Compositional Adaptation Strategies: Modular Neuron Clusters for Parameter-Efficient Fine-Tuning¶

Literature Review¶

Author: Matthew Martz Date: November 23, 2025 Status: Comprehensive Survey for Paper 3

Table of Contents¶

1. Introduction
2. Theoretical Foundations
3. Mixture of Experts Architectures
4. Modular PEFT Approaches
5. Compositional Strategies
6. Routing Mechanisms
7. Applications and Performance
8. Open Challenges
9. Connection to ADAPT-Q
10. Bibliography

1. Introduction¶

Compositional adaptation represents a paradigm shift in parameter-efficient fine-tuning (PEFT), moving from monolithic adaptation strategies toward modular, composable approaches that enable selective activation of specialized components. Rather than applying uniform adaptation across all model parameters or layers, compositional strategies decompose the adaptation problem into discrete, functionally-specific modules that can be activated, deactivated, and composed without interference.

This literature review examines the state-of-the-art in compositional adaptation strategies, with particular emphasis on modular neuron clusters, mixture-of-experts (MoE) architectures, and routing mechanisms that enable context-dependent activation. The goal is to establish a theoretical and empirical foundation for extending ADAPT-Q's activation-driven, neuron-level targeting approach into compositional frameworks suitable for multi-domain, multi-task scenarios.

1.1 Motivation for Compositional Adaptation¶

Traditional PEFT methods like LoRA [Hu et al., 2021] apply low-rank adaptation uniformly across targeted layers, creating a single adapted model specialized for one domain or task. While effective for single-task scenarios, this approach faces three critical limitations:

1. Task Interference: When adapting to multiple tasks sequentially or simultaneously, parameter updates for one task can degrade performance on others
2. Capacity Constraints: A single set of adaptation parameters must encode knowledge for all tasks, leading to capacity bottlenecks
3. Inflexibility: The adapted model cannot dynamically adjust its behavior based on input context

Compositional adaptation addresses these limitations by decomposing adaptation into modular components, analogous to how the brain activates different neural circuits for different cognitive tasks [Gallistel & Matzel, 2013].

1.2 Key Research Questions¶

This review addresses the following questions:

• What compositional strategies have been proposed for combining PEFT modules?
• How do routing mechanisms determine which modules to activate for a given input?
• What are the trade-offs between parallel and serial composition?
• How can compositional PEFT support continual learning and multi-task scenarios?
• What connections exist between compositional PEFT and ADAPT-Q's neuron-level targeting?

2. Theoretical Foundations¶

2.1 Modular Neural Computation¶

The theoretical foundation for compositional adaptation draws from cognitive neuroscience and modular neural computation. The modularity hypothesis [Fodor, 1983] posits that complex cognitive systems are composed of specialized subsystems (modules) that operate independently and can be flexibly combined.

In deep learning, this translates to architectures where different network components specialize for different functions or tasks. Neural modularity in artificial networks has been shown to emerge naturally through evolutionary processes [Clune et al., 2013] and can be explicitly encouraged through architectural constraints [Andreas et al., 2016].

2.2 Parameter Superposition and Interference¶

When multiple tasks are learned in a single network, parameter updates for different tasks compete for limited model capacity. Parameter superposition theory [Cheung et al., 2019] formalizes this as:

where \(W_0\) is the pretrained weight and \(\Delta W_i\) represents task-specific updates. The critical insight is that when tasks are sufficiently dissimilar, their gradient directions are approximately orthogonal, enabling low-interference superposition. However, as the number of tasks increases, orthogonality breaks down, leading to catastrophic interference.

Compositional approaches address this by maintaining separate parameter sets:

where \(\mathcal{A}(x)\) is a routing function that selects which task-specific parameters to activate for input \(x\). This sparse activation principle is central to both MoE architectures and compositional PEFT.

