The Hidden Logic of Learning

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Author: Denis Avetisyan

New research reveals how data distribution shapes the learning process in large language models, exposing distinct patterns in how these systems acquire knowledge.

The analysis of delta effective rank within the MLP up-projection layers of four language models-Qwen3-VL-4B, InternVL3.5-4B, and two versions of AndesVL-4B-reveals that while Qwen3-VL-4B and InternVL3.5-4B exhibit substantial, layer-specific oscillations indicative of targeted rank expansion and contraction during instruction and reasoning alignment, AndesVL-4B-Instruct demonstrates a comparatively static rank geometry, suggesting that its adaptation to reasoning tasks primarily involves parameter magnitude changes rather than broad representational restructuring-a phenomenon consistent with structural limitations in its adaptation capacity.
The analysis of delta effective rank within the MLP up-projection layers of four language models-Qwen3-VL-4B, InternVL3.5-4B, and two versions of AndesVL-4B-reveals that while Qwen3-VL-4B and InternVL3.5-4B exhibit substantial, layer-specific oscillations indicative of targeted rank expansion and contraction during instruction and reasoning alignment, AndesVL-4B-Instruct demonstrates a comparatively static rank geometry, suggesting that its adaptation to reasoning tasks primarily involves parameter magnitude changes rather than broad representational restructuring-a phenomenon consistent with structural limitations in its adaptation capacity.

Analyzing parameter-space signatures offers a deeper understanding of generalization beyond traditional benchmark evaluations, revealing regime-centric learning dynamics.

Despite strong performance on standardized benchmarks, large language models often fail to demonstrate corresponding gains in broader capability, raising questions about the true nature of their learning. This work, ‘Benchmark Shadows: Data Alignment, Parameter Footprints, and Generalization in Large Language Models’, investigates how data distribution shapes learning dynamics, revealing distinct regimes characterized by differing parameter-space signatures. We find that models trained on benchmark-aligned data exhibit narrow optimization, while exposure to more diverse data fosters more distributed parameter adaptation and improved generalization. Can these parameter-space diagnostics provide a more nuanced understanding of model capabilities than traditional evaluation metrics alone?

Beyond Superficial Mastery: Unveiling the Limits of Current Representation Learning

The impressive performance of large language models, such as Qwen3-4B-Base, on standardized benchmarks often obscures a critical limitation: a disconnect between achieving high scores and demonstrating genuine generalization ability. While these models excel at replicating patterns within the training data – and thus performing well on familiar tasks – their capacity to reliably apply learned knowledge to novel, unseen scenarios remains questionable. This discrepancy suggests that current evaluation metrics may not fully capture a model’s true understanding, and that improvements on benchmarks do not necessarily equate to robust, adaptable intelligence. The pursuit of scale, while yielding gains in benchmark performance, may be inadvertently prioritizing memorization over the development of truly transferable representations.

Contemporary representation learning, while achieving remarkable performance through increased model scale, frequently emphasizes quantity over quality in feature extraction. This prioritization can result in models that excel at memorizing training data but struggle to generalize to unseen examples – a phenomenon known as overfitting. The pursuit of larger datasets and parameter counts doesn’t automatically guarantee the development of robust, transferable features; instead, models may learn superficial correlations rather than underlying principles. Consequently, these systems exhibit limited ability to adapt to new tasks or domains, hindering their practical application and raising questions about the true depth of their ‘understanding’ beyond mere pattern recognition. A focus on feature diversity, alongside scale, is therefore crucial for building truly intelligent and adaptable systems.

The impressive performance of contemporary machine learning models raises a fundamental question about the nature of their intelligence: do these systems genuinely understand the data they process, or are they simply adept at memorizing patterns within it? While achieving state-of-the-art results on various benchmarks, models may rely on superficial correlations rather than capturing underlying semantic meaning. This distinction is crucial, as memorization offers limited adaptability to novel situations or variations in input, hindering true generalization. A system that understands data should be able to reason, infer, and apply knowledge flexibly, characteristics that are not necessarily guaranteed by high accuracy on existing datasets. Consequently, evaluating whether a model truly ‘understands’ requires probing beyond simple performance metrics and delving into the qualities of the learned representations themselves.

