We are interested in spike-based theories of neural computation, that is, theories where interactions between neurons are mediated by spikes, in ways that make computation and dynamics fundamentally different from rate-based models (ie, not spike-based implementations of rate-based theories).

Neurons respond to time-varying inputs with precisely timed spikes, which is a general and non trivial mathematical property of spiking models (Brette & Guigon, 2003; Brette, 2008) (for a mathematical theory of spiking models, see (Brette 2003; Brette 2004)). They are also extremely sensitive to coincidences in their inputs (Rossant et al., 2011; see also Platkiewicz & Brette, 2011 and Fontaine et al., 2014). These two properties have motivated the introduction of the “synchrony receptive field” concept (Brette, 2012): this is the set of stimuli that elicit synchronous spiking in a given set of neurons. A neuron that is sensitive to coincidences should fire when the stimulus is in the synchrony receptive field of its presynaptic neurons (or a subset of them). This corresponds to a temporal invariant in the space of stimuli, which can be seen as a model of the world, i.e. a set of relations between observables, the observables between sensory signals. These perceiver-oriented models form what we have called the “subjective physics” of the world (Brette 2013), an idea related to a few of theories in psychology and philosophy of mind (in particular Gibson‘s ecological approach and O’Regan‘s sensorimotor theory).

We have developed the synchrony receptive field concept using spiking neural network models in various sensory contexts, including sound localization (Goodman & Brette 2010a,b; Bénichoux et al., 2014), pitch perception (Laudanski et al 2014), and olfaction (Brette 2012). We are currently looking into learning issues, including intrinsic and synaptic plasticity (partially addressed in Brette 2012), and application to real world problems (i.e. with ecological sensory signals).

**Publications**

- Bénichoux V, Fontaine B, Karino S, Franken TP, Joris PX*, Brette R* (2015).Neural tuning matches frequency-dependent time differences between the ears. eLife 10.7554/eLife.06072.

Brette, R. (2003). Rotation numbers of discontinuous orientation-preserving circle maps. Set-Valued Analysis 11(4): 359-371. - Brette, R. (2004). Dynamics of one-dimensional spiking neuron models. J Math Biol 48(1): 38-56.
- Brette, R. (2008). The Cauchy problem for one-dimensional spiking neuron models. Cognitive Neurodynamics 2(1) 21-27.
- Brette R (2012). Computing with neural synchrony. PLoS Comp Biol. 8(6): e1002561. doi:10.1371/journal.pcbi.1002561. (code)
- Brette R (2013). Subjective physics. arXiv:1311.3129 [q-bio.NC].
- Brette, R. and E. Guigon (2003). Reliability of spike timing is a general property of spiking model neurons. Neural Comput 15(2): 279-308.
- Fontaine B, Peña JL, Brette R (2014).
__Spike-threshold adaptation predicted by membrane potential dynamics in vivo__. PLoS Comp Biol, 10(4): e1003560. - Goodman DF and R Brette (2010a). Spike-timing-based computation in sound localization. PLoS Comp Biol 6(11): e1000993. doi:10.1371/journal.pcbi.1000993.
- Goodman DF and R Brette (2010b). Learning to localise sounds with spiking neural networks, Advances in Neural Information Processing Systems 23, 784-792.
- Laudanski J, Zheng Y, Brette R (2014). A structural theory of pitch. eNeuro. DOI: 10.1523/ENEURO.0033-14.2014
- Platkiewicz J and Brette R (2011). Impact of Fast Sodium Channel Inactivation on Spike Threshold Dynamics and Synaptic Integration. PLoS Comp Biol 7(5): e1001129. doi:10.1371/journal.pcbi.1001129.
- Rossant C, Leijon S, Magnusson AK, Brette R (2011).Sensitivity of noisy neurons to coincident inputs. J Neurosci 31(47):17193-17206.