Two-Stage Training Target

• Two-stage training target is a method that decouples learning into sequential phases, enabling robust representation in Stage 1 and task-specific fine-tuning in Stage 2.
• It improves generalization and performance by addressing challenges such as data scarcity, overfitting, and heterogeneous constraints through distinct optimization steps.
• This approach is applied across domains like deep neural networks, speech processing, computer vision, and reinforcement learning, yielding measurable performance gains.

A two-stage training target refers to an approach in machine learning where model optimization and supervision objectives are decoupled and pursued sequentially, typically to address limitations such as data scarcity, domain adaptation, overfitting, non-convexity, heterogeneous constraints, or task interference. Across a wide range of domains—including deep neural network optimization, sequence modeling, reinforcement learning, graph learning, transfer adaptation, and unsupervised/self-supervised representation learning—this strategy enables models to exploit complementary objectives, improve generalization, enforce constraints, and maximize performance on challenging benchmarks.

1. Conceptual Foundation and General Variants

A two-stage training target decomposes learning into two sequential, functionally distinct objectives, often with a different explicit loss or constraint dominating each phase. The core rationale is that certain capacities—such as general representation, feature robustness, feasibility with respect to constraints, or class separation—are better optimized in isolation before final specialization or fine-tuning for the target task or data regime.

Different variants arise, but most take either of two forms:

• Representation then specialization: Stage 1 usually optimizes for easy, high-coverage, or robust proxies (e.g., pretraining, clustering, unsupervised or auxiliary tasks); Stage 2 fine-tunes or supervises using the limited or high-value data under stricter constraints or downstream objectives.
• Decoupled constraint satisfaction: Stage 1 enforces feasibility or constraint adherence (e.g., via physical constraints, law satisfaction, or mathematical consistency), while Stage 2 seeks loss minimization or optimality within the restricted solution set.

These variants appear across subfields: e.g., multilingual LLM training with a gradual shift in data mix (Akimoto et al., 16 Oct 2024), graph neural network metric pre-training before classification (Do et al., 2020), constraint satisfaction before predictive fitting in Neural ODEs (Coelho et al., 5 Mar 2024), or pretraining/fine-tuning with auxiliary tasks in self-supervised image segmentation (Hu et al., 11 Feb 2024).

2. Formalism and Optimization Schemes

The formal expression of the two-stage target is problem-specific, but involves two optimization problems—each minimizing a designated loss functional (potentially under constraints, or with restricted data):

Stage	Typical Loss/Constraint	Example domain
Stage 1	Proxy loss, constraint, or auxiliary objective	CTC (phoneme), metric loss, constraint violation, data/representation diversity
Stage 2	Target loss, fine-tuning, or constrained optimization	CE/classification, task-specific loss, loss subject to feasibility

For instance:

• In label-proportion learning, Stage 1 minimizes bag-level Kullback-Leibler divergence between predicted and known class proportions; Stage 2 enforces strict per-bag class-count constraints in cross-entropy optimization, using optimal transport (Liu et al., 2021).
• In sequence-to-sequence electrolaryngeal speech enhancement, Stage 1 trains on a noisy mix of synthetic and real parallel data for robust coverage; Stage 2 fine-tunes on only high-fidelity pairs for domain anchoring (Ma et al., 2022).
• In neural ODE constraint modeling, Stage 1 minimizes a scalar constraint violation score $C(\theta)$; Stage 2 minimizes the predictive loss $L(\theta)$ with $\theta$ restricted to parameters with $C(\theta)\leq \text{tol}$, ensuring physics-consistent predictions (Coelho et al., 5 Mar 2024).

This decoupling often leads to a nontrivial interaction: the solution set of Stage 1 seeds the feasible region or representation geometry of Stage 2, effectively conditioning its attainable minima.

3. Architectures, Parameter Schedules, and Training Procedures

A two-stage regime imparts specific architectural, scheduling, and optimization patterns:

• Freeze–Thaw: Pretrained feature extractors, denoising front-ends, or constraint modules are frozen between stages (Li et al., 2019, Mi et al., 29 Sep 2024).
• Cascade or ensemble: Stage 1 outputs (embeddings, pseudo-labels, knowledge distillation teachers) are propagated as fixed or weakly updated inputs for Stage 2 (Do et al., 2020, Hu et al., 11 Feb 2024, Liang et al., 1 Jul 2024).
• Parameter sharing and decoupled updates: Only certain modules (fusion blocks, classifier heads, mixing networks) are trainable per stage, drastically reducing parameter update scope in Stage 2 (e.g., fusion layers in multi-stream ASR (Li et al., 2019) or team-mixing modules in reinforcement learning (Kim et al., 2021)).
• Loss composition and weighting: In joint fine-tuning, a combined loss (with fixed, often equal, weights) aggregates Stage 1 and Stage 2 terms (e.g., $L_{ft} = \alpha L_{SiSNR} + \beta L_{CE}$ for TSE–SER in noisy speech (Mi et al., 29 Sep 2024)).

