arXiv subjects

Yohai Bar Sinai

Publications and source records attributed to Yohai Bar Sinai.

3 recordsLinked to original sources

arXiv2026

The Implicit Bias of Logit Regularization

Logit regularization, the addition of a convex penalty directly in logit space, is widely used in modern classifiers, with label smoothing as a prominent example. While such methods often improve calibration and generalization, their mechanism remains under-explored. In this work, we analyze a general class of such logit regularizers in the context of linear classification, and demonstrate that they induce an implicit bias of logit clustering around finite per-sample targets. For Gaussian data, or whenever logits are sufficiently clustered, we prove that logit clustering drives the weight vector to align exactly with Fisher's Linear Discriminant. To demonstrate the consequences, we study a simple signal-plus-noise model in which this transition has dramatic effects: Logit regularization halves the critical sample complexity and induces grokking in the small-noise limit, while making generalization robust to noise. Our results extend the theoretical understanding of label smoothing and highlight the efficacy of a broader class of logit-regularization methods.

stat.ML↗

arXiv2022

Beyond Quality and Quantity: Contact Distribution Encodes Frictional Strength

Classically, the quantity of contact area $A_R$ between two bodies is considered a proxy for the force of friction. However, bond density across the interface - quality of contact - is also relevant, and contemporary debate often centers around the relative importance of these two factors. In this work, we demonstrate that a third factor, often overlooked, plays a significant role in static frictional strength: the distribution of contact. We perform static friction measurements, $μ$, on three pairs of solid blocks while imaging the contact plane. By using linear regression on hundreds of image-$μ$ pairs, we are able to predict future friction measurements with 3 to 7 times better accuracy than existing benchmarks, including total quantity of contact area. Our model has no access to quality of contact, and we therefore conclude that a large portion of the interfacial state is encoded in the spatial distribution of contact, rather than its quality or quantity.

cond-mat.soft↗

arXiv2013

Slow rupture of frictional interfaces

The failure of frictional interfaces and the spatiotemporal structures that accompany it are central to a wide range of geophysical, physical and engineering systems. Recent geophysical and laboratory observations indicated that interfacial failure can be mediated by slow slip rupture phenomena which are distinct from ordinary, earthquake-like, fast rupture. These discoveries have influenced the way we think about frictional motion, yet the nature and properties of slow rupture are not completely understood. We show that slow rupture is an intrinsic and robust property of simple non-monotonic rate-and-state friction laws. It is associated with a new velocity scale $c_{min}$, determined by the friction law, below which steady state rupture cannot propagate. We further show that rupture can occur in a continuum of states, spanning a wide range of velocities from $c_{min}$ to elastic wave-speeds, and predict different properties for slow rupture and ordinary fast rupture. Our results are qualitatively consistent with recent high-resolution laboratory experiments and may provide a theoretical framework for understanding slow rupture phenomena along frictional interfaces.

cond-mat.mtrl-sci↗