Task Vectors in Neural Networks

• Task Vectors are compact representations in parameter or activation space that encode the precise adjustments required for neural network task adaptation.
• They enable efficient in-context learning, model editing, and multi-task merging through operations like addition, subtraction, and scaling.
• Empirical studies show that task vectors enhance model interpretability, robustness, and memory efficiency across diverse architectures and modalities.

A task vector is a compact, parameter-space or activation-space representation that encodes task-specific information for neural networks. In both weight-space model editing and in-context learning with transformers, task vectors summarize the adjustment or function necessary for a model to perform a particular task, enabling modular, efficient, and interpretable mechanisms for knowledge composition, domain transfer, and task adaptation. Task vectors are central to modern approaches in model merging, in-context learning, parameter-efficient adaptation, robustness, fairness, and interpretability across a range of architectures and modalities.

1. Mathematical Definitions and Core Properties

A task vector, in the weight-space paradigm, is defined as the difference between the fine-tuned parameters for a task and those of the base pre-trained model: $$\tau = \theta_{\mathrm{task}} - \theta_{\mathrm{base}}$$ where $\theta_{\mathrm{task}}$ are the weights after fine-tuning on a downstream task and $\theta_{\mathrm{base}}$ are the pre-trained weights. Task vectors thus encode the “direction and stride” of adaptation for a specific task (Zhang et al., 3 Jul 2024).

For transformer-based in-context learning, a task vector is an intermediate activation or latent vector $\mathbf{z}$ extracted from the model’s internal state after processing in-context examples. This vector encapsulates the essence of the demonstrated task and can be mathematically formalized as

$z = G(S)$

where $S$ is the set of demonstrations and $G$ is a function (typically implemented by a neural network sub-component or an explicit extractor) (Hendel et al., 2023, Luo et al., 29 Oct 2024).

Task vectors can be applied to modulate either model predictions (by injection into hidden activations) or parameter updates (by direct addition or subtraction), serving as a mechanism for efficient model reconfiguration.

2. Task Vectors in In-Context Learning

In LLMs and other sequence models, in-context learning can be interpreted as a two-step process involving task vectors (Hendel et al., 2023, Yang et al., 29 Sep 2025, Yang et al., 16 Jan 2025, Dong et al., 10 Jun 2025):

• Compression: A set of in-context demonstrations $S$ is compressed into a single task vector $z$ at an intermediate layer, summarizing the demonstrated mapping or rule.
• Application: When a query $x$ is presented, the model combines $x$ with the task vector $z$ (patching it into the forward pass) to produce the output.

This behavior is mathematically formalized as

$T([S, x]) = f(x; A(S))$

where $T$ denotes the transformer, $A$ is the network mapping $S$ to the task vector, and $f$ applies the rule parameterized by $z$ to $x$.

Empirical studies show that extracting and patching task vectors reproduces correct task behavior for a wide range of models and tasks, with task vector-driven outputs aligning with ICL performance in $80$–$90$\% of cases (Hendel et al., 2023). The geometry of these vectors exhibits clustering by task and strong alignment across modalities (e.g., using text-derived task vectors on image queries in VLMs) (Luo et al., 29 Oct 2024).

Recent work has formalized the Linear Combination Conjecture: task vectors act as compressed, single-demonstration summaries, formed as linear combinations of hidden states from multiple demonstrations. These vectors effectively drive the model to perform as if a new single demonstration were present, but are limited to rank-one mappings and can fail on complex bijections, a prediction validated on large LLMs (Dong et al., 10 Jun 2025).

Auxiliary training mechanisms (e.g., task vector prompting loss) can be used to enforce robust, localized task vector encoding at prescribed locations, boosting generalization and robustness (Yang et al., 16 Jan 2025).

3. Task Vectors in Model Editing, Merging, and Knowledge Composition

Task vectors in parameter space allow direct model editing through arithmetic operations:

• Addition: Composition of behaviors by adding task vectors.
• Negation: Removal (“unlearning”) of behaviors by subtracting task vectors.
• Scaling: Control of task effect strength by multiplication with scalar coefficients (Naganuma et al., 30 May 2025, Zhang et al., 3 Jul 2024).

These operations underpin task arithmetic, enabling efficient multi-task model construction and targeted editing without full retraining. The equivalence between one-step gradient descent and weight-difference task vectors has been rigorously established: after one epoch of gradient descent,

$$\tau_t^{(1)} = -\eta \nabla\bar{L}_t(\theta_{\mathrm{base}})$$

so merging task vectors is equivalent to a multitask gradient descent update (Zhou et al., 22 Aug 2025). For multiple epochs, deviations from this equivalence are second-order in the learning rate, with explicit error bounds.