The performance of current representation learning models is inextricably linked to the characteristics of the data used for training; understanding these ‘data regimes’ is therefore crucial for improving generalization. Researchers are increasingly focused on how factors like data distribution, label noise, and the presence of spurious correlations influence a model’s ability to learn truly robust features, rather than simply memorizing training examples. Investigating these regimes involves analyzing the statistical properties of datasets and how they impact model behavior, ultimately revealing the conditions under which a model can effectively extrapolate beyond the training data and perform reliably on unseen examples. This shift in focus promises to move the field beyond simply increasing model scale, towards a more nuanced understanding of how to cultivate genuine learning and adaptability.

Analysis of parameter changes in the self-attention projection layer reveals that Qwen3-VL-4B-Thinking exhibits a significant increase of approximately 140-150% across all layers, unlike AndesVL-4B-Thinking which remains near 20%, suggesting that modifications impacting reasoning capabilities are primarily established during visual-language training and are not substantially refined by subsequent reasoning alignment.
Analysis of parameter changes in the self-attention projection layer reveals that Qwen3-VL-4B-Thinking exhibits a significant increase of approximately 140-150% across all layers, unlike AndesVL-4B-Thinking which remains near 20%, suggesting that modifications impacting reasoning capabilities are primarily established during visual-language training and are not substantially refined by subsequent reasoning alignment.

The Data Regime: Shaping Model Capacity Through Statistical Structure

The Regime-Centric Perspective posits that a model’s learning process and the resulting internal representations are not solely determined by model architecture, but are fundamentally conditioned by the characteristics of the training data itself – termed the ‘Data Regime’. This regime encompasses factors such as data distribution, diversity, redundancy, and the presence of spurious correlations. Variations within the Data Regime directly influence which features a model prioritizes, the complexity of learned representations, and ultimately, the model’s capacity to generalize beyond the training set. Consequently, analyzing and manipulating the Data Regime is crucial for understanding and improving model behavior, independent of architectural modifications.

Benchmark-aligned datasets, commonly used for model evaluation due to their standardized format, often result in a concentrated data regime. This means the training data disproportionately represents the specific characteristics of the benchmark tasks, incentivizing models to learn shortcuts or superficial correlations present within those benchmarks rather than developing broadly generalizable features. Consequently, performance on the benchmark may be inflated, masking a lack of true understanding and leading to the ‘Benchmark Shadow’ phenomenon – a divergence between benchmark performance and real-world applicability. This concentrated regime limits the model’s ability to perform reliably when faced with data distributions differing from those encountered during training, effectively hindering its capacity for robust generalization.

Coverage-Expanding Data strategies are designed to counteract the limitations of Benchmark-Aligned datasets by intentionally increasing the diversity of examples used during model training. This approach moves beyond simply maximizing performance on established benchmarks and instead focuses on exposing the model to a wider range of inputs and edge cases. The resulting learned representations exhibit improved robustness because the model is forced to develop more generalizable features, rather than relying on spurious correlations present in concentrated datasets. This ultimately aims to reduce overfitting to the benchmark distribution and enhance performance on unseen data, promoting a more reliable and adaptable model.

Analysis of model layer conditioning reveals a statistically significant improvement achieved through data de-duplication. Specifically, models trained on de-duplicated datasets exhibit 61.61% well-conditioned layers, a 2.68% increase compared to the 58.93% observed with duplicated training data. This result indicates that the data regime – in this case, the presence or absence of redundant examples – directly influences internal model structure and the proportion of effectively trainable parameters. The observed improvement suggests that de-duplication promotes a more robust and generalizable model architecture by reducing the impact of potentially biasing, repetitive data points.

Training under repetition- or frequency-concentrated regimes (conditions C and D) demonstrably improves performance compared to baseline coverage-expanding approaches with standard (A) or modified (B) learning rates.
Training under repetition- or frequency-concentrated regimes (conditions C and D) demonstrably improves performance compared to baseline coverage-expanding approaches with standard (A) or modified (B) learning rates.

Diagnosing Representation Structure: Peering Inside the “Black Box”

Parameter Space Diagnostics encompass a suite of techniques used to characterize the dimensionality and geometric properties of learned representations within neural networks. Effective Rank assesses the number of active dimensions in a layer’s parameter space, indicating the capacity for distinct feature encoding; it is calculated as the number of singular values exceeding a defined threshold. Spectral Analysis, specifically examining the singular value spectrum of a layer’s weight matrix, provides insights into the layer’s intrinsic dimensionality and potential for information compression or expansion. By analyzing these spectra, researchers can quantify the layer’s capacity to represent complex data and identify potential bottlenecks or redundancies in the network’s architecture. These diagnostics move beyond simple performance metrics to provide a more granular understanding of how a model represents information, rather than merely that it does.

