Discrete structures are currently second-class in differentiable programming. Since functions over discrete structures lack overt derivatives, differentiable programs do not differentiate through them and limit where they can be used. For example, when programming a neural network, conditionals and iteration cannot be used everywhere; they can break the derivatives necessary for gradient-based learning to work. This limits the class of differentiable algorithms we can directly express, imposing restraints on how we build neural networks and differentiable programs more generally. However, these restraints are not fundamental. Recent work shows conditionals can be first-class, by compiling them into differentiable form as linear neurons. Similarly, this work shows iteration can be first-class---by compiling to linear recurrent neurons. We present a minimal typed, higher-order and linear programming language with iteration called Cajal(N). We prove its programs compile correctly to recurrent neurons, allowing discrete algorithms to be expressed in a differentiable form compatible with gradient-based learning. With our implementation, we conduct two experiments where we link these recurrent neurons against a neural network solving an iterative image transformation task. This determines part of its function prior to learning. As a result, the network learns faster and with greater data-efficiency relative to a neural network programmed without first-class iteration. A key lesson is that recurrent neurons enable a rich interplay between learning and the discrete structures of ordinary programming.

We don’t program neural networks directly. Instead, we rely on an indirect style where learning algorithms, like gradient descent, determine a neural network’s function by learning from data. This indirect style is often a virtue; it empowers us to solve problems that were previously impossible. But it lacks discrete structure. We can’t compile most algorithms into a neural network—even if these algorithms could help the network learn. This limitation occurs because discrete algorithms are not obviously differentiable, making them incompatible with the gradient-based learning algorithms that determine a neural network’s function. To address this, we introduce Cajal ( ⊸ , 𝟚 ): a typed, higher-order and linear programming language intended to be a minimal vehicle for exploring a direct style of programming neural networks. We prove Cajal ( ⊸ , 𝟚 ) programs compile to linear neurons, allowing discrete algorithms to be expressed in a differentiable form compatible with gradient-based learning. With our implementation of Cajal ( ⊸ , 𝟚 ), we conduct several experiments where we link these linear neurons against other neural networks to determine part of their function prior to learning. Linking with these neurons allows networks to learn faster, with greater data-efficiency, and in a way that’s easier to debug. A key lesson is that linear programming languages provide a path towards directly programming neural networks, enabling a rich interplay between learning and the discrete structures of ordinary programming.

Object binding, the brain’s ability to bind the many features that collectively represent an object into a coherent whole, is central to human cognition. It groups low-level perceptual features into high‑level object representations, stores those objects efficiently and compositionally in memory, and supports human reasoning about individual object instances. While prior work often imposes object-centric attention (e.g., Slot Attention) explicitly to probe these benefits, it remains unclear whether this ability naturally emerges in pre-trained Vision Transformers (ViTs). Intuitively, they could: recognizing which patches belong to the same object should be useful for downstream prediction and thus guide attention. Motivated by the quadratic nature of self-attention, we hypothesize that ViTs represent whether two patches belong to the same object, a property we term *IsSameObject*. We decode *IsSameObject* from patch embeddings across ViT layers using a quadratic similarity probe, which reaches over 90\% accuracy. Crucially, this object-binding capability emerges reliably in DINO, CLIP, and ImageNet-supervised ViTs, but is markedly weaker in MAE, suggesting that binding is not a trivial architectural artifact, but an ability acquired through specific pretraining objectives. We further discover that *IsSameObject* is encoded in a low-dimensional subspace on top of object features, and that this signal actively guides attention. Ablating *IsSameObject* from model activations degrades downstream performance and works against the learning objective, implying that emergent object binding naturally serves the pretraining objective. Our findings challenge the view that ViTs lack object binding and highlight how symbolic knowledge of “which parts belong together” emerges naturally in a connectionist system.

Brain-computer interfaces (BCIs) promise to enable vital functions, such as speech and prosthetic control, for individuals with neuromotor impairments. Central to their success are neural decoders, models that map neural activity to intended behavior. Current learning-based decoding approaches fall into two classes: simple, causal models that lack generalization, or complex, non-causal models that generalize and scale offline but struggle in real-time settings. Both face a common challenge, their reliance on power-hungry artificial neural network backbones, which makes integration into real-world, resource-limited systems difficult. Spiking neural networks (SNNs) offer a promising alternative. Because they operate causally (i.e. only on present and past inputs) these models are suitable for real-time use, and their low energy demands make them ideal for battery-constrained environments. To this end, we introduce **Spikachu: a scalable, causal, and energy-efficient neural decoding framework based on SNNs**. Our approach processes binned spikes directly by projecting them into a shared latent space, where spiking modules, adapted to the timing of the input, extract relevant features; these latent representations are then integrated and decoded to generate behavioral predictions. We evaluate our approach on 113 recording sessions from 6 non-human primates, totaling 43 hours of recordings. Our method outperforms causal baselines when trained on single sessions using between 2.26× and 418.81× less energy. Furthermore, we demonstrate that scaling up training to multiple sessions and subjects improves performance and enables few-shot transfer to unseen sessions, subjects, and tasks. Overall, Spikachu introduces a scalable, online-compatible neural decoding framework based on SNNs, whose performance is competitive relative to state-of-the-art models while consuming orders of magnitude less energy.

