m)$$

where μ denotes a downstream metric and Φ the full pipeline. Unlike conventional practice (isolated prompt engineering, then fine-tuning), the BetterTogether optimizer alternates between two bootstrapped steps:

• Prompt Optimization: Using the BootstrapFewShotRS (BFRS) algorithm, high-performing few-shot examples from self-generated traces are selected to improve prompt templates.
• Weight Optimization: Using BootstrapFinetune (BFT) with LoRA, LM weights are adapted based on traces filtered by the downstream task metric.

This alternating schedule leverages the synergy between prompt and weight updates: an improved prompt generates better traces for fine-tuning, while updated weights allow for further gains in prompt efficacy. Empirical results show that this joint strategy achieves up to 78% accuracy improvements in multi-hop QA and notable gains in mathematical reasoning and classification tasks (see Section 4).

4. Predictive Criteria and Decision-Theoretic Justification

Model selection within the BetterTogether framework is guided by out-of-sample predictive performance. This is formalized by log-score–based selection:

$$\log p(Y^{1:n}) = \sum_{i=1}^n \log \left(\int\text{likelihood}(Y^i|\theta)\,\pi(\theta|Y^{1:i-1})\,d\theta\right)$$

and, equivalently, optimization of a utility function (negative log-score plus a KL divergence regularization). The two-stage plan of action is:

• Select, within each module, the update (full, modular/cut, or plug-in) with the best predictive score.
• Among joint models whose marginals match the module-level winner, select the overall joint posterior with the best downstream predictive performance.

This criterion was applied in epidemiological modeling, meta-analysis, and causal inference scenarios, consistently validating the benefit of restricted modular updates when model trust is asymmetric (Jacob et al., 2017).

5. Empirical Applications and Experimental Results

The framework has been demonstrated in a range of settings:

Application Domain	Architecture	Observed Benefit
Biased Data Analysis	Two-Module Graph	Modular feedback control yielded superior inference.
Epidemiological Study	Factorized Models	Modularization improved HPV prevalence estimates.
Meta-Analysis	Hierarchical	Isolated paper-level inference retained robustness.
Multi-Hop QA (NLP)	LM Pipelines	Up to 78% accuracy gain versus non-alternating opt.

In all scenarios, empirical selection based on predictive accuracy confirms the advantage of modularization or joint alternating optimization—especially under suspected or confirmed model misspecification.

6. Implementation Practices and Platform Integration

The BetterTogether algorithms are released in the DSPy platform (http://dspy.ai) (Soylu et al., 15 Jul 2024), facilitating definition and optimization of multi-stage LM programs. Key implementation practices include:

• Containerized deployments via HuggingFace’s inference toolkit.
• Use of BFRS for prompt optimization and BFT (with LoRA, rank=32, alpha=64) for fine-tuning.
• Subset-splitting of training data to support robust prompt and weight update validation.
• Averaging results over multiple random seeds for reproducibility.
• Execution on A100 GPUs, tracking per-task and per-model statistical consistency.

The modular approach to both architecture (graph-based in statistics, pipeline-based in NLP) and optimization ensures extensibility to new tasks, languages, or modeling paradigms.

7. Future Directions and Theoretical Implications

Current work addresses open questions such as the optimal scope and schedule of alternating optimization, the interaction of prompt and weight improvements, and the possible substitution of more powerful fine-tuning for prompt selection (or vice versa). Potential expansions include:

• Generalizing joint optimization to larger and more complex LM programs.
• Leveraging larger models to bootstrap smaller ones via trace generation.
• Theorizing the convergence and generalization properties of alternating modular updates in deep probabilistic and neural models.

A plausible implication is that the BetterTogether family of algorithms will underpin next-generation methods for scalable, robust, and interpretable integration of modular systems, particularly in settings where data supply, model misspecification, or annotation scarcity preclude naïve holistic approaches.