Spectral inertness, as measured through analysis of the eigenvalues of the Jacobian of a model’s output with respect to its parameters, indicates a limited ability of the model to alter its learned representations in response to parameter updates. This condition manifests as minimal changes in the geometry of the representational subspace despite alterations to the model’s weights. A high degree of spectral inertness suggests the model possesses reduced flexibility and, consequently, diminished capacity for acquiring and encoding new concepts or adapting to shifts in data distribution. Essentially, the model’s representational space becomes resistant to change, potentially hindering its ability to generalize beyond the training data or learn complex relationships.

Parameter Space Diagnostics, including Effective Rank and Spectral Analysis, enable the quantification of how data regimes influence information distribution within a model’s parameter space. Variations in training data lead to differing patterns of parameter modification; certain subspaces become more or less active depending on the statistical properties of the input. This reshaping of the parameter landscape directly affects the model’s representational capacity and, consequently, its ability to generalize to unseen data. Specifically, data regimes that induce larger changes in parameter subspaces, as measured by metrics like delta effective rank, correlate with alterations in the model’s representational geometry and its capacity to encode new information, while stable regimes indicate a more rigid, less adaptable representation.

Analysis of attention projection parameters revealed substantial changes during training, with relative alterations reaching 140-150% in select layers. This magnitude of change indicates significant reparametrization occurring within the model, specifically affecting how attention mechanisms process information. The observed parameter shifts are directly correlated with the training regime employed, suggesting that the data and optimization process induce substantial restructuring of the model’s internal representations, rather than simply fine-tuning existing parameters. These large-scale adjustments highlight the dynamic nature of the learned representations and emphasize the importance of considering the training process when interpreting model behavior.

Layer-wise analysis of \lambda_{min} – the smallest singular value of a layer’s weight matrix – reveals quantifiable differences in spectral resolution between models trained on distinct datasets. A lower \lambda_{min} indicates a reduced capacity to capture fine-grained distinctions in the input data, signifying a lower-dimensional representation. Observed variations in \lambda_{min} across layers and models demonstrate that the training data directly influences the model’s representational capacity; datasets requiring more complex feature extraction result in models with higher spectral resolution – that is, smaller \lambda_{min} values – in relevant layers, while simpler datasets yield models with correspondingly lower resolution.

Delta effective rank provides a method for isolating the impact of training data from the effects of optimization algorithms on model representations. Effective rank quantifies the dimensionality of the representational subspace utilized by a model. By calculating the change in effective rank (Δ effective rank) during training, researchers can determine the extent to which data is actively reshaping the model’s representations, independent of adjustments made solely for optimization purposes. A significant Δ effective rank indicates that the incoming data is driving substantial changes in the representational geometry, suggesting the model is adapting its internal structure to accommodate the new information, while a minimal change may suggest optimization is dominating and limiting the model’s ability to fully utilize the data’s information content.

Changes in variance within the MLP up-projection layer during the thinking stage suggest that AndesVL actively updates parameters during reasoning alignment, even with a stable effective rank, supporting the concept of spectral inertness described in Section 5.
Changes in variance within the MLP up-projection layer during the thinking stage suggest that AndesVL actively updates parameters during reasoning alignment, even with a stable effective rank, supporting the concept of spectral inertness described in Section 5.

Implications for Future Architectures and Training Strategies

The ability of a machine learning model to perform well on unseen data – its generalization performance – is fundamentally linked to the diversity of the data it trains on and the avoidance of what researchers term ‘Concentrated Regimes’. These regimes arise when models are disproportionately exposed to similar data points during training, leading to overfitting and a diminished capacity to handle real-world variability. Studies demonstrate that prioritizing a broad spectrum of inputs, encompassing diverse scenarios and representations, effectively combats this issue. By strategically curating datasets and employing techniques to balance representation across different data categories, models learn more robust and transferable features. Consequently, they exhibit improved performance not only on the training data, but also on previously unseen data, signifying a genuine ability to generalize and adapt to new challenges.

The integration of multimodal learning-training models on data from multiple sensory inputs-holds significant promise for building more capable and resilient artificial intelligence systems. However, realizing this potential isn’t simply a matter of adding more data streams; it fundamentally depends on the quality of that data and how it’s presented. A thoughtfully constructed Data Regime-carefully considering the diversity, balance, and potential biases within the training dataset-is essential to unlock the full representational capacity of multimodal models. Such an approach not only expands the breadth of information the model can process, but also enhances its robustness by mitigating the risks of overfitting to specific, limited data patterns, ultimately leading to improved generalization performance across a wider range of real-world scenarios.