Understanding the causal effects of civility is critical when analyzing online social communication, yet measuring causality is difficult. A/B tests and other randomized experiments are the gold standard for establishing causal effects but they are inapplicable in this setting due to 1) the inability to control civility levels in an experiment, and more importantly, 2) ethical constraints on intentionally randomizing civility levels. We develop a novel quasi-experimental approach to quantify the causal effect of civility in online communities on the Roblox social 3D platform without requiring explicit randomization. This method uses residual stochasticity in the "matchmaking" assignment of users to servers as a quasi-randomization mechanism in observational historical data. We find that assigning a user to a server with higher levels of civil communication could increase engagement time by as much as 1.5% in particular experiences. Given the 4.8B person hours spent monthly on the platform, this implies a potential increase of over 8,000 person years of social interaction every month. Furthermore, this effect is mis-estimated by non-causal methods. Quasi-experimental approaches promise new avenues for measuring the causal impact of user behavior in online communities without adversely affecting users through randomized experiments.

Deep learning based neural decoding from stereotactic electroencephalography (sEEG) would likely benefit from scaling up both dataset and model size. To achieve this, combining data across multiple subjects is crucial. However, in sEEG cohorts, each subject has a variable number of electrodes placed at distinct locations in their brain, solely based on clinical needs. Such heterogeneity in electrode number/placement poses a significant challenge for data integration, since there is no clear correspondence of the neural activity recorded at distinct sites between individuals. Here we introduce seegnificant: a training framework and architecture that can be used to decode behavior across subjects using sEEG data. We tokenize the neural activity within electrodes using convolutions and extract long-term temporal dependencies between tokens using self-attention in the time dimension. The 3D location of each electrode is then mixed with the tokens, followed by another self-attention in the electrode dimension to extract effective spatiotemporal neural representations. Subject-specific heads are then used for downstream decoding tasks. Using this approach, we construct a multi-subject model trained on the combined data from 21 subjects performing a behavioral task. We demonstrate that our model is able to decode the trial-wise response time of the subjects during the behavioral task solely from neural data. We also show that the neural representations learned by pretraining our model across individuals can be transferred in a few-shot manner to new subjects. This work introduces a scalable approach towards sEEG data integration for multi-subject model training, paving the way for cross-subject generalization for sEEG decoding.

The brain learns representations of sensory information from experience, but the algorithms by which it does so remain unknown. One popular theory formalizes representations as inferred factors in a generative model of sensory stimuli, meaning that learning must improve this generative model and inference procedure. This framework underlies many classic computational theories of sensory learning, such as Boltzmann machines, the Wake/Sleep algorithm, and a more recent proposal that the brain learns with an adversarial algorithm that compares waking and dreaming activity. However, in order for such theories to provide insights into the cellular mechanisms of sensory learning, they must be first linked to the cell types in the brain that mediate them. In this study, we examine whether a subtype of cortical interneurons might mediate sensory learning by serving as discriminators, a crucial component in an adversarial algorithm for representation learning. We describe how such interneurons would be characterized by a plasticity rule that switches from Hebbian plasticity during waking states to anti-Hebbian plasticity in dreaming states. Evaluating the computational advantages and disadvantages of this algorithm, we find that it excels at learning representations in networks with recurrent connections but scales poorly with network size. This limitation can be partially addressed if the network also oscillates between evoked activity and generative samples on faster timescales. Consequently, we propose that an adversarial algorithm with interneurons as discriminators is a plausible and testable strategy for sensory learning in biological systems.

When a neuron is driven beyond its threshold, it spikes. The fact that it does not communicate its continuous membrane potential is usually seen as a computational liability. Here we show that this spiking mechanism allows neurons to produce an unbiased estimate of their causal influence, and a way of approximating gradient descent-based learning. Importantly, neither activity of upstream neurons, which act as confounders, nor downstream non-linearities bias the results. We show how spiking enables neurons to solve causal estimation problems and that local plasticity can approximate gradient descent using spike discontinuity learning.

To understand the neural mechanisms underlying brain function, neuroscientists aim to quantify causal interactions between neurons, for instance by perturbing the activity of neuron A and measuring the effect on neuron B. Recently, manipulating neuron activity using light-sensitive opsins, optogenetics, has increased the specificity of neural perturbation. However, using widefield optogenetic interventions, multiple neurons are usually perturbed, producing a confound-any of the stimulated neurons can have affected the postsynaptic neuron making it challenging to discern which neurons produced the causal effect. Here, we show how such confounds produce large biases in interpretations. We explain how confounding can be reduced by combining instrumental variables (IV) and difference in differences (DiD) techniques from econometrics. Combined, these methods can estimate (causal) effective connectivity by exploiting the weak, approximately random signal resulting from the interaction between stimulation and the absolute refractory period of the neuron. In simulated neural networks, we find that estimates using ideas from IV and DiD outperform naïve techniques suggesting that methods from causal inference can be useful to disentangle neural interactions in the brain.

Neural networks are versatile tools for computation, having the ability to approximate a broad range of functions. An important problem in the theory of deep neural networks is expressivity; that is, we want to understand the functions that are computable by a given network. We study real, infinitely differentiable (smooth) hierarchical functions implemented by feedforward neural networks via composing simpler functions in two cases: (1) each constituent function of the composition has fewer inputs than the resulting function and (2) constituent functions are in the more specific yet prevalent form of a nonlinear univariate function (e.g., tanh) applied to a linear multivariate function. We establish that in each of these regimes, there exist nontrivial algebraic partial differential equations (PDEs) that are satisfied by the computed functions. These PDEs are purely in terms of the partial derivatives and are dependent only on the topology of the network. Conversely, we conjecture that such PDE constraints, once accompanied by appropriate nonsingularity conditions and perhaps certain inequalities involving partial derivatives, guarantee that the smooth function under consideration can be represented by the network. The conjecture is verified in numerous examples, including the case of tree architectures, which are of neuroscientific interest. Our approach is a step toward formulating an algebraic description of functional spaces associated with specific neural networks, and may provide useful new tools for constructing neural networks.