Procedures are typically modular, involving explicit checkpointing and validation between phases; in some architectures, rapid convergence and stability benefits are observed due to the isolation of difficult optimization subproblems (see (Dudar et al., 2018, Coelho et al., 5 Mar 2024, Ma et al., 2022)).

4. Application Domains and Empirical Impact

Two-stage targets are prominent in:

• Speech and audio: Pretrain-denoise-classify cascades for robust SER (Mi et al., 29 Sep 2024); multi-stream ASR with frozen universal feature extraction before attention fusion (Li et al., 2019); dialect recognition with acoustic modeling (CTC) followed by dialect classification (Ren et al., 2019).
• Computer vision and segmentation: Synthetic anomaly detection with negative-guided contrastive learning (Liang et al., 1 Jul 2024); medical image segmentation using auxiliary self-supervised tasks and ensemble distillation (Hu et al., 11 Feb 2024).
• Low-resource/few-shot learning: Multilingual LLM training with staged data-mixing strategies (Akimoto et al., 16 Oct 2024); semi-supervised domain adaptation with a UDA-to-target adaptation sequence (Jin et al., 2023); graph neural networks leveraging metric embeddings before classification (Do et al., 2020).
• Reinforcement and multi-agent learning: Heterogeneous agent teams first maximize individual (role-wise) rewards before training for coordinated behavior using joint rewards (Kim et al., 2021); visual navigation decouples collision prediction from reward-based navigation (Lian et al., 19 Feb 2025).

Quantitative metrics consistently show relative improvements over joint/all-in-one or inadequately staged pipelines, particularly in low-data and high-noise scenarios: e.g., 14.33% UA gain in SER under human speech noise (Mi et al., 29 Sep 2024); over 32% relative WER reduction in multi-stream ASR (Li et al., 2019); up to 5.4-point accuracy gain in graph classification (Do et al., 2020).

5. Theoretical Analysis and Dynamics

Rigorous two-stage analyses have elucidated the optimization geometry and learning dynamics:

• Transformer training: Disentangled feature models for syntax/semantics exhibit provable two-stage training dynamics. Stage 1 rapidly fits elementary (syntactic) structure; Stage 2, operating at a reduced rate, refines to semantically correct representations. This is shown both in theoretical gradient flow (Chen et al., 8 Oct 2025) and feature block separation (Gong et al., 28 Feb 2025). Spectral signatures (principal directions, rank collapse in self-attention modules) empirically corroborate these phases.
• Nonconvex optimization: The two-stage subspace trust region method first exploits positive curvature via Newton steps, then employs gradient descent to escape saddle points, thereby achieving both fast convergence and escape from low-curvature traps (Dudar et al., 2018).
• Constraint satisfaction: Theoretical guarantees assert equivalence to the constrained global optimum when sequentially applying feasibility and optimality sub-targets (Sec. 3.1 in (Coelho et al., 5 Mar 2024)).

These results position two-stage paradigms as both empirically robust and analytically tractable for difficult, structured optimization.

6. Limitations, Open Questions, and Future Directions

Several practical and theoretical challenges persist:

• Transition heuristics: Criteria for determining stage switches (e.g., when to transition from constraint violation minimization to loss minimization (Coelho et al., 5 Mar 2024), or from representation to fine-tuning (Gong et al., 28 Feb 2025)) can be domain-specific and may lack generality.
• Stage coupling: Imperfect transfer between stages—e.g., noise in synthetic data (Ma et al., 2022), limited representational support in pseudo-labels (Liu et al., 2021), or negative transfer in joint multi-task settings (Hu et al., 11 Feb 2024)—can propagate errors or bias.
• Scalability and automation: For scalable low-resource pretraining, automatic hyperparameter and schedule synthesis remains partially heuristic; however, recent work demonstrates that scaling laws and threshold formulas can accurately predict optimal regime switches (Akimoto et al., 16 Oct 2024).
• Generalization of theoretical results: While linearized or simplified models yield clean two-stage proofs, extending these to deep, multi-layer, or highly nonlinear architectures (or into the multitask/multiobjective setting) is an open technical frontier (Chen et al., 8 Oct 2025, Gong et al., 28 Feb 2025).

Ongoing research continues to refine the operational recipes, theoretical underpinnings, and automated deployment of two-stage targets across a broader expanse of machine learning subfields.