Title: Contribution of task-irrelevant stimuli to drift of neural representations
Venue: NeurIPS 2025
Accepted: yes
Keywords: Neuroscience

computational neuroscience

representational drift

continual learning

linear neural networks

representation learning

stochastic gradient descent

Hebbian learning

learning rule
Abstract: Biological and artificial learners are inherently exposed to a stream of data and experience throughout their lifetimes and must constantly adapt to, learn from, or selectively ignore the ongoing input. Recent findings reveal that, even when the performance remains stable, the underlying neural representations can change gradually over time, a phenomenon known as representational drift. Studying the different sources of data and noise that may contribute to drift is essential for understanding lifelong learning in neural systems. However, a systematic study of drift across architectures and learning rules, and the connection to task, are missing. Here, in an online learning setup, we characterize drift as a function of data distribution, and specifically show that the learning noise induced by task-irrelevant stimuli, which the agent learns to ignore in a given context, can create long-term drift in the representation of task-relevant stimuli. Using theory and simulations, we demonstrate this phenomenon both in Hebbian-based learning---Oja's rule and Similarity Matching---and in stochastic gradient descent applied to autoencoders and a supervised two-layer network. We consistently observe that the drift rate increases with the variance and the dimension of the data in the task-irrelevant subspace. We further show that this yields different qualitative predictions for the geometry and dimension-dependency of drift than those arising from Gaussian synaptic noise. Overall, our study links the structure of stimuli, task, and learning rule to representational drift and could pave the way for using drift as a signal for uncovering underlying computation in the brain.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nIn this paper, the authors show how the task-irrelevant portion of input can lead to a drift in internal representations of networks even after the learning in the relevant subspace has stabilized. The authors derive theoretical results for such drift for several network architectures and learning rules, establishing its dependence on factors like the learning rate and the dimension of the task-irrelevant subspace. Numerical results are presented which agree closely with the theory.\n\nSTRENGTHS AND WEAKNESSES:\nThe paper is well-written, and the ideas are presented in a way making them easy to follow. The motivating example is quite useful for developing intuition before jumping into the theory. I was unfamiliar with a fair bit of the background work, but the paper does an excellent job at providing enough pointers to not have to jump back and forth between references in order to understand the core ideas. Interestingly, even though the results are developed for linear networks, they seem to generalize to non-linear ones leaving venues for future investigations. The results show close correspondence between theory and simulations. Overall, I recommend the paper to be accepted. Some concerns:\n\n1. While the work provides insight into drift in representational learning, it likely has limited practical applications owing to the limitations authors acknowledge – simple linear networks, assumptions around small perturbations making a differential analysis possible.\n2. Minor: in Fig. 1 consider using another variable name for number of stimuli since m is used for the dimension of relevant subspace, “we systematically this” (line 85); line 128, the dimensions are different on the two sides of the equation $WW^T = I_m$.\n\nQUESTIONS:\nSee strengths and weaknesses\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nRepresentational drift occurs in neural networks, yet its mechanisms remain unclear. This study investigates how task-irrelevant stimuli contribute to drift in neural representations of task-relevant inputs, even when these irrelevant stimuli are learned to be ignored. Through theoretical analysis and simulations across various architectures including Hebbian-based learning and stochastic gradient descent models, the research demonstrates that drift rate increases with both the variance and dimensionality of task-irrelevant data. These findings establish important connections between stimulus structure, task context, and learning mechanisms in representational drift, potentially offering new approaches to understand underlying neural information processing in the brain.\n\nSTRENGTHS AND WEAKNESSES:\n***Strengths***: \nThis paper employs theoretical analysis and computational simulation methods to study how task-irrelevant stimuli promote neural representation drift during continuous learning, with solid results. \n\n***Weaknesses***:\n\n1) The theoretical analysis results in this paper are only applicable to linear networks, and the input-output functions can only be linear, having certain limitations.\n\n2) Both sections 4.2 and 4.3 indicate that task-irrelevant signals can cause neural representation drift during the learning process. What impact does this drift have on online learning performance?\n\nQUESTIONS:\n1）Please further explain the rationale for using Eq. 2 to define the first m dimensions as task-relevant and the remaining n-m dimensions as task-irrelevant. Specifically, what kind of neural representation or feature is this \"task\" intended to learn?\n\n2）Please explain why in Eq. 2 all task-relevant dimension feature values are uniformly set to 1, while all task-irrelevant dimension feature values are set to the same constant less than 1?