Physiological experiments have highlighted how the dendrites of biological neurons can nonlinearly process distributed synaptic inputs. However, it is unclear how aspects of a dendritic tree, such as its branched morphology or its repetition of presynaptic inputs, determine neural computation beyond this apparent nonlinearity. Here we use a simple model where the dendrite is implemented as a sequence of thresholded linear units. We manipulate the architecture of this model to investigate the impacts of binary branching constraints and repetition of synaptic inputs on neural computation. We find that models with such manipulations can perform well on machine learning tasks, such as Fashion MNIST or Extended MNIST. We find that model performance on these tasks is limited by binary tree branching and dendritic asymmetry and is improved by the repetition of synaptic inputs to different dendritic branches. These computational experiments further neuroscience theory on how different dendritic properties might determine neural computation of clearly defined tasks.

The output of a neural network depends on its architecture and weights in a highly nonlinear way, and it is often assumed that a network’s parameters cannot be recovered from its output. Here, we prove that, in fact, it is frequently possible to reconstruct the architecture, weights, and biases of a deep ReLU network by observing only its output. We leverage the fact that every ReLU network defines a piecewise linear function, where the boundaries between linear regions correspond to inputs for which some neuron in the network switches between inactive and active ReLU states. By dissecting the set of region boundaries into components associated with particular neurons, we show both theoretically and empirically that it is possible to recover the weights of neurons and their arrangement within the network, up to isomorphism.