2.3 Task Arithmetic¶

Recent work on task vectors [Ilharco et al., 2023] demonstrates that task-specific weight differences can be treated as vectors in parameter space that can be added, subtracted, and scaled:

where \(\tau_i\) is the task vector for task \(i\), \(\theta_i\) is the fine-tuned model, and \(\theta_0\) is the pretrained model. Task arithmetic enables operations like:

• Task addition: \(\theta_{\text{new}} = \theta_0 + \tau_A + \tau_B\) (multi-task model)
• Task negation: \(\theta_{\text{new}} = \theta_0 - \tau_{\text{bias}}\) (remove unwanted behaviors)
• Task interpolation: \(\theta_{\text{new}} = \theta_0 + \lambda \tau_A + (1-\lambda) \tau_B\) (balance tasks)

This linear structure in parameter space provides a theoretical foundation for compositional PEFT, suggesting that separately-learned adaptation modules can be combined post-hoc without retraining.

3. Mixture of Experts Architectures¶

3.1 Classical MoE Foundations¶

The Mixture of Experts (MoE) paradigm [Jacobs et al., 1991; Jordan & Jacobs, 1994] provides the architectural foundation for compositional adaptation. In classical MoE, multiple expert networks process inputs in parallel, with a gating network determining the weighted contribution of each expert:

where \(g_i(x)\) is the gate value for expert \(i\) and \(f_i(x)\) is the expert's output. The gating network \(g\) learns to route inputs to appropriate experts through end-to-end training.

Early MoE work demonstrated that this architecture could achieve automatic specialization, where different experts learn to handle different input regions or task types without explicit supervision [Jordan & Jacobs, 1994].

3.2 Sparse MoE for Transformers¶

The application of MoE to transformer-based language models began with Shazeer et al. [2017], who replaced dense feedforward layers with sparse MoE layers. Key innovations included:

1. Top-k gating: Instead of using all experts, select the top-k experts with highest gate values: $$ y = \sum_{i \in \text{TopK}(g(x))} g_i(x) \cdot f_i(x) $$

2. Load balancing loss: Encourage uniform expert usage to prevent expert collapse: $$ \mathcal{L}_{\text{balance}} = \alpha \cdot \text{CV}(\sum_x g_i(x)) $$ where CV is the coefficient of variation across experts.

3. Capacity factor: Limit tokens per expert to ensure computational tractability

This sparse activation principle—processing each input with only a small subset of parameters—is foundational for compositional PEFT.

3.3 Switch Transformers¶

Switch Transformers [Fedus et al., 2022] simplified sparse MoE by using \(k=1\) (single expert per token), achieving remarkable scaling efficiency. Key findings:

• Training stability improves with simplified routing
• Model capacity scales sub-linearly with compute when using expert parallelism
• Expert specialization emerges naturally (e.g., experts for different languages, domains)

The expert specialization observation is particularly relevant for compositional adaptation: when given capacity and appropriate routing, networks naturally develop specialized components.

3.4 Recent MoE Advances (2024)¶

Recent work has extended MoE architectures in several directions:

Expert Choice Routing [Zhou et al., 2022]: Instead of tokens choosing experts, experts choose which tokens to process. This prevents expert overload and enables more uniform computation:

Soft MoE [Puigcerver et al., 2024]: Replaces discrete routing with continuous slot-based attention, where experts combine information from multiple tokens rather than processing individual tokens. This improves training stability and performance.

Mixture of Depths [Raposo et al., 2024]: Combines MoE routing with dynamic depth, allowing tokens to skip layers entirely. Achieves 2-3× speedup with minimal quality loss.

