Alper T. Erdogan

Serdar Ozsoy, Shadi Hamdan, Sercan Ö. Arik et al.

Self-supervised learning allows AI systems to learn effective representations from large amounts of data using tasks that do not require costly labeling. Mode collapse, i.e., the model producing identical representations for all inputs, is a central problem to many self-supervised learning approaches, making self-supervised tasks, such as matching distorted variants of the inputs, ineffective. In this article, we argue that a straightforward application of information maximization among alternative latent representations of the same input naturally solves the collapse problem and achieves competitive empirical results. We propose a self-supervised learning method, CorInfoMax, that uses a second-order statistics-based mutual information measure that reflects the level of correlation among its arguments. Maximizing this correlative information measure between alternative representations of the same input serves two purposes: (1) it avoids the collapse problem by generating feature vectors with non-degenerate covariances; (2) it establishes relevance among alternative representations by increasing the linear dependence among them. An approximation of the proposed information maximization objective simplifies to a Euclidean distance-based objective function regularized by the log-determinant of the feature covariance matrix. The regularization term acts as a natural barrier against feature space degeneracy. Consequently, beyond avoiding complete output collapse to a single point, the proposed approach also prevents dimensional collapse by encouraging the spread of information across the whole feature space. Numerical experiments demonstrate that CorInfoMax achieves better or competitive performance results relative to the state-of-the-art SSL approaches.

Mustafa Uzun, Mete Erdogan, Cengiz Pehlevan et al.

We introduce Score Broadcast and Decorrelation (SBD), a principled framework for broadcast-based credit assignment for general families of differentiable losses. Error broadcast is a biologically plausible alternative to backpropagation that sends output information to hidden layers without weight transport. The Error Broadcast and Decorrelation (EBD) framework, recently introduced for the mean-squared-error (MSE) setting, grounded this mechanism in the stochastic orthogonality of optimal estimators, under which the optimal residual is orthogonal to functions of the input. We generalize that foundation by introducing an orthogonality principle between the output score (the gradient of loss with respect to the final-layer output) and hidden-layer activations, which holds whenever the optimal score has conditional mean zero. This single principle unifies broadcast-based credit assignment across the standard differentiable-loss families, including cross-entropy, Bregman divergences, proper scoring rules, and exponential-family negative log-likelihoods. The framework supplies a theoretical grounding for the three-factor learning rule under general losses, with the neuromodulatory factor derived as the broadcast loss score. We derive the cross-entropy case explicitly, characterize the admissible loss class, and introduce a score vector expansion technique that enriches the broadcast signal while preserving the orthogonality framework. Experiments on CIFAR-10 and Tiny ImageNet show that SBD substantially improves over existing broadcast approaches, with score vector expansion delivering further gains. Overall, this work identifies the loss score as the signal to broadcast, supplies the orthogonality theory and theoretical grounding for the three-factor learning rule from neuroscience, and shows how score vector expansion enriches the decorrelation directions of the resulting objective.

Bariscan Bozkurt, Cengiz Pehlevan, Alper T. Erdogan

Extraction of latent sources of complex stimuli is critical for making sense of the world. While the brain solves this blind source separation (BSS) problem continuously, its algorithms remain unknown. Previous work on biologically-plausible BSS algorithms assumed that observed signals are linear mixtures of statistically independent or uncorrelated sources, limiting the domain of applicability of these algorithms. To overcome this limitation, we propose novel biologically-plausible neural networks for the blind separation of potentially dependent/correlated sources. Differing from previous work, we assume some general geometric, not statistical, conditions on the source vectors allowing separation of potentially dependent/correlated sources. Concretely, we assume that the source vectors are sufficiently scattered in their domains which can be described by certain polytopes. Then, we consider recovery of these sources by the Det-Max criterion, which maximizes the determinant of the output correlation matrix to enforce a similar spread for the source estimates. Starting from this normative principle, and using a weighted similarity matching approach that enables arbitrary linear transformations adaptable by local learning rules, we derive two-layer biologically-plausible neural network algorithms that can separate mixtures into sources coming from a variety of source domains. We demonstrate that our algorithms outperform other biologically-plausible BSS algorithms on correlated source separation problems.

Bariscan Bozkurt, Ates Isfendiyaroglu, Cengiz Pehlevan et al.