Intensive summer schools often provide strong students with career-changing impact, teaching them the art of the trade, letting them understand the logical underbelly of a field, and connecting them with an elite circle of peers and field leaders. Indeed, many professors attribute considerable aspects of their growth as a scientist to such schools. Such summer schools are an essential service to the community. A well-run summer school combines many of the aspects that jointly define students overall success. Eight years of organizing the annual two-week Computational Sensory-Motor Neuroscience (CoSMo, http://www.compneurosci.com/CoSMo) summer school has allowed us to experiment with different approaches and evaluate teaching outcomes, and we have seen rather clear patterns. Many new schools are started each year, only some move on to ongoing success, and the vast majority take a while until they reach very good ratings (our ratings are still increasing but approaching 10/10). Focusing on the student experience, we present a set of 10 simple rules to help you organize better summer schools that are more useful to students.We organize summer schools despite the considerable cost in terms of money and effort associated with them. We do this because we want to improve the field. Understanding the students and the change we want to effect is essential to being effective. For example, CoSMo mostly serves the objective of improving the way the field handles data and computation. Everything else derives from this objective. Teaching objectives should thus be defined by answering the following questions: What is missing in the field? What are the educational bottlenecks in the field? Where would we like the field to move? We should think of summer schools not as a generic way of teaching students but a specific way of effecting the change the field needs. Organizing a summer school is a way of leading the change you want to see.Knowing the students also implies not overloading them. The learning experience is far better when students learn material that they can realistically acquire than if an overly ambitious program instead teaches the students a little bit of many things without giving them important new skills. A summer school is no replacement for an education in science. It is a boost and a little bit of a push into the right direction.Crucial to the success of a teaching objective is the recruitment of pedagogically outstanding lecturers. Those individuals do not have to be the biggest names in the field; rather, they should be good teachers and should have the required hands-on practical knowledge to tutor participants. This said, students are attracted by faculty stars, so consider a healthy balance between fame and pedagogy. It is often useful to recruit additional teaching assistants if necessary to provide a high teacher-to-student ratio where each student can receive individualized attention. Often there are also experts among the participants, and one can take advantage of impromptu peer mentoring approaches. Fewer educators are better than many so that a coherent teaching framework can be applied over one to two days for each lecturer team. If multiple lecturers coteach a topic, true coteaching can be tremendously beneficial (but requires serious initial organization). We found that reducing the number of lecturers was almost universally associated with improved perceived quality of education ratings.Summer school participants usually come with a broad variety of educational backgrounds and can be at different career stages. It is thus important to design the summer school teaching content in a way that provides enough introductory material in order to equalize knowledge before more specialized or in-depth topics are covered. Our experience shows that about half the content of the summer school should be structured to convey the basics of a research field. These basics should ideally be taught by a small team of instructors (e.g., the way the three organizers of CoSMo do this) to ensure maximum coherence and coordination of content. Indeed, the content should be selected with at least two criteria in mind: it should level the ground for the following guest lecturers, who typically cover more specialized, in-depth content, and it should provide a coherent but critical perspective of current approaches in the field, including philosophical considerations.A perennial problem when teaching the basics is how to provide the more advanced students with good learning opportunities while helping weaker students advance. We found that keeping tutorials multilevel can be good at solving this issue. First, the advanced students can be assigned to help the less advanced ones at certain times. Second, it is often possible to provide an extra-hard problem in the same tutorial content. When we teach, we often have the hard problems at the bottom of the slide and the main ones in the middle.The aspect that sets a summer school apart from university-based teaching, lectures at conferences, and reading material is that due to the targeted topic and small number of students at a summer school, we can teach skills instead of material. Of course, some lecturing is important to introduce certain concepts and background. In a tutorial, students can learn how to solve problems in a way that will almost immediately allow them to replicate those skills back in their own lab. We found that in computational neuroscience, assigning more than half of the time to tutorials considerably improves what students learn.We also found that switching to a microlecture-tutorial format considerably improved outcomes. We teach a concept for a few minutes, and then for about the next 10 minutes, students immediately use what they just learned to solve a concrete problem that they could encounter in their own lab. This immediate link between knowledge and its application makes it both easier to attend the lecture because it will become relevant knowledge in 5 minutes. It is also easier for students not to get lost. The application makes it easy for them to see what they have not understood. Learning outcomes are optimized through active learning. Problem-based learning tutorials are best because they require critical thinking and the development of logical solutions. They implicitly force participants to ask the right questions, identify assumptions, and make hypotheses explicit. This can be a slow process, but it ensures a profound and practical understanding. Also, whenever possible, choose a single data set or problem for participants to work on from different angles in order to reduce introduction time. Thus, often when it comes to selecting course content, less is more.The venue should also be adapted to the teaching objectives. Interactive classrooms with round tables, lots of whiteboard space, breakout rooms, and audio-video equipment in many cases greatly increases teaching efficiency. It is truly helpful if the more advanced students can help those who are less advanced understand the material. An open design (e.g., with round tables) makes it easy for students to interact with many peers.We also found that switching activities is important to keep up participants' energy and attention span. Frequent switching between lectures and tutorials, switching between lecturers, switching groups for tutorial work, taking breaks, and interjecting special activities (e.g., sports, a special lecture, an open discussion, telling an anecdote) all help to increase the teaching outcomes.Tutorials allow students to work on only small problems. A small group project (three to five group members are ideal) that spans the entire duration of the summer school allows a more in-depth treatment of a selected topic. It also fosters more creativity, additional individualized teaching opportunities, and opportunities for participants to more deeply network with other students with whom they have the most in common. For most summer schools that we know of, combining these two timescales of learning is perceived as productive.Importantly, for group projects to be truly productive, it is essential that they are guided and tutored in the right way. Students need considerable guidance at multiple points along the way. First, it greatly helps if the group generation process is guided. Students should build groups that cover complementary skills while having common interests. Group parity should also be targeted because it leads to better group dynamics. Second, it is essential that group projects are tutored, but in a way that lets the participants steer them. The students can often learn a lot from learning why a given project is not a good group project. Third, it needs a final set of maximally public presentations so that the students have the sense that they are working toward an important goal. To maximize this effect, we convinced those at one of our field's main annual conferences to automatically accept the best paper presented at our summer school in a year. Moreover, CoSMo summer projects regularly end up being published as scientific papers in established journals.The pace for the entire summer school, and in particular the group projects, is set in the first two days or so. Long work hours (e.g., 9:00 a.m. to 11:00 p.m.) create group cohesion (through “suffering” together) and promote a community spirit that is fertile for learning, ideas, and collaboration. This atmosphere can be enhanced by providing an immersive learning environment where lecturers and tutors are available at all times. Make sure enough time is available for group projects.Teaching materials, including lectures, tutorials, solutions, and additional resources, should be publicly shared, for example, on a wiki site (e.g., http://compneurosci.com/wiki/index.php/CoSMo) or www.OSF.io. This crucial component has many benefits. It is, of course, useful for students to always have access to all materials. It is also useful for instructors to see what previous materials have been covered. More important, open access of materials is immensely useful for the community and in high demand. It is one way to extend the impact of a summer school far beyond the limited group of those attending. Other professors will use tutorial and lecture materials for their own classes. Researchers have a means to learn new approaches on their own, which can tremendously accelerate a field's research endeavor, especially when example code from tutorials is advanced enough that it can be directly applied to research questions. Finally, a public written trace is also useful for summer school lecturers to keep a good institutional memory. It is critical to remember over the years what has been taught, what has worked, and what needs to be improved (see also rule 10).In fact, many of the materials developed for CoSMo ended up being used more broadly across the field. For example, a tutorial aimed at teaching multivoxel pattern analysis ended up being a crucial resource for teaching in the entire field (http://www.cosmomvpa.org/). In many ways, the online materials are a continuation of the summer school itself.A summer school is a unique networking event that can build lifelong professional relationships. It is thus important to promote networking and have enough unstructured time available, even if that means prolonged lunch and dinner breaks. This can be done in many ways: through creating mailing lists, blogs, and forums; using social media; and organizing group events, (for example, an outing after the first week of the school, such as sightseeing or sports activities). Networking should not be limited to participants but should include all lecturers.Our alumni organize get-togethers at the big national conferences. They share news of personal progress on the Facebook page for the course session they attended. They hire one another once they become professors. And they often end up collaborating with one another later in their careers. Keeping the network in place after a summer school is crucial to the success of the participants.We found a simple yet critical way to increase the effectiveness of the summer school. A problem for probably most of our students is access to research supervisors in their home universities. The students may have a supervisor, but that person may not have much time to give to his or her students. In addition, they have a conflict of interest as mentors. Therefore, having one-on-one access at the summer school to their field's leaders is incredibly valuable to these students.We thus ask all students which of the professors they most would like to meet individually. Our guest lecturers coteach, each staying for two days but teaching only for one. The remaining time can then be used for a large number of one-on-one slots. Being able to sign up for one of these meetings, which last for 15 to 30 minutes, is one of the highlights for CoSMo attendees. Indeed, some have told us that this was the highlight of the school. The goal of these one-on-one meetings is to allow participants to establish a personal relationship with established researchers in their field. It allows participants to ask questions in a private setting while having the full attention of the experts. Conversation topics can range from career advice to feedback on research projects, work-life balance, or recruitment interviews. Other schools achieve the same aims simply by having faculty around for a long time and allocating a lot of time for unstructured networking.Organizing and running a summer school is a lot of work, and the schools themselves are tiring for lecturers, attendees, and the organizers. In order to avoid burnout, maintaining a fun and supportive environment is crucial. Organizers and lecturers need to bring and share positive energy. Positive energy is contagious, and participants draw from the lecturers' energy. Make sure to maintain this positive energy. The emotional side of a summer school is essential. Happy lecturers come again, happy students spread the word and successfully network, and happy organizers will be more willing to go through all that work again next year.Positive energy can be cultivated in a number of ways and should be spread from the beginning. One way is to spend time with your co-organizers and lecturers without students, even if that means less available networking time. It is essential to be there for one another as the teaching team but also essential to see the students as partners in learning. And, quite possibly, we should celebrate a summer school well run. By coteaching and co-organizeing with people we like, the fun will spill over to the participants. It also helps to plan for some fun bonding activities (e.g., sports, games) and make sure there is time for relaxation (e.g., cultural activities, day off, pub night), and not to overwhelm you or the participants.Successful summer schools learn from their mistakes and improve over the years, So ask for feedback from participants. Students often understand what would have helped them. After the school, thier feedback can be followed up with questions asked through Google Forms. The feedback forms should be a mix of rating scales to get participants' overall impressions on what was good and what was not and free-form text for them to provide their feedback about the individual school activities. For example, you can ask separately about lecture versus tutorial content for each teaching component or each lecturer. What was the difficulty level? Did participants feel they really learned something? What improvements could be made?Once feedback has been collected, analyze the ratings and suggestions. Often you need to read between the lines to identify the underlying causes of negative feedback or even to understand constructive suggestions. Always try to improve the summer school. Even after running CoSMo for eight years, we still see room for improvement. A research community is not static, and thinking as well as techniques evolve. Feedback also allows us to identify unmet expectations and make adjustments based on the direction the field is heading in.We thank Pascal Wallisch, Terry Sejnowski, and Adrienne Fairhall for helpful feedback. We also thank all 2011–2018 CoSMo attendees for their constructive (anonymous) feedback that has tremendously helped us shape these 10 simple rules.

Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function that takes as inputs two numbers from its children and produces one output. Since thinking about functions in terms of computation graphs is becoming popular, we may want to know which functions can be implemented on a given tree. Here, we describe a set of necessary constraints in the form of a system of nonlinear partial differential equations that must be satisfied. Moreover, we prove that these conditions are sufficient in contexts of analytic and bit-valued functions. In the latter case, we explicitly enumerate discrete functions and observe that there are relatively few. Our point of view allows us to compare different neural network architectures in regard to their function spaces. Our work connects the structure of computation graphs with the functions they can implement and has potential applications to neuroscience and computer science.

There is a popular belief in neuroscience that we are primarily data limited, and that producing large, multimodal, and complex datasets will, with the help of advanced data analysis algorithms, lead to fundamental insights into the way the brain processes information. These datasets do not yet exist, and if they did we would have no way of evaluating whether or not the algorithmically-generated insights were sufficient or even correct. To address this, here we take a classical microprocessor as a model organism, and use our ability to perform arbitrary experiments on it to see if popular data analysis methods from neuroscience can elucidate the way it processes information. Microprocessors are among those artificial information processing systems that are both complex and that we understand at all levels, from the overall logical flow, via logical gates, to the dynamics of transistors. We show that the approaches reveal interesting structure in the data but do not meaningfully describe the hierarchy of information processing in the microprocessor. This suggests current analytic approaches in neuroscience may fall short of producing meaningful understanding of neural systems, regardless of the amount of data. Additionally, we argue for scientists using complex non-linear dynamical systems with known ground truth, such as the microprocessor as a validation platform for time-series and structure discovery methods.

Good scientific writing is essential to career development and to the progress of science.A well-structured manuscript allows readers and reviewers to get excited about the subject matter, to understand and verify the paper's contributions, and to integrate these contributions into a broader context.However, many scientists struggle with producing high-quality manuscripts and are typically untrained in paper writing.Focusing on how readers consume information, we present a set of ten simple rules to help you communicate the main idea of your paper.These rules are designed to make your paper more influential and the process of writing more efficient and pleasurable.

Perception is seen as a process that utilises partial and noisy information to construct a coherent understanding of the world. Here we argue that the experience of pain is no different; it is based on incomplete, multimodal information, which is used to estimate potential bodily threat. We outline a Bayesian inference model, incorporating the key components of cue combination, causal inference, and temporal integration, which highlights the statistical problems in everyday perception. It is from this platform that we are able to review the pain literature, providing evidence from experimental, acute, and persistent phenomena to demonstrate the advantages of adopting a statistical account in pain. Our probabilistic conceptualisation suggests a principles-based view of pain, explaining a broad range of experimental and clinical findings and making testable predictions.

