A language model p_θ(y | x) trained on reasoning tasks learns to solve problems via multiple distinct strategies, yet these strategies are implicit and entangled within the model's response distribution. We study the problem of decomposing the response distribution of a given pretrained language model into a structured, strategy-conditioned representation. Specifically, we learn a latent-variable factorization p_θ(y | x) (r_ϕ(z | x), g_ϕ(y | x,z)), where a router r maps each input to a distribution over latent strategies z and a generator g produces the response conditioned on that strategy. A key challenge is that the generator, initialized from the base model, already represents p_θ(y | x) without using z. Standard variational inference therefore gives the model no incentive to route information through z and can yield a severe form of posterior collapse. To address this, we propose a variational objective that measures fractional information gain relative to the base model's response loss and concentrates reconstruction pressure on tokens with high base model surprisal, encouraging z to encode strategy-relevant response variation. We introduce a benchmark of multi-strategy algorithmic tasks and show that this objective recovers latent codes aligned with distinct reference strategies while preserving the base model's response distribution.

Systematic, compositional generalization beyond the training distribution remains a core challenge in machine learning – and a critical bottleneck for the emergent reasoning abilities of modern language models. This work investigates out-of-distribution (OOD) generalization in Transformer networks using a GSM8K-style modular arithmetic on computational graphs task as a testbed. We introduce and explore a set of four architectural mechanisms aimed at enhancing OOD generalization: (i) input-adaptive recurrence; (ii) algorithmic supervision; (iii) anchored latent representations via a discrete bottleneck; and (iv) an explicit error-correction mechanism. Collectively, these mechanisms yield an architectural approach for native and scalable latent space reasoning in Transformer networks with robust algorithmic generalization capabilities. We complement these empirical results with a detailed mechanistic interpretability analysis that reveals how these mechanisms give rise to robust OOD generalization abilities.

We study the task of noiseless linear regression under Gaussian covariates in the presence of additive oblivious contamination. Specifically, we are given i.i.d.\ samples from a distribution $(x, y)$ on $\mathbb R^d \times \mathbb R$ with $x \sim \mathcal N(0,I_d)$ and $y = x^\top \beta + z$, where $z$ is drawn from an unknown distribution that is independent of $x$. Moreover, $z$ satisfies $\mathbb P[z = 0] = \alpha>0$. The goal is to accurately recover the regressor $\beta$ to small $\ell_2$-error. Ignoring computational considerations, this problem is known to be solvable using $O(d/\alpha)$ samples. On the other hand, the best known polynomial-time algorithms require $\Omega(d/\alpha^2)$ samples. Here we provide formal evidence that the quadratic dependence in $1/\alpha$ is inherent for efficient algorithms. Specifically, we show that any efficient Statistical Query algorithm for this task requires VSTAT complexity at least $\tilde{\Omega}(d^{1/2}/\alpha^2)$.

Relational reasoning is a central component of generally intelligent systems, enabling robust and data-efficient inductive generalization. Recent empirical evidence shows that many existing neural architectures, including Transformers, struggle with tasks requiring relational reasoning. In this work, we distinguish between two types of information: sensory information about the properties of individual objects, and relational information about the relationships between objects. While neural attention provides a powerful mechanism for controlling the flow of sensory information between objects, the Transformer lacks an explicit computational mechanism for routing and processing relational information. To address this limitation, we propose an architectural extension of the Transformer framework that we call the Dual Attention Transformer (DAT), featuring two distinct attention mechanisms: sensory attention for directing the flow of sensory information, and a novel relational attention mechanism for directing the flow of relational information. We empirically evaluate DAT on a diverse set of tasks ranging from synthetic relational benchmarks to complex real-world tasks such as language modeling and visual processing. Our results demonstrate that integrating explicit relational computational mechanisms into the Transformer architecture leads to significant performance gains in terms of data efficiency and parameter efficiency.

