Samuel Kostousov, Abhinn Kaushik, Brokoslaw Laschowskics.LG cs.AI
Recent work has shown that representational alignment between biological and artificial neural networks is asymmetric: model representations predict neural responses much better than neural responses predict model representations. This asymmetry raises the question of whether representational geometry contributes to bidirectional representational alignment. We hypothesized that steering representational geometry during training can systematically influence bidirectional alignment. To test this hypothesis, we developed a computational framework that integrates spectral regularization with bidirectional predictivity analyses. As an initial demonstration, we evaluated our framework using self-supervised contrastive vision models. Steering the spectral geometry of the learned representations substantially increased reverse predictivity with modest reductions in forward predictivity, yielding a 55% relative improvement in bidirectional predictivity. These improvements were accompanied by reduced effective dimensionality and a reorganization of the shared representational subspace, within which forward and reverse predictivity became approximately symmetric at intermediate spectral exponents. Overall, these findings demonstrate that representational geometry can be systematically steered to modulate bidirectional representational alignment between biological and artificial neural networks.
Analytic Continual Learning (ACL) offers a computationally efficient alternative to gradient-based approaches. Recent ACL methods are based on Recursive Least Squares (RLS) and have achieved the state-of-the-art results compared to other alternatives. However, they falter significantly in Class-Incremental Learning scenarios characterized by Long-Tailed distributions. While the ill-conditioning of the autocorrelation (Gram) matrix is a known limitation of RLS, we demonstrate that class imbalance exacerbates this issue into a distinct spectral pathology: "tail" classes suffer from severe spectral collapse, rendering their subspaces numerically indistinguishable from noise. Standard Ridge Regression ($L_2$) fails to address this effectively as it applies isotropic regularization - a uniform penalty that is insufficient to stabilize the tail without over-shrinking the head. To address this, we propose Geometry-Spectral Rectification (GSR), a theoretically grounded framework that treats long-tailed learning as a spectral regularization problem. Unlike standard isotropic regularization (Ridge) which uniformly penalizes all eigenvalues, GSR acts as an anisotropic spectral filter, selectively inflating the collapsed eigenvalues of tail classes. We construct a structured, data-dependent spectral perturbation matrix $Δ$ that selectively inflates collapsed tail eigen-directions of the Gram matrix. Theoretical analysis proves that GSR guarantees an improved stable rank for the Gram matrix, ensuring numerical stability. Extensive experiments show that GSR establishes a new state-of-the-art for analytic CIL, offering a superior trade-off between computational efficiency and robust generalization in long-tailed settings.
In overparameterized linear regression, many weak spectral directions act like a ridge penalty on the signal-bearing spectrum; negative ridge is the natural correction, pushing filters above one. The stable negative-ridge endpoint, however, is structurally limited: its pole must stay below the smallest nonzero empirical eigenvalue, and it anti-shrinks smaller eigenvalues more than larger ones. Early-stopped negative-shifted gradient descent escapes this constraint. Its filter is smooth at the would-be pole and mixed-sign-capable: above-ridgeless directions form a leading prefix, with lower directions shrunk or exposure-controlled while stopping sets the crossover. In a Gaussian spike-plus-flat model we discover a Marchenko-Pastur barrier: the shift that cancels the implicit penalty lies a bulk width above the smallest empirical eigenvalue, and the stopped path improves on every admissible endpoint by a polynomial factor in risk under explicit conditions. Our main theorem permits a general high-effective-rank tail: its trace sets the implicit floor, its squared spectrum controls exposure, and the floor-critical path recovers all head scales at once, beyond positive shrinkage and, once scales separate, every uniform rescaling of ridgeless. Handling the noncontractive shifted dynamics is the central technical challenge; localized Duhamel integrals control them. A finite-grid hold-out inequality transfers the separations to the validation-selected algorithm.
We present Spectral Consistent Flow (SC-Flow), a 3D medical image translation framework with a single function evaluation (1-NFE) in the latent space. This approach reformulates medical image translation as a stochastic Brownian bridge process that directly constructs a mapping between source and target modalities by predicting the support regularized mean velocity field. To mitigate modality entanglement, over-smoothing, and artifacts induced by the implicit low-pass modulation of the latent average velocity, we introduce a Spectral Consistency Corrector that dynamically regularizes the evolution of the power spectral density via learnable frequency-domain gain modulation. This mechanism establishes an explicit bridge between spatial textures and spectral energy flow, enabling the model to recover fine-grained anatomical fidelity while maintaining global structural coherence. Extensive experiments on four datasets demonstrate that SC-Flow delivers significantly more accurate, consistent, and robust performance across various translation scenarios.
Jason R. Brown, Patrick Leask, Lev McKinneycs.LG cs.AI
Emergent misalignment (EM) is a recently discovered phenomenon in LLMs where fine-tuning on a narrow misaligned task, such as writing insecure code, leads to broadly misaligned behaviour on unrelated prompts. Previous work has noted that the severity of EM is highly sensitive to training choices; however, we still lack a systematic characterisation of this sensitivity. We perform a sweep over several Qwen3 models, optimisers, datasets, and batch sizes, and find that the choice of optimiser has the largest effect, producing a 7x spread in misalignment rate. Surprisingly, model size has a negligible effect within the Qwen3 family. An additional sweep over 12 models from three families using Adam confirms that model scale (1B-235B) and family have negligible effects for that optimiser. Analysing the loss-alignment relationship on Qwen3-8B, we find that final log training loss is a strong predictor of alignment, and that stratifying by optimiser captures nearly all the residual variance. Training dynamics reveal that each optimiser follows a different trajectory through loss-alignment space, and that after significant training, the optimiser becomes more important than training loss as a predictor of alignment. Muon, the adaptive optimiser that preserves alignment the best, implicitly regularises for a more uniform distribution of singular values of the LoRA adapter. We evaluate this insight by training with an additional loss term that incentivises a flatter singular value spectrum, and find that this substantially recovers alignment for the more EM-prone adaptive optimisers (Adam and Lion), with negligible cost to training loss. These results identify optimiser choice as a key factor in EM severity, but show that spectral regularisation can substantially mitigate the effects of EM-prone optimisers.