The brain effortlessly extracts latent causes of stimuli, but how it does this at the network level remains unknown. Most prior attempts at this problem proposed neural networks that implement independent component analysis which works under the limitation that latent causes are mutually independent. Here, we relax this limitation and propose a biologically plausible neural network that extracts correlated latent sources by exploiting information about their domains. To derive this network, we choose maximum correlative information transfer from inputs to outputs as the separation objective under the constraint that the outputs are restricted to their presumed sets. The online formulation of this optimization problem naturally leads to neural networks with local learning rules. Our framework incorporates infinitely many source domain choices and flexibly models complex latent structures. Choices of simplex or polytopic source domains result in networks with piecewise-linear activation functions. We provide numerical examples to demonstrate the superior correlated source separation capability for both synthetic and natural sources.

Gokcan Tatli, Alper T. Erdogan

We introduce a Bayesian perspective for the structured matrix factorization problem. The proposed framework provides a probabilistic interpretation for existing geometric methods based on determinant minimization. We model input data vectors as linear transformations of latent vectors drawn from a distribution uniform over a particular domain reflecting structural assumptions, such as the probability simplex in Nonnegative Matrix Factorization and polytopes in Polytopic Matrix Factorization. We represent the rows of the linear transformation matrix as vectors generated independently from a normal distribution whose covariance matrix is inverse Wishart distributed. We show that the corresponding maximum a posteriori estimation problem boils down to the robust determinant minimization approach for structured matrix factorization, providing insights about parameter selections and potential algorithmic extensions.

Mete Erdogan, Cengiz Pehlevan, Alper T. Erdogan

We introduce Error Broadcast and Decorrelation (EBD), a novel learning framework for neural networks that addresses credit assignment by directly broadcasting output errors to individual layers, circumventing weight transport of backpropagation. EBD is rigorously grounded in the stochastic orthogonality property of Minimum Mean Square Error estimators. This fundamental principle states that the error of an optimal estimator is orthogonal to functions of the input. Guided by this insight, EBD defines layerwise loss functions that directly penalize correlations between layer activations and output errors, thereby establishing a principled foundation for error broadcasting. This theoretically sound mechanism naturally leads to the experimentally observed three-factor learning rule and integrates with biologically plausible frameworks to enhance performance and plausibility. Numerical experiments demonstrate EBD's competitive or better performance against other error-broadcast methods on benchmark datasets. Our findings establish EBD as an efficient, biologically plausible, and principled alternative for neural network training. The implementation is available at: https://github.com/meterdogan07/error-broadcast-decorrelation.

Gokcan Tatli, Alper T. Erdogan

We introduce Polytopic Matrix Factorization (PMF) as a novel data decomposition approach. In this new framework, we model input data as unknown linear transformations of some latent vectors drawn from a polytope. In this sense, the article considers a semi-structured data model, in which the input matrix is modeled as the product of a full column rank matrix and a matrix containing samples from a polytope as its column vectors. The choice of polytope reflects the presumed features of the latent components and their mutual relationships. As the factorization criterion, we propose the determinant maximization (Det-Max) for the sample autocorrelation matrix of the latent vectors. We introduce a sufficient condition for identifiability, which requires that the convex hull of the latent vectors contains the maximum volume inscribed ellipsoid of the polytope with a particular tightness constraint. Based on the Det-Max criterion and the proposed identifiability condition, we show that all polytopes that satisfy a particular symmetry restriction qualify for the PMF framework. Having infinitely many polytope choices provides a form of flexibility in characterizing latent vectors. In particular, it is possible to define latent vectors with heterogeneous features, enabling the assignment of attributes such as nonnegativity and sparsity at the subvector level. The article offers examples illustrating the connection between polytope choices and the corresponding feature representations.

Alper T. Erdogan, Cengiz Pehlevan

An important problem encountered by both natural and engineered signal processing systems is blind source separation. In many instances of the problem, the sources are bounded by their nature and known to be so, even though the particular bound may not be known. To separate such bounded sources from their mixtures, we propose a new optimization problem, Bounded Similarity Matching (BSM). A principled derivation of an adaptive BSM algorithm leads to a recurrent neural network with a clipping nonlinearity. The network adapts by local learning rules, satisfying an important constraint for both biological plausibility and implementability in neuromorphic hardware.