We study confidence interval construction for linear regression under Huber's contamination model, where an unknown fraction of noise variables is arbitrarily corrupted. While robust point estimation in this setting is well understood, statistical inference remains challenging, especially because the contamination proportion is not identifiable from the data. We develop a new algorithm that constructs confidence intervals for individual regression coefficients without any prior knowledge of the contamination level. Our method is based on a Z-estimation framework using a smooth estimating function. The method directly quantifies the uncertainty of the estimating equation after a preprocessing step that decorrelates covariates associated with the nuisance parameters. We show that the resulting confidence interval has valid coverage uniformly over all contamination distributions and attains an optimal length of order $O(1/\sqrt{n(1-ε)^2})$, matching the rate achievable when the contamination proportion $ε$ is known. This result stands in sharp contrast to the adaptation cost of robust interval estimation observed in the simpler Gaussian location model.

Learning complex functions that involve multi-step reasoning poses a significant challenge for standard supervised learning from input-output examples. Chain-of-thought (CoT) supervision, which augments training data with intermediate reasoning steps to provide a richer learning signal, has driven recent advances in large language model reasoning. This paper develops a statistical theory of learning under CoT supervision. Central to the theory is the *CoT information*, which measures the additional discriminative power offered by the chain-of-thought for distinguishing hypotheses with different end-to-end behaviors. The main theoretical results demonstrate how CoT supervision can yield significantly faster learning rates compared to standard end-to-end supervision, with both upper bounds and information-theoretic lower bounds characterized by the CoT information.

An evolving area of research in deep learning is the study of architectures and inductive biases that support the learning of relational feature representations. In this paper, we address the challenge of learning representations of hierarchical relations—that is, higher-order relational patterns among groups of objects. We introduce “relational convolutional networks”, a neural architecture equipped with computational mechanisms that capture progressively more complex relational features through the composition of simple modules. A key component of this framework is a novel operation that captures relational patterns in groups of objects by convolving graphlet filters—learnable templates of relational patterns—against subsets of the input. Composing relational convolutions gives rise to a deep architecture that learns representations of higher-order, hierarchical relations. We present the motivation and details of the architecture, together with a set of experiments to demonstrate how relational convolutional networks can provide an effective framework for modeling relational tasks that have hierarchical structure.

An extension of Transformers is proposed that enables explicit relational reasoning through a novel module called the Abstractor. At the core of the Abstractor is a variant of attention called relational cross-attention. The approach is motivated by an architectural inductive bias for relational learning that disentangles relational information from object-level features. This enables explicit relational reasoning, supporting abstraction and generalization from limited data. The Abstractor is first evaluated on simple discriminative relational tasks and compared to existing relational architectures. Next, the Abstractor is evaluated on purely relational sequence-to-sequence tasks, where dramatic improvements are seen in sample efficiency compared to standard Transformers. Finally, Abstractors are evaluated on a collection of tasks based on mathematical problem solving, where consistent improvements in performance and sample efficiency are observed.

A central challenge for cognitive science is to explain how abstract concepts are acquired from limited experience. This has often been framed in terms of a dichotomy between connectionist and symbolic cognitive models. Here, we highlight a recently emerging line of work that suggests a novel reconciliation of these approaches, by exploiting an inductive bias that we term the relational bottleneck. In that approach, neural networks are constrained via their architecture to focus on relations between perceptual inputs, rather than the attributes of individual inputs. We review a family of models that employ this approach to induce abstractions in a data-efficient manner, emphasizing their potential as candidate models for the acquisition of abstract concepts in the human mind and brain.

Data Science (JDS) is a joint journal of the Association for Computing Machinery (ACM) and the Institute of Mathematical Statistics (IMS), publishing high-impact research from all areas of data science, across foundations, applications, and systems.The scope of the journal is multi-disciplinary and broad, spanning statistics, machine learning, computer systems, and the societal implications of data science.JDS accepts original papers and novel surveys that summarize and organize critical subject areas, as well as opinion papers.The journal bridges communities across the two scientific societies, representing diverse areas of research expertise.By combining elements of journal and conference publishing, the journal aims to serve the needs of a rapidly evolving research landscape.The journal accepts submissions three times a year.Each submission receives three expert reviews from a standing reviewing board, and the three-month initial reviewing process includes author feedback, review quality analysis, and reviewer discussions to reach a decision and provide constructive feedback.After the initial review process, which proceeds on a fixed schedule typical of conferences, authors prepare revisions, taking as much time as required.Accepted papers are published online on the JDS website immediately after the camera-ready sources have been prepared and checked, followed by full publication in the first available issue.This inaugural issue of the journal includes four research papers that intersect the areas of machine learning, artificial intelligence, databases, and data management systems.The papers were submitted upon invitation by the editors to area experts.Following JDS guidelines, the papers were reviewed by experts in the relevant communities.The topics and perspectives seen in this work are signs of the diversity, impact, and high standards that JDS aims to achieve as the journal ramps up.The subsequent two issues will also include invited submissions, representing additional research at the interface of statistics, machine learning, computer systems, and other areas that make up the growing landscape of data science.