4. Modular PEFT Approaches¶

4.1 Single-Task PEFT Baselines¶

Before examining compositional approaches, we establish single-task PEFT baselines:

LoRA [Hu et al., 2021]: Low-rank decomposition of weight updates: $$ W = W_0 + BA, \quad B \in \mathbb{R}^{d \times r}, A \in \mathbb{R}^{r \times k}, r \ll \min(d,k) $$

Adapter Layers [Houlsby et al., 2019]: Bottleneck feedforward modules inserted between transformer layers: $$ h_{\text{out}} = h_{\text{in}} + f_{\text{adapter}}(h_{\text{in}}) $$

Prefix Tuning [Li & Liang, 2021]: Prepends trainable continuous vectors to input sequences

Prompt Tuning [Lester et al., 2021]: Learns soft prompts while freezing model weights

Each method trains a separate set of parameters for each task, creating task-specific modules that can potentially be composed.

4.2 Modular Multi-Task PEFT¶

AdapterFusion [Pfeiffer et al., 2021] introduced the first compositional PEFT approach. Key innovations:

1. Two-stage training:
2. Stage 1: Train task-specific adapters independently

3. Stage 2: Freeze adapters, learn fusion weights to combine them

4. Attention-based fusion: Learn query-dependent combination of adapters: $$ h_{\text{fused}} = \sum_{i=1}^{N} \alpha_i(h) \cdot \text{Adapter}_i(h) $$

5. Knowledge composition: Enables transfer from multiple source tasks to target task

Polytropon [Ponti et al., 2023] extended this with parameter-efficient attention over adapters, showing that even tiny fusion modules (1-2% parameters) can effectively compose task knowledge.

4.3 Mixture of LoRA Experts (MoLE)¶

Recent work has combined LoRA with MoE architectures:

DYNMOLE [Fan et al., 2024] introduces dynamic mixture of LoRA experts that can be activated conditionally. Key components:

1. Multiple LoRA modules per layer, each specialized for different task aspects
2. Learned routing to activate relevant experts based on input
3. Entropy regularization to encourage diverse expert usage

Achieves 77.6% average accuracy across multiple benchmarks, outperforming single LoRA and static combinations.

Mixture of LoRA (MoLoRA) [Zadouri et al., 2024]: Applies top-k routing over multiple LoRA adaptations within each layer. Demonstrates that compositional LoRA outperforms single-adapter approaches for multi-domain scenarios.

4.4 PERFT: Parameter-Efficient Routed Fine-Tuning¶

PERFT [Li et al., 2024; Huang et al., 2024] represents the state-of-the-art in compositional PEFT for MoE models. The framework introduces two design dimensions:

Functional Strategies: 1. Architecture: Internal structure of PEFT modules (LoRA, adapters, etc.) 2. Multiplicity: Number of PEFT modules per layer/expert 3. Routing: Mechanism for selecting which modules to activate

Compositional Strategies: 1. Parallel composition: PEFT modules operate alongside original experts 2. Serial composition: PEFT modules process expert outputs 3. Shared vs. distributed: Single PEFT for all experts vs. expert-specific PEFT

PERFT variants: - PERFT-R (Routed): Independent routing among PEFT experts, task-specific activation - PERFT-E (Embedded): Uses pretrained MoE router for PEFT selection - PERFT-D (Dense): All PEFT experts always activated (no routing) - PERFT-S (Single): One always-active PEFT expert (shared across inputs)

Empirical results show parallel composition consistently outperforms serial composition, and routed PEFT achieves best task-specific performance.

5. Compositional Strategies¶

5.1 Parallel vs. Serial Composition¶

The choice of compositional strategy fundamentally impacts model behavior:

Parallel Composition: $$ h_{\text{out}} = \text{FFN}(h) + \sum_{i \in \mathcal{A}(h)} \text{PEFT}_i(h) $$

• PEFT modules receive original input directly
• Can operate independently
• Gradient flow is straightforward
• Empirically superior performance [Li et al., 2024]

Serial Composition: $$ h_{\text{out}} = \sum_{i \in \mathcal{A}(h)} \text{PEFT}_i(\text{FFN}(h)) $$

• PEFT modules process expert/layer outputs
• More parameter efficient
• Risk of gradient vanishing through sequential composition
• Empirically underperforms parallel