The aTLAS algorithm demonstrates the utility of anisotropic scaling, learning blockwise scaling coefficients for parameter blocks of task vectors to enable disentangled, modular knowledge composition—improving few-shot learning, test-time adaptation, and memory efficiency (Zhang et al., 3 Jul 2024). Layerwise approaches (e.g., TSV-Compress, TSV-Merge) exploit the low-rank structure of layerwise task matrices, reducing storage and interference by compressing and decorrelating singular vector subspaces (Gargiulo et al., 26 Nov 2024).

For cross-model transfer, orthogonal alignment of task vectors via few-shot learning with only small amounts of data preserves norm and rank while enabling transfer between models with different pre-training (Kawamoto et al., 17 May 2025).

4. Robustness, Security, Fairness, and Safe Deployment

Task vectors introduce new opportunities and challenges for robustness and safety:

• Robust Concept Erasure: Task vector subtraction, carefully tuned with techniques such as Diverse Inversion, effectively erases unwanted concepts from models in a prompt-independent manner, outperforming input-dependent methods in safety-sensitive applications (Pham et al., 4 Apr 2024).
• Backdoor Threats: Task vectors are susceptible to composite backdoor attacks, such as BadTV, which encode triggers that survive different types of arithmetic composition, remain undetectable by standard defenses, and maintain clean-task performance (Hsu et al., 4 Jan 2025). This exposes a significant security risk for “task vector as a service” platforms.
• Fairness Control: Arithmetic on subgroup-specific task vectors affects fairness metrics (demographic parity, equalized odds) in nontrivial ways. Merging and scaling these vectors enables tailored control of group-specific fairness outcomes, but the effects are non-additive and must be carefully tuned to avoid bias transfer across subgroups (Naganuma et al., 30 May 2025).
• Safe Guardrails: Safety behaviors can be transferred across models and languages by differencing guardrail models and pre-trained models to form “Guard Vectors,” which are then composed with target models and adapted using streaming-aware training for efficient, language-agnostic safety deployment (Lee et al., 27 Sep 2025).

5. Mechanistic and Geometric Insights

Several studies provide mechanistic accounts of task vectors’ inner action within networks:

• In transformers, task vectors primarily steer predictions via attention-head Output-Value (OV) circuits, especially a small subset of “key heads.” The effect propagates mostly linearly: early injected task vectors are rotated toward task-relevant directions, while later layers tend to scale their influence (Yang et al., 29 Sep 2025).
• The evolution of hidden states during in-context learning follows a geometric two-stage process: early layers maximize separability (via previous token heads), while later layers boost alignment with label directions (via induction heads and task vectors), ultimately compressing demonstration information into task-steering vectors (Yang et al., 24 May 2025).
• In multi-modal architectures, task vectors form a shared representation space across modalities and can be derived from examples or instructions, enabling cross-modal transfer and unifying specification approaches (Luo et al., 29 Oct 2024).
• In visual prompting, task vectors are average activations at certain attention heads; reinforcement learning (e.g., REINFORCE search) can identify the subset to be patched for zero-shot adaptation to new tasks (Hojel et al., 8 Apr 2024).

6. Memory Efficiency and Practical Implementation

Task vectors captured as weight differences have a much smaller dynamic range than full model checkpoints. Quantizing task vectors (rather than entire checkpoints) to low-precision (e.g., 2–4 bits) substantially reduces memory use (to as little as 8% of full-precision requirements) without degrading, and sometimes even improving, model merging performance (Kim et al., 10 Mar 2025). Residual Task Vector Quantization (RTVQ) partitions each task vector into a shared high-precision base and an ultra-low-precision per-task offset, exploiting both scale and structure.

In realistic settings, disparities in task vector norms and low source model confidence degrade merging quality; the DisTaC algorithm uses knowledge distillation to precondition task vectors, re-scaling their norms and improving confidence, thereby restoring mergeability and accuracy under adverse conditions (Yoshida et al., 2 Aug 2025).

7. Limitations, Enhancement Strategies, and Future Directions

While task vectors enable efficient compression and knowledge transfer, several limitations persist:

• For ICL, single task vectors cannot faithfully represent high-rank tasks; injecting multiple task vectors as a “multi-vector” compressed demonstration partially overcomes this by enhancing the effective rank (Dong et al., 10 Jun 2025).
• The effectiveness of task vectors may depend on architectural choices and training regimes, with deeper networks or less carefully controlled input formats producing diffused or noisy task encodings (Yang et al., 16 Jan 2025).
• Security, fairness, and domain-transfer challenges highlight the need for further research on robust verification, anomaly detection, and adaptive task vector construction.

Future directions include adaptive quantization strategies, theoretical analysis of parameter-space geometry for multitask merging, task vector-based interpretability tools, and extensions to continual learning and multi-modal architectures. As task vectors gain prominence, ensuring their safe, fair, and effective integration into real-world systems remains a central concern for the field.