World models are increasingly used for planning, yet most analyses of rollout error assume vector-valued states and scalar error amplification. Many planning environments, however, are naturally graph-structured: agents, tools, skills, routes, and dependencies interact through evolving relations. In this work, we study how prediction errors accumulate in Graph World Models (GWMs). We formulate fixed-edge and dynamic-edge GWM rollouts under a unified state-action transition framework and derive topology-aware error bounds. For fixed-edge rollouts, we show that long-horizon node error separates into a topology factor, governed by the graph spectral radius, and a model factor, governed by layer spectral norms. For dynamic-edge rollouts, we introduce a joint node-edge error operator that captures feedback between feature prediction and structure prediction, revealing when edge errors amplify future message passing. Motivated by these bounds, we propose Error-Aware GWM, a training objective that combines spectral regularization, rollout consistency, and critical-node weighting. Across synthetic graph topologies and heterogeneous agent-graph testbeds, we find that rollout error and planning regret grow with horizon, that dynamic-edge training is necessary when structure evolves, and that Error-Aware GWM improves long-horizon stability without sacrificing one-step accuracy. Our results characterize when graph world models remain reliable under autoregressive planning and when topology makes them fail.
Catastrophic forgetting in continual adaptation is usually studied through parameter drift, replay, or distillation, but these views do not identify which output-space directions are vulnerable. We give a function-space account in the NTK regime: new-task training induces old-task prediction drift through the cross-task kernel, yielding a closed-form predictor for the forgetting vector before any new-task gradient step. In frozen-backbone linear-head PEFT-CL, where the model is linear in the trainable parameters, the predictor is exact up to numerical precision; for nonlinear adapters/full fine-tuning, it is a local NTK approximation. The same expression reveals that forgetting concentrates in a small number of old-task NTK eigenmodes and under frozen linear heads gives a Kronecker scaling rule for the vulnerable rank. These results clarify the relation to prior NTK-overlap theory, explain why parameter-space regularizers can miss output-space interference, and motivate a targeted spectral regularizer.
Recent respiratory sound classification (RSC) studies largely rely on CLS-token driven self-attention architectures such as the Audio Spectrogram Transformer (AST). While effective at modeling global context, recent analyses suggest a low-pass filtering behavior that may reduce sensitivity to localized abnormal patterns. In this work, we investigate State Space Models (SSMs) as an alternative backbone for RSC. Using the Distilled Audio State Space model, we analyze intermediate representations through spectral response curves and observe stronger preservation of mid-to-high spatial-frequency components. Based on these observations, we introduce spectral-aware layer regularization using Gaussian convolution applied to selected layers. We further propose Dual-Axis Patch-Mix contrastive learning tailored to SSM-based audio models for robust representation learning. Experiments on the ICBHI benchmark show that our approach achieves 64.48% score, outperforming the AST baseline by 5%. Code is available at https://github.com/RSC-Toolkit/Lung-SRAD.
Latent diffusion and flow matching have emerged as leading approaches for synthetic turbulence generation, yet they systematically under-represent dissipation-range amplitudes. We introduce a latent flow matching framework with a spectrally regularized compression stage that directly targets this failure mode. On a 256^2 DNS dataset at Re_f \approx 2250, replacing an MSE-trained VAE with a zone-weighted log-spectral objective raises deep-dissipation retained spectral power from 25% to 94% in reconstruction and from 20% to 79% in unconditional generation. The improved latent representation also yields a substantially better sampling cost-fidelity tradeoff: the MSE-trained latent space imposes a fundamental quality ceiling near DD bias -0.70 that no integrator or step-count can overcome, while the spectrally regularized latent space reaches DD bias -0.117 at just 20 function evaluations. Mechanistically, encoder-decoder swap experiments show that the improvement is driven primarily by encoder-induced latent reorganization rather than decoder capacity, while a support-amplitude decomposition reveals that MSE-trained models behave as conservative suppression models, minimizing pointwise error by attenuating intermittent high-wavenumber structure. Both pipelines recover the second-order structure function and the correct sign of S_3, indicating the correct cascade direction without explicit supervision. A small residual gap in the magnitude of S_3 suggests that phase-coherent triadic organization remains a complementary axis to amplitude fidelity for future generative turbulence models.
Modern Transformer architectures frequently employ normalization mechanisms such as RMSNorm and Query-Key Normalization, making parts of the model approximately scale-invariant with respect to weight magnitudes. In this regime, standard Frobenius-norm weight decay acts purely along the radial direction of the weight space and cannot directly simplify the function represented by the normalized layer. We study grokking in small algorithmic tasks through this lens and propose \emph{Low-Rank Decay} (LRD), a nuclear-norm-like spectral regularizer whose subgradient -- the polar factor $UV^\top$ -- retains a tangential component even in the scale-invariant setting. This distinction has a concrete dynamical consequence: after the model memorizes the training set and task gradients vanish, L2 decay can no longer reshape the weight spectrum, whereas LRD continues to compress singular values in an $\ell_1$-like fashion. On modular arithmetic tasks, we find that LRD induces rapid effective-rank collapse in Query/Key matrices and expands the data-fraction boundary at which delayed generalization (grokking) occurs. We further provide a spectral-geometric interpretation through the ``needle-to-fan'' expansion of the nuclear-norm subdifferential near low-rank strata.