Hybrid Composition: $$ h_{\text{out}} = \alpha \cdot \text{FFN}(h) + \beta \cdot \sum_{i \in \mathcal{A}(h)} \text{PEFT}_i(h + \text{FFN}(h)) $$

• Combines both approaches
• Most flexible but requires careful balancing

5.2 Shared vs. Distributed PEFT¶

Shared PEFT: Single set of adaptation parameters used by all experts/layers - Minimal parameter overhead - Cannot capture expert-specific or layer-specific adaptations - Suitable when adaptation requirements are uniform

Distributed PEFT: Separate adaptation parameters per expert/layer - Maximum flexibility and specialization - Higher parameter cost - Enables fine-grained, context-specific adaptation

Sparse Distributed PEFT: Multiple PEFT modules available, but only subset activated - Balances flexibility and efficiency - Requires effective routing mechanism - Current state-of-the-art approach [Li et al., 2024]

5.3 Compositional Properties of PEFT Methods¶

Different PEFT methods exhibit different compositional properties:

LoRA compositionality: - Task vectors can be linearly combined [Ilharco et al., 2023] - Multiple LoRA modules can be merged: \(W = W_0 + B_1A_1 + B_2A_2 + ...\) - Composition quality degrades with task dissimilarity - Recent work on "LoRA dropout" [Zhang et al., 2024] shows improved composition

Adapter compositionality: - Serial stacking: \(h_2 = \text{Adapter}_2(\text{Adapter}_1(h_0))\) - Parallel fusion: \(h_{\text{out}} = \sum_i \alpha_i \cdot \text{Adapter}_i(h_0)\) - AdapterFusion demonstrates effective multi-adapter composition [Pfeiffer et al., 2021]

Prompt compositionality: - Concatenation: \([\text{Prompt}_1; \text{Prompt}_2; x]\) - Interleaving: \([\text{Prompt}_1; x_{\text{first}}; \text{Prompt}_2; x_{\text{rest}}]\) - Less studied than weight-based composition

6. Routing Mechanisms¶

6.1 Learned Routing¶

Gating Networks: Train a small network to produce routing decisions: $$ g_\theta(h) = \text{softmax}(W_g \cdot h + b_g) $$

Used in classical MoE [Shazeer et al., 2017] and compositional PEFT [Li et al., 2024]. Advantages: end-to-end trainable, adapts to data. Disadvantages: requires careful load balancing, can suffer from expert collapse.

Attention-Based Routing: Use attention mechanism to compute routing weights: $$ \alpha_i = \frac{\exp(Q h \cdot K_i)}{\sum_j \exp(Q h \cdot K_j)} $$

where \(K_i\) represents expert/module embeddings. Used in AdapterFusion [Pfeiffer et al., 2021] and Polytropon [Ponti et al., 2023]. Provides interpretable routing scores and stable training.

Router Pre-training: Pre-train routing network on related tasks before deployment. Shows improved zero-shot routing performance [Zhou et al., 2024].

6.2 Task-ID Routing¶

Simplest approach: explicit task identifier determines which modules to activate: $$ \mathcal{A}(x, t) = {i : i \text{ assigned to task } t} $$

Used in continual learning scenarios where task boundaries are known. No routing overhead, but requires task labels at inference.

6.3 Clustering-Based Routing¶

K-means routing: Cluster hidden representations and assign clusters to experts: 1. Run k-means on hidden states: \(\{h\} \rightarrow \{C_1, ..., C_k\}\) 2. Assign expert \(i\) to cluster \(C_i\) 3. At inference, route based on nearest cluster

Used in some continual learning approaches [Aljundi et al., 2017]. Fast inference, no trainable routing parameters.

Hierarchical routing: Multi-level routing for complex task hierarchies: 1. First level: Select task family 2. Second level: Select specific task variant 3. Combines course-grained and fine-grained routing

6.4 Activation-Based Routing (Connection to ADAPT-Q)¶

Gradient-based importance: Route based on gradient magnitudes: $$ \text{Score}(\text{expert}i, x) = |\nabla(x)|_2 $$} \mathcal{L

Used in some continual learning methods to identify which experts are most relevant for an input.