\n\n3）It is suggested to add the related works in the introduction about the existing contributions of task-irrelevant stimuli in continuous learning tasks, and clearly articulate the innovation points of this research.\n\n4）Regarding section 4.2, please elaborate on the task setting: the input consists of x1, x2, and n-2 dimensions of task-irrelevant Gaussian white noise, while the output is x1 and x2. How does this training method form receptive fields in the hidden layer? What is the mechanism? What role do task-irrelevant signals play, especially in reorganizing receptive fields?\n\nLIMITATIONS:\nPlease see the weaknesses and questions.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\n- The paper aims to understand the mechanisms of representational drift from a dual perspective of Hebbian and SGD-based learning.\n- The authors present theory and experiments in both settings to show that task-irrelevant stimuli, which agents learn to ignore, can be sufficient to create long-term drift of representations of task-relevant stimuli.\n- Through a motivating example of Hebbian-based learning, the authors show that drift rate increases with the variance and dimensionality of the data in the task-irrelevant subspace.\n    - The authors show similar results using a non-linear network and SGD-based learning in the experiments section.\n- With the assumption of continuous-time dynamics, the paper considers that a point on the solution manifold can be decomposed into local normal and tangential spaces. The authors particularly focus on late phase learning where the dynamics in the tangential space are purely diffusive.\n- The authors derive the analytic form of angular diffusion in terms of task-irrelevant subspace properties in four settings: multidimensional Oja's network, similarity matching network, autoencoder, and a two-layer network.\n- Using Gaussian toy data and MNIST, the authors show that drift rates closely match those predicted by the paper's theory.\n- Finally, the authors contrast the dynamics under learning noise and external synaptic noise, showing that they have different characteristics.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths\n\n- Quality\n    - The paper is motivated by citing relevant work to show that a similar notion of representational drift exists in neuroscience and machine learning.\n    - Both Hebbian and SGD-based learning settings are studied to support the generality of the presented principles.\n- Clarity\n    - The paper is mostly clear and easy to follow.\n- Originality\n    - The analysis performed in the paper is novel.\n\n### Weaknesses\n\n- Quality\n    - The central object of this paper, the notion of representational drift, needs to be more explicitly and rigorously defined, at least in the context of machine learning. Currently, part of this definition has to be inferred from the theoretical and experimental setups.\n    - The notion of \"task\" is discussed very generally throughout the paper. However, a majority of the analysis is specific to the task of principal subspace tracking, so the generality of the notion of task-relevance and task-irrelevance is not supported. In general, depending on the task, task-irrelevant stimuli can have higher variance and dimensionality.\n        - If more general tasks can be reduced to the studied problem of learning principal subspaces, this reduction procedure needs to be described.\n- Significance\n    - The limited theoretical and empirical setup of the paper makes it difficult to evaluate its significance for the community.\n\nQUESTIONS:\n- Can a more general class of tasks be reduced to the problem of principal subspace tracking? If so, what is this class of tasks and how general is it?\n- Beyond the observation that the two sources of noise have different impacts on the drift rate, are there any other takeaways from Section 5 comparing learning noise and synaptic noise?\n- Typography (no impact on score)\n    - Line 85: missing word: \"we systematically ___ this\"\n    - Line 94: missing space before $\\Delta$.\n\nLIMITATIONS:\nThe paper does not discuss the limitation that it only considers the task of principal subspace tracking.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 4, "DATE": "2025-07-03"}

comments: SUMMARY:
In this article, the authors analytically study drift of neural representation under continual learning of stimuli with 'non-relevant' directions in linear networks. They provide a general framework to study and quantify the phenomenon, and apply it to a variety of setups. They find good agreement with numerical simulations, and differentiate the resulting dynamics from drift induced by explicit noise added to the weights.

STRENGTHS AND WEAKNESSES:
## Strengths
1. The article addresses a relevant question, and provides explicit and understandable results. The selection of learning setups is sensible and comprehensive.
## Minor Weaknesses
2. When introducing the local coordinates for the main SDE (4), the authors could improve the clarity by clearly explaining what the expansion point is, and being more explicit about the assumption underlying the equations.
3. The results for non-linear models could be extended by investigating how the input spectrum determines the drift rate, and how this compares to the linear case.
4. Representational drift and its geometry has been studied and characterized in various cortical areas. A brief discussion on which aspects of the experimental observations are consistent with the effects seen in the model and which ones are not would be a valuable addition.

QUESTIONS:
See above.

LIMITATIONS:
N/A
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-03