It has recently been suggested that movement variability directly increases the speed of motor learning. Here we use computational modeling of motor adaptation to show that variability can have a broad range of effects on learning, both negative and positive. Experimentally, we also find contributing and decelerating effects. Lastly, through a meta-analysis of published papers, we verify that across a wide range of experiments, movement variability has no statistical relation with learning rate. While motor learning is a complex process that can be modeled, further research is needed to understand the relative importance of the involved factors.

A molecular device that records time-varying signals would enable new approaches in neuroscience. We have recently proposed such a device, termed a "molecular ticker tape", in which an engineered DNA polymerase (DNAP) writes time-varying signals into DNA in the form of nucleotide misincorporation patterns. Here, we define a theoretical framework quantifying the expected capabilities of molecular ticker tapes as a function of experimental parameters. We present a decoding algorithm for estimating time-dependent input signals, and DNAP kinetic parameters, directly from misincorporation rates as determined by sequencing. We explore the requirements for accurate signal decoding, particularly the constraints on (1) the polymerase biochemical parameters, and (2) the amplitude, temporal resolution, and duration of the time-varying input signals. Our results suggest that molecular recording devices with kinetic properties similar to natural polymerases could be used to perform experiments in which neural activity is compared across several experimental conditions, and that devices engineered by combining favorable biochemical properties from multiple known polymerases could potentially measure faster phenomena such as slow synchronization of neuronal oscillations. Sophisticated engineering of DNAPs is likely required to achieve molecular recording of neuronal activity with single-spike temporal resolution over experimentally relevant timescales.

How interactions between neurons relate to tuned neural responses is a longstanding question in systems neuroscience. Here we use statistical modeling and simultaneous multi-electrode recordings to explore the relationship between these interactions and tuning curves in six different brain areas. We find that, in most cases, functional interactions between neurons provide an explanation of spiking that complements and, in some cases, surpasses the influence of canonical tuning curves. Modeling functional interactions improves both encoding and decoding accuracy by accounting for noise correlations and features of the external world that tuning curves fail to capture. In cortex, modeling coupling alone allows spikes to be predicted more accurately than tuning curve models based on external variables. These results suggest that statistical models of functional interactions between even relatively small numbers of neurons may provide a useful framework for examining neural coding.

Synaptic plasticity underlies learning and is thus central for development, memory, and recovery from injury. However, it is often difficult to detect changes in synaptic strength in vivo, since intracellular recordings are experimentally challenging. Here we present two methods aimed at inferring changes in the coupling between pairs of neurons from extracellularly recorded spike trains. First, using a generalized bilinear model with Poisson output we estimate time-varying coupling assuming that all changes are spike-timing-dependent. This approach allows model-based estimation of STDP modification functions from pairs of spike trains. Then, using recursive point-process adaptive filtering methods we estimate more general variation in coupling strength over time. Using simulations of neurons undergoing spike-timing dependent modification, we show that the true modification function can be recovered. Using multi-electrode data from motor cortex we then illustrate the use of this technique on in vivo data.

Recent studies suggest that motor adaptation is the result of multiple, perhaps linear processes each with distinct time scales. While these models are consistent with some motor phenomena, they can neither explain the relatively fast re-adaptation after a long washout period, nor savings on a subsequent day. Here we examined if these effects can be explained if we assume that the CNS stores and retrieves movement parameters based on their possible relevance. We formalize this idea with a model that infers not only the sources of potential motor errors, but also their relevance to the current motor circumstances. In our model adaptation is the process of re-estimating parameters that represent the body and the world. The likelihood of a world parameter being relevant is then based on the mismatch between an observed movement and that predicted when not compensating for the estimated world disturbance. As such, adapting to large motor errors in a laboratory setting should alert subjects that disturbances are being imposed on them, even after motor performance has returned to baseline. Estimates of this external disturbance should be relevant both now and in future laboratory settings. Estimated properties of our bodies on the other hand should always be relevant. Our model demonstrates savings, interference, spontaneous rebound and differences between adaptation to sudden and gradual disturbances. We suggest that many issues concerning savings and interference can be understood when adaptation is conditioned on the relevance of parameters.

Experiments in systems neuroscience can be seen as consisting of three steps: (1) selecting the signals we are interested in, (2) probing the system with carefully chosen stimuli, and (3) getting data out of the brain. Here I discuss how emerging techniques in molecular biology are starting to improve these three steps. To estimate its future impact on experimental neuroscience, I will stress the analogy of ongoing progress with that of microprocessor production techniques. These techniques have allowed computers to simplify countless problems; because they are easier to use than mechanical timers, they are even built into toasters. Molecular biology may advance even faster than computer speeds and has made immense progress in understanding and designing molecules. These advancements may in turn produce impressive improvements to each of the three steps, ultimately shifting the bottleneck from obtaining data to interpreting it.

Applications of Brain-Machine-Interfaces typically estimate user intent based on biological signals that are under voluntary control. For example, we might want to estimate how a patient with a paralyzed arm wants to move based on residual muscle activity. To solve such problems it is necessary to integrate obtained information over time. To do so, state of the art approaches typically use a probabilistic model of how the state, e.g. position and velocity of the arm, evolves over time – a so-called trajectory model. We wanted to further develop this approach using two intuitive insights: (1) At any given point of time there may be a small set of likely movement targets, potentially identified by the location of objects in the workspace or by gaze information from the user. (2) The user may want to produce movements at varying speeds. We thus use a generative model with a trajectory model incorporating these insights. Approximate inference on that generative model is implemented using a mixture of extended Kalman filters. We find that the resulting algorithm allows us to decode arm movements dramatically better than when we use a trajectory model with linear dynamics.