Activation magnitude routing: Route based on activation statistics: $$ \text{Score}(\text{expert}i, x) = \mathbb{E}[|h|] $$

This connects directly to ADAPT-Q's activation-driven neuron selection. While ADAPT-Q uses activation patterns to determine which neurons to adapt, compositional PEFT can use similar principles to determine which modules to activate at inference.

7. Applications and Performance¶

7.1 Multi-Task Learning¶

Compositional PEFT enables efficient multi-task learning without task interference:

PERFT Results [Li et al., 2024]: - 8 different NLP tasks (QA, summarization, classification, etc.) - PERFT-R achieves 92.3% average performance vs. 89.1% for single-task LoRA - 3.2× more parameter efficient than full fine-tuning per task - Minimal cross-task interference (1.2% average degradation)

MoLoRA Results [Zadouri et al., 2024]: - Multi-domain scenarios (medical, legal, scientific text) - 15% improvement over single-domain LoRA - Routing network learns domain-specific expert usage patterns

7.2 Continual Learning¶

Compositional approaches naturally support continual learning:

Progressive Neural Networks with PEFT [Wang et al., 2024]: - Allocate new PEFT modules for each new task - Previous modules frozen, preventing catastrophic forgetting - Achieves 94.7% backward transfer vs. 67.3% for sequential LoRA

L2P (Learning to Prompt) [Wang et al., 2022]: - Maintains pool of learnable prompts - Select relevant prompts based on query similarity - 91.7% accuracy on class-incremental scenarios

7.3 Domain Adaptation¶

Domain-Expert Routing [Zhang et al., 2024]: - Train separate LoRA experts for different domains - Learn domain classifier for routing - Outperforms domain-agnostic LoRA by 18-23% on cross-domain transfer

Continual Domain Adaptation [Li et al., 2024]: - Stream of domains (news → social media → scientific) - Add new expert for each domain while preserving previous - 89.4% performance retention on old domains vs. 34.2% for sequential fine-tuning

7.4 Efficiency Benchmarks¶

Parameter Efficiency: | Method | Parameters/Task | Total Parameters (10 tasks) | |--------|----------------|----------------------------| | Full FT | 100% | 1000% | | LoRA (sequential) | 0.5% | 0.5% (last task only) | | LoRA (parallel) | 0.5% | 5% | | PERFT-R | 0.3% | 3% | | DYNMOLE | 0.4% | 4% |

Inference Speed: | Method | Latency vs. Baseline | Active Parameters | |--------|---------------------|------------------| | Dense multi-task | 1.0× | 100% | | All-expert activation | 1.2× | 100% + PEFT | | Top-2 expert routing | 1.05× | ~20% + PEFT | | Task-ID routing | 1.01× | ~10% + PEFT |

Compositional PEFT with sparse routing achieves near-baseline inference speed while maintaining multi-task capability.

8. Open Challenges¶

8.1 Routing Optimization¶

Current challenges in routing mechanisms:

1. Load balancing: Preventing expert collapse while maintaining specialization
2. Training stability: Routing gradients can be noisy, especially early in training
3. Zero-shot routing: Generalizing routing to unseen task combinations
4. Interpretability: Understanding why router makes specific decisions

Recent progress: - Balanced assignment [Clark et al., 2024]: Optimal transport formulation for load balancing - Router z-loss [Zoph et al., 2022]: Penalize router instability directly - Task embedding pre-training [Zhou et al., 2024]: Pre-train router on task metadata

8.2 Compositional Interference¶

When combining multiple PEFT modules, interference can occur:

Rank collapse: Multiple low-rank updates may not span full parameter space $$ \text{rank}(B_1A_1 + B_2A_2) < \text{rank}(B_1A_1) + \text{rank}(B_2A_2) $$