Inner products of neural network feature maps arises in a wide variety of machine learning frameworks as a method of modeling relations between inputs. This work studies the approximation properties of inner products of neural networks. It is shown that the inner product of a multi-layer perceptron with itself is a universal approximator for symmetric positive-definite relation functions. In the case of asymmetric relation functions, it is shown that the inner product of two different multi-layer perceptrons is a universal approximator. In both cases, a bound is obtained on the number of neurons required to achieve a given accuracy of approximation. In the symmetric case, the function class can be identified with kernels of reproducing kernel Hilbert spaces, whereas in the asymmetric case the function class can be identified with kernels of reproducing kernel Banach spaces. Finally, these approximation results are applied to analyzing the attention mechanism underlying Transformers, showing that any retrieval mechanism defined by an abstract preorder can be approximated by attention through its inner product relations. This result uses the Debreu representation theorem in economics to represent preference relations in terms of utility functions.

Much of what we remember is not because of intentional selection, but simply a by-product of perceiving. This raises a foundational question about the architecture of the mind: how does perception interface with and influence memory? Here, inspired by a classic proposal relating perceptual processing to memory durability, the level-of-processing theory, we present a sparse coding model for compressing feature embeddings of images, and show that the reconstruction residuals from this model predict how well images are encoded into memory. In an open memorability dataset of scene images, we show that reconstruction error not only explains memory accuracy, but also response latencies during retrieval, subsuming, in the latter case, all of the variance explained by powerful vision-only models. We also confirm a prediction of this account with ‘model-driven psychophysics’. This work establishes reconstruction error as an important signal interfacing perception and memory, possibly through adaptive modulation of perceptual processing. Using a computational model to quantify difficulty in reconstructing images from compressed codes, Lin et al. show that reconstruction errors interface perception and memory by modulating how well images are encoded.

A maturing area of research in deep learning is the development of architectures that can learn explicit representations of relational features. In this paper, we focus on the problem of learning representations of hierarchical relations, proposing an architectural framework we call"relational convolutional networks". Given a sequence of objects, a"multi-dimensional inner product relation"module produces a relation tensor describing all pairwise relations. A"relational convolution"layer then transforms the relation tensor into a sequence of new objects, each describing the relations within some group of objects at the previous layer. Graphlet filters, analogous to filters in convolutional neural networks, represent a template of relations against which the relation tensor is compared at each grouping. Repeating this yields representations of higher-order, hierarchical relations. We present the motivation and details of the architecture, together with a set of experiments to demonstrate how relational convolutional networks can provide an effective framework for modeling relational tasks that have hierarchical structure.

Much of what we remember is not due to intentional selection, but simply a by-product of perceiving. This raises a foundational question about the architecture of the mind: How does perception interface with and influence memory? Here, inspired by a classic proposal relating perceptual processing to memory durability, the level-of-processing theory, we present a sparse coding model for compressing feature embeddings of images, and show that the reconstruction residuals from this model predict how well images are encoded into memory. In an open memorability dataset of scene images, we show that reconstruction error not only explains memory accuracy but also response latencies during retrieval, subsuming, in the latter case, all of the variance explained by powerful vision-only models. We also confirm a prediction of this account with 'model-driven psychophysics'. This work establishes reconstruction error as a novel signal interfacing perception and memory, possibly through adaptive modulation of perceptual processing.