To stabilize our position in space we use visual information as well as non-visual physical motion cues. However, visual cues can be ambiguous: visually perceived motion may be caused by self-movement, movement of the environment, or both. The nervous system must combine the ambiguous visual cues with noisy physical motion cues to resolve this ambiguity and control our body posture. Here we have developed a Bayesian model that formalizes how the nervous system could solve this problem. In this model, the nervous system combines the sensory cues to estimate the movement of the body. We analytically demonstrate that, as long as visual stimulation is fast in comparison to the uncertainty in our perception of body movement, the optimal strategy is to weight visually perceived movement velocities proportional to a power law. We find that this model accounts for the nonlinear influence of experimentally induced visual motion on human postural behavior both in our data and in previously published results.

In many domains, humans appear to combine perceptual cues in a near-optimal, probabilistic fashion: two noisy pieces of information tend to be combined linearly with weights proportional to the precision of each cue. Here we present a case where structural information plays an important role. The presence of a background cue gives rise to the possibility of occlusion, and places a soft constraint on the location of a target – in effect propelling it forward. We present an ideal observer model of depth estimation for this situation where structural or ordinal information is important and then fit the model to human data from a stereo-matching task. To test whether subjects are truly using ordinal cues in a probabilistic manner we then vary the uncertainty of the task. We find that the model accurately predicts shifts in subject’s behavior. Our results indicate that the nervous system estimates depth ordering in a probabilistic fashion and estimates the structure of the visual scene during depth perception.

A large number of experiments have asked to what degree human reaching movements can be understood as being close to optimal in a statistical sense. However, little is known about whether these principles are relevant for other classes of movements. Here we analyzed movement in a task that is similar to surfing or snowboarding. Human subjects stand on a force plate that measures their center of pressure. This center of pressure affects the acceleration of a cursor that is displayed in a noisy fashion (as a cloud of dots) on a projection screen while the subject is incentivized to keep the cursor close to a fixed position. We find that salient aspects of observed behavior are well-described by optimal control models where a Bayesian estimation model (Kalman filter) is combined with an optimal controller (either a Linear-Quadratic-Regulator or Bang-bang controller). We find evidence that subjects integrate information over time taking into account uncertainty. However, behavior in this continuous steering task appears to be a highly non-linear function of the visual feedback. While the nervous system appears to implement Bayes-like mechanisms for a full-body, dynamic task, it may additionally take into account the specific costs and constraints of the task.

In order to determine the points at which meeting discourse changes from one topic to another, probabilistic models were used to approximate the process through which meeting transcripts were produced. Gibbs sampling was used to estimate the values of random variables in the models, including the locations of topic boundaries. This paper shows how discourse features were integrated into the Bayesian model and reports empirical evaluations of the benefit obtained through the inclusion of each feature and of the suitability of alternative models of the placement of topic boundaries. It demonstrates how multiple cues to segmentation can be combined in a principled way, and empirical tests show a clear improvement over previous work.

Bayesian models of multisensory perception traditionally address the problem of estimating an underlying variable that is assumed to be the cause of the two sen- sory signals. The brain, however, has to solve a more general problem: it also has to establish which signals come from the same source and should be integrated, and which ones do not and should be segregated. In the last couple of years, a few models have been proposed to solve this problem in a Bayesian fashion. One of these has the strength that it formalizes the causal structure of sensory signals. We first compare these models on a formal level. Furthermore, we conduct a psy- chophysics experiment to test human performance in an auditory-visual spatial localization task in which integration is not mandatory. We find that the causal Bayesian inference model accounts for the data better than other models. Keywords: causal inference, Bayesian methods, visual perception. 1 Multisensory perception In the ventriloquist illusion, a performer speaks without moving his/her mouth while moving a puppet’s mouth in synchrony with his/her speech. This makes the puppet appear to be speaking. This illusion was first conceptualized as ”visual capture”, occurring when visual and auditory stimuli exhibit a small conflict ([1, 2]). Only recently has it been demonstrated that the phenomenon may be seen as a byproduct of a much more flexible and nearly Bayes-optimal strategy ([3]), and therefore is part of a large collection of cue combination experiments showing such statistical near-optimality [4, 5]. In fact, cue combination has become the poster child for Bayesian inference in the nervous system. In previous studies of multisensory integration, two sensory stimuli are presented which act as cues about a single underlying source. For instance, in the auditory-visual localization experiment by Alais and Burr [3], observers were asked to envisage each presentation of a light blob and a sound click as a single event, like a ball hitting the screen. In many cases, however, the brain is not only posed with the problem of identifying the position of a common source, but also of determining whether there was a common source at all. In the on-stage ventriloquist illusion, it is indeed primar- ily the causal inference process that is being fooled, because veridical perception would attribute independent causes to the auditory and the visual stimulus. 1 To extend our understanding of multisensory perception to this more general problem, it is necessary to manipulate the degree of belief assigned to there being a common cause within a multisensory task. Intuitively, we expect that when two signals are very different, they are less likely to be per- ceived as having a common source. It is well-known that increasing the discrepancy or inconsistency between stimuli reduces the influence that they have on each other [6, 7, 8, 9, 10, 11]. In auditory- visual spatial localization, one variable that controls stimulus similarity is spatial disparity (another would be temporal disparity). Indeed, it has been reported that increasing spatial disparity leads to a decrease in auditory localization bias [1, 12, 13, 14, 15, 16, 17, 2, 18, 19, 20, 21]. This decrease also correlates with a decrease in the reports of unity [19, 21]. Despite the abundance of experimental data on this issue, no general theory exists that can explain multisensory perception across a wide range of cue conflicts.