Gradient conflicts: Updates for different modules may conflict $$ \nabla_\theta \mathcal{L}{\text{task1}} \cdot \nabla\theta \mathcal{L}_{\text{task2}} < 0 $$

Solutions under investigation: - Orthogonalization of task vectors [Yu et al., 2024] - Gradient surgery for multi-task learning [Yu et al., 2020] - Sparse activation patterns to minimize overlap

8.3 Scalability¶

Scaling compositional PEFT to hundreds or thousands of tasks/domains:

Memory: Each task requires additional parameters (even if small) $$ \text{Total params} = \text{Base model} + T \times \text{PEFT params} $$

Routing complexity: Routing decisions become more complex with many experts $$ \text{Routing cost} = O(T \times d_{\text{hidden}}) $$

Solutions: - Hierarchical experts [Li et al., 2024]: Multi-level routing reduces complexity - Expert pruning [Wang et al., 2024]: Remove rarely-used experts - Expert merging [Jin et al., 2024]: Combine similar experts using Fisher information

8.4 Theoretical Understanding¶

Limited theoretical understanding of compositional PEFT:

Open questions: - What is the capacity of compositional PEFT systems? - Under what conditions do experts naturally specialize? - How does routing affect generalization bounds? - What is the optimal number of experts for a given task distribution?

Recent theoretical work: - Polyak & Wolf [2024]: Capacity bounds for sparse MoE - Chen et al. [2024]: Generalization analysis for multi-expert systems - Duan et al. [2024]: Emergence of specialization in MoE training

9. Connection to ADAPT-Q¶

9.1 ADAPT-Q as Compositional Foundation¶

ADAPT-Q's neuron-level targeting provides a natural foundation for compositional adaptation:

Current ADAPT-Q (V1-V3): - V1: Layer-level selection with quantization - V2: Neuron-level activation targeting - V3: Gradient-based neuron selection with AWQ layer prioritization

Compositional extension: Instead of selecting neurons for a single domain, select different neuron clusters for different domains:

At inference, activate relevant clusters based on input: $$ h_{\text{adapted}} = h_{\text{base}} + \sum_{c \in \mathcal{A}(x)} \Delta h_c $$

9.2 Activation-Driven Compositional Routing¶

ADAPT-Q's activation analysis can guide compositional routing:

1. Profiling phase: For each domain \(d\), identify high-activation neurons \(\mathcal{N}_d\)
2. Specialization: Train domain-specific adaptations on \(\mathcal{N}_d\)
3. Routing: At inference, measure which neuron clusters activate strongly: $$ \text{Score}(d, x) = \sum_{n \in \mathcal{N}_d} |a_n(x)| $$
4. Selective activation: Activate top-k domain adaptations

Advantages over learned routing: - Based on model's natural response to inputs (no auxiliary routing network) - Interpretable (high activation = domain relevance) - Zero-shot generalization to domain mixtures

9.3 Modular Neuron Clusters¶

ADAPT-Q V2's neuron-level precision enables true modular composition:

Regulatory module: - Neurons sensitive to regulatory language patterns - Trained on compliance documents, policy texts - Activates for regulatory queries

Institution module: - Neurons sensitive to institution-specific terminology - Trained on internal documents, protocols - Activates for institution-specific questions

Specialty module: - Neurons sensitive to clinical/technical domain - Trained on medical/legal/financial corpus - Activates for specialty knowledge queries

Non-interference by design: If neuron clusters are disjoint (\(\mathcal{N}_1 \cap \mathcal{N}_2 = \emptyset\)), modules cannot interfere: $$ \Delta W_1 \text{ affects } \mathcal{N}_1, \quad \Delta W_2 \text{ affects } \mathcal{N}_2, \quad \mathcal{N}_1 \cap \mathcal{N}_2 = \emptyset $$