Decades of work have established the reconstructive nature of memory. Yet these works focus almost exclusively on retrieval. Here we ask whether the brain recruits reconstructive processing -- in a more automatic and fast form -- even at the earliest stage of memory formation, during perceptual encoding. Image memorability -- that some images are systematically better remembered than others -- provides an opportunity to investigate what bridges perception and memory. Existing accounts of memorability solely evaluate bottom-up feature hierarchies optimized for image classification (using standard deep convolutional neural networks [DCNNs]) as the underlying mechanism but fail to consider the role of reconstructive processes during visual encoding, which can support generative functions and compression during memory formation. In computational models, such reconstructive processes are often implemented in non-feedforward modules (e.g., top-down, lateral) and we hypothesize that they should express a distinct temporal signature in behavior. To test this hypothesis, we used two models to capture reconstructive processing during visual encoding: a sparse coding model and a generative adversarial network. In Study 1, in a scene memorability dataset with over 2000 images, we found that images with larger reconstruction error are more memorable (ps<.001), and that reconstruction error captures additional variance in memorability (ps<.001) beyond what can be explained using distinctiveness, a measure derived from the feature space of a DCNN trained for classification. To demonstrate that the variances captured by distinctiveness and reconstruction error result from functionally distinct processes, we ran a pre-registered Study 2 (N=45) using the rapid serial visual presentation (RSVP) paradigm with varying encoding times (34 to 167 ms). We found that images with large reconstruction error benefit more from longer encoding times than images with small reconstruction error, controlling for distinctiveness (all ps<.05). These results reveal reconstruction error as a previously unrecognized source of image memorability.

Animals have evolved sophisticated visual circuits to solve a vital inference problem: detecting whether or not a visual signal corresponds to an object on a collision course. Such events are detected by specific circuits sensitive to visual looming, or objects increasing in size. Various computational models have been developed for these circuits, but how the collision-detection inference problem itself shapes the computational structures of these circuits remains unknown. Here, inspired by the distinctive structures of LPLC2 neurons in the visual system of Drosophila, we build anatomically-constrained shallow neural network models and train them to identify visual signals that correspond to impending collisions. Surprisingly, the optimization arrives at two distinct, opposing solutions, only one of which matches the actual dendritic weighting of LPLC2 neurons. Both solutions can solve the inference problem with high accuracy when the population size is large enough. The LPLC2-like solutions reproduces experimentally observed LPLC2 neuron responses for many stimuli, and reproduces canonical tuning of loom sensitive neurons, even though the models are never trained on neural data. Thus, LPLC2 neuron properties and tuning are predicted by optimizing an anatomically-constrained neural network to detect impending collisions. More generally, these results illustrate how optimizing inference tasks that are important for an animal's perceptual goals can reveal and explain computational properties of specific sensory neurons.

Local patterns of excitation and inhibition that can generate neural waves are studied as a computational mechanism underlying the organization of neuronal tunings. Sparse coding algorithms based on networks of excitatory and inhibitory neurons are proposed that exhibit topographic maps as the receptive fields are adapted to input stimuli. Motivated by a leaky integrate-and-fire model of neural waves, we propose an activation model that is more typical of artificial neural networks. Computational experiments with the activation model using both natural images and natural language text are presented. In the case of images, familiar "pinwheel" patterns of oriented edge detectors emerge; in the case of text, the resulting topographic maps exhibit a 2-dimensional representation of granular word semantics. Experiments with a synthetic model of somatosensory input are used to investigate how the network dynamics may affect plasticity of neuronal maps under changes to the inputs.

Stochastic gradient descent with backpropagation is the workhorse of artificial neural networks. It has long been recognized that backpropagation fails to be a biologically plausible algorithm. Fundamentally, it is a non-local procedure-updating one neuron's synaptic weights requires knowledge of synaptic weights or receptive fields of downstream neurons. This limits the use of artificial neural networks as a tool for understanding the biological principles of information processing in the brain. Lillicrap et al. (2016) propose a more biologically plausible "feedback alignment" algorithm that uses random and fixed backpropagation weights, and show promising simulations. In this paper we study the mathematical properties of the feedback alignment procedure by analyzing convergence and alignment for two-layer networks under squared error loss. In the overparameterized setting, we prove that the error converges to zero exponentially fast, and also that regularization is necessary in order for the parameters to become aligned with the random backpropagation weights. Simulations are given that are consistent with this analysis and suggest further generalizations. These results contribute to our understanding of how biologically plausible algorithms might carry out weight learning in a manner different from Hebbian learning, with performance that is comparable with the full non-local backpropagation algorithm.