The attention mechanism proves instrumental in unlocking the full potential of learned representations, functioning as a dynamic weighting system that prioritizes relevant information. Rather than treating all encoded features equally, attention allows the model to focus on the most salient aspects of the input data, effectively filtering noise and amplifying crucial signals. This selective focus isn’t merely about highlighting strong features; it enables the model to discern relationships and dependencies within the data, creating a richer, more nuanced understanding. Studies reveal that the efficacy of complex models heavily relies on a well-implemented attention mechanism, as it directly impacts the model’s ability to generalize to unseen data and perform robustly across varying conditions. By intelligently allocating computational resources to the most informative parts of the representation, attention significantly enhances the model’s capacity to extract meaning and make accurate predictions.

The prevalence of prompt duplication within training datasets represents a significant, yet often overlooked, contributor to data concentration and its detrimental effects on model performance. Research indicates that when a model encounters the same or highly similar prompts repeatedly, it can lead to an artificial inflation of perceived skill and an inability to generalize to unseen scenarios – a form of overfitting. By actively identifying and mitigating instances of prompt duplication, through techniques like dataset diversification or prompt rephrasing, learning efficiency can be substantially optimized. This targeted approach prevents the model from becoming overly reliant on memorized responses and instead encourages the development of robust, generalized representations capable of handling a wider range of inputs and tasks. Consequently, addressing prompt duplication isn’t merely a matter of data hygiene, but a critical strategy for unlocking the full potential of large language models.

Research indicates a noteworthy disparity in how different neural network components respond to variations in training data. Specifically, the change in variance within Multilayer Perceptron (MLP) layers demonstrated remarkable stability across diverse data conditions, suggesting a consistent operational mode regardless of data regime. In contrast, attention mechanisms exhibited a significantly greater sensitivity to these changes. This finding highlights a fundamental difference in how these components process information; MLPs appear to maintain a relatively uniform internal state, while attention mechanisms dynamically adjust their focus based on the characteristics of the input data. Consequently, optimizing data regimes and training strategies should consider these differing sensitivities, potentially prioritizing techniques that enhance the robustness of attention mechanisms while leveraging the inherent stability of MLP layers to build more generalized and reliable models.

At the final training stage, layer-wise α values in the MLP up-projection remain consistently similar across different data conditions, highlighting an asymmetry with attention projections and supporting the analysis in Section 4.
At the final training stage, layer-wise α values in the MLP up-projection remain consistently similar across different data conditions, highlighting an asymmetry with attention projections and supporting the analysis in Section 4.

The pursuit of robust generalization in large language models, as explored in this work, hinges on a deep understanding of the underlying data distribution. The study reveals how distinct learning regimes emerge, each leaving a unique footprint within the parameter space. This echoes Claude Shannon’s assertion that, “The most important thing is to get the information across as efficiently as possible.” Just as Shannon prioritized efficient communication, this research emphasizes the importance of identifying and monitoring these parameter-space signatures-the essential signals-to truly gauge a model’s capacity to generalize beyond superficial benchmark evaluations. The work advocates moving beyond simple performance metrics to analyze how a model learns, rather than merely what it achieves, aligning with a systems-level view of intelligence.

What’s Next?

The work presented here shifts the focus from aggregate performance to the internal choreography of learning. Establishing a link between data distribution and parameter-space dynamics is a crucial step, yet it simultaneously reveals how little is truly understood about the emergent properties of these vast models. The identification of ‘regimes’ is not an endpoint, but rather a call for more nuanced diagnostic tools – instruments that can map the contours of parameter space with greater fidelity, and trace the flow of information as a model navigates its training landscape.

Future investigation must grapple with the inherent complexities of multimodal learning and the insidious effects of data concentration. While spectral analysis offers a promising avenue for detecting shifts in learning behavior, it remains unclear how these signatures translate to generalization capabilities in novel scenarios. A deeper theoretical framework is needed, one that can predict the emergence of these regimes a priori, rather than simply observing them post hoc. The challenge is not merely to improve benchmark scores, but to build models that exhibit robust, predictable behavior across a broader spectrum of inputs.

Ultimately, the pursuit of artificial intelligence will be defined not by what these systems can do, but by how they do it. Good architecture is invisible until it breaks, and only then is the true cost of decisions visible.

Original article: https://arxiv.org/pdf/2604.07363.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2026-04-12 18:14