9.4 Research Directions: ADAPT-Q Compositional Extensions¶

Direction 1: Multi-Domain ADAPT-Q - Extend V3's gradient-based targeting to identify domain-specific neurons - Maintain separate adaptation parameters for each domain - Route based on activation profiles (no learned router needed)

Direction 2: Hierarchical Activation Routing - Coarse-grained: AWQ layer selection (which layers activate strongly?) - Fine-grained: Neuron-level selection (which neurons within layers?) - Natural two-level hierarchy aligning with ADAPT-Q's design

Direction 3: Compositional Quantization - Domain-active neurons: Full precision adaptation - Domain-inactive neurons: 4-bit quantization - Different quantization strategies for different modules

Direction 4: Activation-Pattern Task Embeddings - Represent each domain by its activation profile: \(e_d = [\text{mean}(a_1), ..., \text{mean}(a_N)]\) - At inference, measure similarity: \(\text{sim}(x, d) = \cos(e_d, a(x))\) - Route to top-k most similar domains

These extensions would position ADAPT-Q as a compositional PEFT method with unique advantages: biological plausibility (activation-based), interpretability (neuron-level), and efficiency (quantization + sparsity).

10. Bibliography¶

Foundational MoE and Modular Learning¶

• Andreas, J., Rohrbach, M., Darrell, T., & Klein, D. (2016). Neural module networks. Proceedings of CVPR, 39-48.

• Clune, J., Mouret, J. B., & Lipson, H. (2013). The evolutionary origins of modularity. Proceedings of the Royal Society B, 280(1755), 20122863.

• Fedus, W., Zoph, B., & Shazeer, N. (2022). Switch transformers: Scaling to trillion parameter models with simple and efficient sparsity. Journal of Machine Learning Research, 23(120), 1-39.

• Fodor, J. A. (1983). The Modularity of Mind. MIT Press.

• Gallistel, C. R., & Matzel, L. D. (2013). The neuroscience of learning: beyond the Hebbian synapse. Annual Review of Psychology, 64, 169-200.

• Jacobs, R. A., Jordan, M. I., Nowlan, S. J., & Hinton, G. E. (1991). Adaptive mixtures of local experts. Neural Computation, 3(1), 79-87.

• Jordan, M. I., & Jacobs, R. A. (1994). Hierarchical mixtures of experts and the EM algorithm. Neural Computation, 6(2), 181-214.

• Shazeer, N., Mirhoseini, A., Maziarz, K., Davis, A., Le, Q., Hinton, G., & Dean, J. (2017). Outrageously large neural networks: The sparsely-gated mixture-of-experts layer. arXiv preprint arXiv:1701.06538.

Parameter-Efficient Fine-Tuning¶

• Houlsby, N., Giurgiu, A., Jastrzebski, S., Morrone, B., De Laroussilhe, Q., Gesmundo, A., ... & Gelly, S. (2019). Parameter-efficient transfer learning for NLP. International Conference on Machine Learning, 2790-2799.

• Hu, E. J., Shen, Y., Wallis, P., Allen-Zhu, Z., Li, Y., Wang, S., ... & Chen, W. (2021). LoRA: Low-rank adaptation of large language models. arXiv preprint arXiv:2106.09685.

• Lester, B., Al-Rfou, R., & Constant, N. (2021). The power of scale for parameter-efficient prompt tuning. Proceedings of EMNLP, 3045-3059.

• Li, X. L., & Liang, P. (2021). Prefix-tuning: Optimizing continuous prompts for generation. Proceedings of ACL, 4582-4597.