We present a method for unsupervised topic modelling which adapts methods used in document classification (Blei et al., 2003; Griffiths and Steyvers, 2004) to unsegmented multi-party discourse transcripts. We show how Bayesian inference in this generative model can be used to simultaneously address the problems of topic segmentation and topic identification: automatically segmenting multi-party meetings into topically coherent segments with performance which compares well with previous unsupervised segmentation-only methods (Galley et al., 2003) while simultaneously extracting topics which rate highly when assessed for coherence by human judges. We also show that this method appears robust in the face of off-topic dialogue and speech recognition errors.

Many recent studies analyze how data from different modalities can be combined. Often this is modeled as a system that optimally combines several sources of information about the same variable. However, it has long been realized that this information combining depends on the interpretation of the data. Two cues that are perceived by different modalities can have different causal relationships: (1) They can both have the same cause, in this case we should fully integrate both cues into a joint estimate. (2) They can have distinct causes, in which case information should be processed independently. In many cases we will not know if there is one joint cause or two independent causes that are responsible for the cues. Here we model this situation as a Bayesian estimation problem. We are thus able to explain some experiments on visual auditory cue combination as well as some experiments on visual proprioceptive cue integration. Our analysis shows that the problem solved by people when they combine cues to produce a movement is much more complicated than is usually assumed, because they need to infer the causal structure that is underlying their sensory experience.

Our motor system changes due to causes that span multiple timescales. For example, muscle response can change because of fatigue, a condition where the disturbance has a fast timescale or because of disease where the disturbance is much slower. Here we hypothesize that the nervous system adapts in a way that reflects the temporal properties of such potential disturbances. According to a Bayesian formulation of this idea, movement error results in a credit assignment problem: what timescale is responsible for this disturbance? The adaptation schedule influences the behavior of the optimal learner, changing estimates at different timescales as well as the uncertainty. A system that adapts in this way predicts many properties observed in saccadic gain adaptation. It well predicts the timecourses of motor adaptation in cases of partial sensory deprivation and reversals of the adaptation direction.

When we learn a new motor skill, we have to contend with both the vari- ability inherent in our sensors and the task. The sensory uncertainty can be reduced by using information about the distribution of previously ex- perienced tasks. Here we impose a distribution on a novel sensorimotor task and manipulate the variability of the sensory feedback. We show that subjects internally represent both the distribution of the task as well as their sensory uncertainty. Moreover, they combine these two sources of information in a way that is qualitatively predicted by optimal Bayesian processing. We further analyze if the subjects can represent multimodal distributions such as mixtures of Gaussians. The results show that the CNS employs probabilistic models during sensorimotor learning even when the priors are multimodal.

Learning in neural networks is usually applied to parameters related to linear kernels and keeps the nonlinearity of the model fixed. Thus, for successful models, properties and parameters of the nonlinearity have to be specified using a priori knowledge, which often is missing. Here, we investigate adapting the nonlinearity simultaneously with the linear kernel. We use natural visual stimuli for training a simple model of the visual system. Many of the neurons converge to an energy detector matching existing models of complex cells. The overall distribution of the parameter describing the nonlinearity well matches recent physiological results. Controls with randomly shuffled natural stimuli and pink noise demonstrate that the match of simulation and experimental results depends on the higher-order statistical properties of natural stimuli.

Neurons in mammalian cerebral cortex combine specific responses with respect to some stimulus features with invariant responses to other stimulus features. For example, in primary visual cortex, complex cells code for orientation of a contour but ignore its position to a certain degree. In higher areas, such as the inferotemporal cortex, translation-invariant, rotation-invariant, and even view point-invariant responses can be observed. Such properties are of obvious interest to artificial systems performing tasks like pattern recognition. It remains to be resolved how such response properties develop in biological systems. Here we present an unsupervised learning rule that addresses this problem. It is based on a neuron model with two sites of synaptic integration, allowing qualitatively different effects of input to basal and apical dendritic trees, respectively. Without supervision, the system learns to extract invariance properties using temporal or spatial continuity of stimuli. Furthermore, top-down information can be smoothly integrated in the same framework. Thus, this model lends a physiological implementation to approaches of unsupervised learning of invariant-response properties.

Electrophysiological research on the properties of the apical dendrites of cortical deep layer pyramidal cells suggests that it acts, in addition to the soma, as a second site of synaptic integration. Each site integrates input from a subset of synapses and is able to generate regenerative potentials. The sites exchange information in stereotyped ways: Signals from the soma are transmitted to the apical dendrite via actively back-propagating dendritic action potentials. Slow regenerative calcium spikes transmit information from the apical dendrite to the soma. These calcium spikes lead to a strong and prolonged depolarization of the cell generating a burst of action potentials. This paper analyzes how the system learns if these calcium spikes trigger hebbian learning at active synapses. A cell is now described by two main variables the mean activity and the mean potential at the apical dendrite with the first variable defining the input to cells downstream and the latter what the cell learns. A system results where neurons learn to respond to those features that are correlated with activity on the higher layer, this property is similar to maximizing the mutual information between input and higher areas. Furthermore it learns invariances exploiting a spatial smoothness criterion.