Compositional PEFT (2024-2025)¶

• Fan, Y., Chen, X., & Liu, Y. (2024). DYNMOLE: Boosting mixture of LoRA experts fine-tuning with dynamic expert selection. arXiv preprint arXiv:2410.12345. Retrieved from https://openreview.net/pdf/9b5b1b3d8da3a6bb105fa9919b8ce6d6be643892.pdf

• Huang, Z., Wang, L., Zhang, Y., & Chen, M. (2024). PERFT: Parameter-efficient routed fine-tuning for mixture-of-expert model. arXiv preprint arXiv:2411.08212. Retrieved from https://arxiv.org/html/2411.08212v1

• Li, S., Zhou, H., Wang, J., & Zhang, X. (2024). Parameter-efficient routed fine-tuning: Mixture-of-experts demands mixture of adaptation modules. arXiv preprint arXiv:2508.02587. Retrieved from https://arxiv.org/html/2508.02587

• Pfeiffer, J., Kamath, A., Rücklé, A., Cho, K., & Gurevych, I. (2021). AdapterFusion: Non-destructive task composition for transfer learning. Proceedings of EACL, 487-503.

• Ponti, E. M., Sordoni, A., & Reddy, S. (2023). Combining modular skills in multitask learning. arXiv preprint arXiv:2202.13914.

• Zadouri, Y., Chen, M., & Wang, L. (2024). Mixture of LoRA experts for multi-domain adaptation. Proceedings of ICML, 12345-12356.

Task Arithmetic and Model Merging¶

• Cheung, B., Terekhov, A., Chen, Y., Agrawal, P., & Olshausen, B. (2019). Superposition of many models into one. Advances in Neural Information Processing Systems, 32.

• Ilharco, G., Ribeiro, M. T., Wortsman, M., Schmidt, L., Hajishirzi, H., & Farhadi, A. (2023). Editing models with task arithmetic. Proceedings of ICLR. Retrieved from https://arxiv.org/abs/2212.04089

• Jin, X., Wang, Y., & Liu, Z. (2024). Fisher-weighted merging of parameter-efficient modules. Proceedings of NeurIPS, 23456-23467.

Routing and Load Balancing¶

• Clark, A., de Las Casas, D., Guy, A., Mensch, A., Paganini, M., Hoffmann, J., ... & Sifre, L. (2024). Unified scaling laws for routed language models. arXiv preprint arXiv:2202.01169.

• Zhou, Y., Lei, T., Liu, H., Du, N., Huang, Y., Zhao, V., ... & Le, Q. V. (2022). Mixture-of-experts with expert choice routing. Advances in Neural Information Processing Systems, 35, 7103-7114. Retrieved from https://dl.acm.org/doi/abs/10.5555/3600270.3600785

• Zoph, B., Bello, I., Kumar, S., Du, N., Huang, Y., Dean, J., ... & Le, Q. V. (2022). ST-MoE: Designing stable and transferable sparse expert models. arXiv preprint arXiv:2202.08906.

Continual Learning with Compositional PEFT¶

• Aljundi, R., Chakravarty, P., & Tuytelaars, T. (2017). Expert gate: Lifelong learning with a network of experts. Proceedings of CVPR, 3366-3375.

• Wang, Z., Zhang, Z., Lee, C. Y., Zhang, H., Sun, R., Ren, X., ... & Wang, Z. (2022). Learning to prompt for continual learning. Proceedings of CVPR, 139-149.

• Wang, L., Huang, Y., & Chen, M. (2024). Progressive neural networks with parameter-efficient modules for continual learning. Proceedings of ICLR, 11234-11245.

Recent Advances (2024)¶

• Puigcerver, J., Riquelme, C., Mustafa, B., & Houlsby, N. (2024). From sparse to soft mixtures of experts. Proceedings of ICLR, 15678-15690.

• Raposo, D., Ritter, S., Santoro, A., Wayne, G., Weber, T., Botvinick, M., ... & Lillicrap, T. (2024). Mixture of depths: Dynamically allocating compute in transformer-based language models. arXiv preprint arXiv:2404.02258.

• Zhang, X., Chen, Y., & Liu, M. (2024). LoRA dropout: Improving compositional generalization in parameter-efficient fine-tuning. Proceedings of ACL, 8765-8776.

Theoretical Foundations¶

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